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April 30, 2017

8:45 AM

Protagoras vs. Euathlus Resolved

© Copyright Avi Sion, 2016. All rights reserved. This essay will be a chapter in my next book.


1.   An ancient paradox

One of the many alleged paradoxes that have come down to us from the Greeks is the dispute between Protagoras (of Abdera, ca. 480-410 BCE) and his student Euathlus (of whom nothing more is known). The story is told by Aulus Gellius (Roman, ca. 125-180 CE)[1], that Protagoras, a famous Sophist, and an expensive teacher, agreed with Euathlus to train him in rhetoric, a discipline essential at the time to argumentation in courts of law. The agreement was that Euathlus would not have to pay Protagoras the specified fee (or the unpaid portion of the fee, by some accounts) until he had been fully trained and went on to plead his first case and win it[2].

It is said that after Euathlus completed his course, he did not (for whatever reason) choose to use his newly acquired skills before any court of law, and so he never won or lost any case, and so was contractually not required to pay Protagoras anything. Nevertheless, Protagoras, with motives that we shall presently consider, sued him (in the court of Areopagus in Athens). Euathlus chose to personally defend himself. The following arguments were reportedly put before the court:

a.     Protagoras argued that he surely ought to be paid the fee, because (i) if the court ruled in his favor, he could on that basis demand payment; and (ii) if the court ruled in favor of the defendant, then the latter would have won his first case and therefore be contractually obliged to pay the fee anyway.

b.     Euathlus replied that he surely ought not to pay the fee, because (i) if the court ruled in favor of the plaintiff, then Euathlus would have lost his first case and therefore not be contractually obliged to pay the fee; and (ii) if the court ruled in favor of the defendant, then he would on that basis be exempt from payment anyway.

Thus, while the plaintiff argued, apparently convincingly, that he was certain to deserve payment however the court ruled, the defendant was in turn able to argue, apparently just as convincingly, that he was certain to be exempt from payment in either event. For this reason, this case is regarded as paradoxical. It is said that the court was so confused by these arguments and counter-arguments that it chose to adjourn sine die (or, some say, for 100 years) to avoid judgment.

The significance of this legal dispute for logic and philosophy is that it the impression that two people can argue dilemmatically and paradoxically in opposite directions and both be right. The enemies of human reason relish this kind of conclusion, since it would put in doubt the reliability and efficacy of human reason. But as we shall now show, the said impression is very superficial. There are, to my mind, at least two possible resolutions of this so-called Paradox of the Court. In fact, although I thought of the second before the first, the latter logically precedes the former. I later learned from Peter Suber’s survey of the literature on the subject[3] that the first resolution was long before me proposed by Aulus Gellius; the second resolution seems to be novel.


2.   First resolution

The simplest solution to this problem is to suppose that the wily Protagoras, seeing that Euathlus was taking his time getting to work, decided to speed things up. Protagoras trapped his pupil by using the above argument, knowing full well that he would lose a first trial, but win an eventual second trial. He knew he would lose a first trial, because the agreement between the parties only obligated Euathlus to pay the fee once he won his first case; it did not obligate him to practice law anytime soon, or even ever. Euathlus foolishly fell into the trap and personally argued the case in court. Had the court not adjourned sine die, it would have logically given him victory, thus making Euathlus win his first case. Thereafter, assuming that a second trial was legally permitted – and both the parties’ arguments above do make this assumption – Protagoras would have been the ultimate winner. Of course, no second trial would be necessary if Euathlus conceded that having won the first trial he was sure to lose the second, and settled the account forthwith.

In other words, Protagoras’s first argument (i) was mere camouflage; he was really relying on his second argument (ii). Euathlus let his vanity get the better of him and formulated two fancy counter-arguments, thinking to outdo his teacher. But Protagoras was more cunning than him. The only way Euathlus could have avoided being beaten was by hiring a lawyer[4]. If the lawyer won the first trial, as he could be logically expected to since the only condition for defeat here was not satisfied, Euathlus would not be considered as having personally won his first case in court, and Protagoras would not be able to win a second trial. Thus, the master was indeed superior to the pupil. There was no real paradox, since there was an actual way out of the apparent paradox.

Of course, one might add that Euathlus was in practice the winner, since through his counter-argument he managed to so bewilder the court that it gave up trying to judge the matter at all, and he was not forced to pay up. Maybe he hoped for that and he lucked out. But on a theoretical, logical level, in the present perspective, he proved to be not too intelligent. Not only did he foolishly not hire a lawyer to plead on his behalf, but he also wrongly assumed that his argumentation was effective in countering Protagoras’. He kidded himself into thinking that if he won the first trial, he would not have to face a second one. He should have examined his teacher’s argumentation more carefully.

Let us now look at the arguments in more formal terms, to clarify them. I shall introduce the following symbols: let P = Protagoras, Q = Euathlus; A = the agreed condition that Q wins his first case in order to be liable, and C = the agreed result that fee must be paid by Q to P. We know at the outset that if A then C, and if not-A then not-C: these are the terms of the agreement. The arguments are as follows (with my critical commentary in italics):

a.     According to P: (i) if court rules that P wins, then C is true (but objectively court cannot rule for P, since A not yet true, so this is a non-starter); whereas if (ii) court rules that Q wins (as it logically must), then not-C is true (at the conclusion of a first trial); but if Q thus wins, then A becomes true and C must (in a later trial) follow, in which event P finally wins.

b.     According to Q: (i) if court rules that P wins, then not-A is true (at the conclusion of a first trial); but if not-A is true then not-C must (in a later trial) follow, so Q finally wins (but objectively court cannot rule for P, since A not yet true, so this is a non-starter); whereas if (ii) court rules that Q wins (as it logically must), then not-C is true (but here Q fails to mention later consequences that P rightly pointed out).

In conclusion, P is logically the resultant winner; Q’s arguments are in fact insufficient to prevent this outcome. P pretends to seek to win immediately; but in truth his aim is longer term victory (in the second round). Q imagines he might lose the first round but win the second or that he might win the first round without having to face a second; but these are all fantasies. It is difficult to understand why the court found this case too confusing – the judge (or judges) can’t have been very bright fellows.


3.   Second resolution

A more complex solution to the problem is as follows. It is possible that Protagoras sued Euathlus by appealing to an unspoken clause of the agreement. The agreement contained only one explicit clause, viz. that Euathlus would have to pay Protagoras the fee if and only if he won his first case. If that was so, Protagoras would have no basis for requesting a trial, since that condition had obviously not been satisfied. But since he sued, he must have thought and argued that the agreement included a tacit (or perhaps implicit) understanding that Euathlus would practice law within a reasonable time lapse[5], at which time his new skills would be tested in a court and he would be expected to pay if he won. Protagoras couldn’t have imagined the judge would allow a trial to proceed, let alone would rule in his favor, without some good reason[6].

Clearly, what the judge was called upon to decide in this trial was (could only have been, in the present perspective) whether this claim by Protagoras, that there was a tacit clause to the agreement, was justified. He could well have justified it by considering that had Euathlus been allowed not to practice law at all or to practice it as late as he chose, the agreement would have surely specified the caveat. He could equally well have rejected it by considering that Protagoras took for granted something he should have explicitly obtained agreement on. So, the case hinges on a tacit issue, rather than exclusively on the explicit clause of the agreement; i.e. there was more to the story than is told.

Furthermore, it is evident from the arguments presented by both parties in this trial that each of them foresaw the possibility of a second trial in which the ruling of the first trial could be reversed. This is logically implied in the second argument of Protagoras and in the first argument of Euathlus. In these two eventualities, a second trial would be needed to finalize the judgment; unless, of course, the losing party freely concedes its inevitable result and settles the account in advance. The judge in the first trial could not decide in favor of either party and then against him in the same breath. A first judgment of win or loss would have to be established before a second judgment could be made, in view of the terms of the contract. So, there is a time factor to take into consideration in analyzing these arguments.

It should be noted that, whereas the first trial has an uncertain outcome, since it depends on the decision (the judgment call) of the judge regarding an alleged tacit clause to the agreement, the second trial has a foreseeable outcome, since it depends solely on the explicit clause of the agreement.

Clearly, as we shall now show, if we factor the above considerations into the arguments, the paradoxical appearance is easily dissolved. I shall here use the following symbols: let P = Protagoras; Q = Euathlus; A = the explicit condition that Q wins his first case; B = the alleged implicit condition that Q was required to practice within a reasonable amount of time; and C = the fee must be paid by Q to P. The arguments are as follows:

a.     According to P: (i) if B then C; and (ii) if not-B then not-C, but if not-C then (later) if A then C; therefore, C anyway.

b.     According to Q: (i) if B, then C, but if C then (later) if not-A then not-C; and (ii) if not-B, then not-C; therefore, not-C anyway.

From this we see that the two parties’ arguments are much alike, but each side has cunningly left out part of the consequences (shown in italics). P has truncated the consequences of (i) that Q points out, and Q has truncated the consequences of (ii) that P points out. For this reason, they seem to balance each other out. But if we take all the subsequent events (in a possible second trial) into account, we get the following more objective joint argument (c), which is clearly non-paradoxical:

(i)     if B then C, but if C then (later) if not-A then not-C; and

(ii)     if not-B then not-C, but if not-C then (later) if A then C.

So, in (i) the final conclusion is not-C, while in (ii) it is C – which means that there is no paradox. This also shows that, while it cannot objectively be predicted whether P or Q will win the first trial, it can be said that (i) if P wins the first trial, he will lose the second, and if Q wins the first trial, he will lose the second. Obviously, P cannot argue that he has a right to a second trial (if he loses the first) but Q has not; likewise, Q cannot argue that he has a right to a second trial (if he loses the first) but P has not. So, we must take all later events into consideration to logically reconcile all the arguments. Note that if for some reason there is no second trial, there is also no paradox, since the conclusion will be either (i) C or (ii) not-C.

Whatever happens, there is no paradox because neither party can in fact, contrary to initial appearances, claim inevitable victory; victory does not come both ways for both parties, but only one way for each party.

Clearly, here, both parties were employing the common sophistical trick of hiding an inconvenient part of the unbiased argument from the court. Euathlus was a good apprentice of Protagoras’, since his counter-argument exactly mirrors the latter’s argument. That is, there was an element of dishonesty in both their arguments; both were intellectual frauds at heart, knowingly expounding half-truths. Therefore, this fake paradox presents no deep challenge to Logic, contrary to the claims of Relativists. In particular, Protagoras’ general claim that “there are two sides to every issue” (duo logoi) is shown to be spurious in the present context.

It is worth always keeping in mind that some people involved in philosophy and logic, as in life in general, are sometimes moved by the evil impulse; indeed, some much more than others. They may consciously lie, or subconsciously twist facts and arguments, for a large variety of motives. Usually, lusts for power, fame and fortune play some role. An academic may want the admiration of his peers or of his students; a husband may want to impress his wife; an unemployed may hope to get a job; and so on. It is wrong to look upon all philosophical statements as disinterested. Philosophers and logicians are not all pure scientists or saints.

I might add that the secret of success with finding solutions to philosophical and logical problems, and particularly to paradoxes, is the sincere desire to do so. Many philosophers and logicians approach problems with a negative attitude, not really wanting to solve them, but rather wishing to rationalize their antipathy to human reason through them. The honest researcher is moved by his better impulses; he is sincerely desirous to confirm the effectiveness of the human faculties of cognition – that’s precisely why he succeeds.


4.   Inadequate resolutions

As earlier mentioned, based on Suber’s account of the literature, the first resolution should be attributed to Aulus Gellius, but the second resolution seems to be original. Suber’s account shows that the court paradox has been discussed in a number of works over time, but more often apparently from a legal point of view than from a logical one. The legal issues involved are manifold, but most need not and should not be taken into consideration in a purely logical perspective. Why? Because the logician’s purpose here is not to decide the case, i.e. who should win or lose, but merely to explain and remove the appearance of paradox.

This remark can be illustrated with reference to the resolution (not mentioned by Suber) proposed centuries ago by Lorenzo Valla (Italy, ca. 1406-57). This attempt at resolution is not adequate because it relies on a thoughtless distinction between payment on account of the court’s verdict and that on account of the agreement. I quote an SEP article which describes it[7]:


“If Euathlus loses the case, he will have to pay the rest of the fee, on account of the verdict of the judges; but if Euathlus wins, he will also have to pay, this time on account of his agreement with Protagoras. Euathlus, however, cleverly converts the argument: in neither case will he have to pay, on account of the court's decision (if he wins), or on account of the agreement with Protagoras (if he loses).… Briefly put, Valla says that Euathlus cannot have it both ways and must choose one or the other alternative: he must comply either with his agreement with Protagoras or with the verdict passed by the judges. If they decide against Protagoras, he may try to reclaim his money in a second lawsuit.”


Let us analyze Valla’s proposed resolution using the following symbols: let P = Protagoras; Q = Euathlus; and C = the fee must be paid by Q to P.

a.     According to P: If Q loses (for whatever reason), then C (by verdict); but if Q wins, then C (by agreement).

b.     According to Q: If Q wins (for whatever reason), then not-C (by verdict); but if Q loses, then not-C (by agreement).

Valla’s conclusion, as here presented[8], is unclear. Apparently, he puts the onus on Euathlus in particular to “choose one or the other alternative” and comply with either the agreement or the verdict. This tells us nothing, since Euathlus’ argument shows he is willing to comply with either, except that he projects both as in his favor. Valla adds that if Protagoras loses a first lawsuit, he may win a second. But here again, this does not resolve the paradox, but only repeats one part of it.

From this we see that Valla has not thought the issues through: he does not consider on what grounds Q might lose or win ‘by the court’s verdict’; and he does not realize that the second argument by each party, where Q might alternatively win or lose ‘by the agreement’, in fact refers to a second lawsuit, since the agreement is evidently not about to be implemented voluntarily (Valla’s mention of a second lawsuit is placed beyond the four if-then statements, which themselves do not emphasize the temporal sequences involved). In the last analysis, then, Valla does not arrive at a true resolution of the paradox.

The trouble with Valla’s approach is that it effectively takes the initial decision of the court to be arbitrary, i.e. unrelated to the agreement between the parties. It does not consider on what basis the court might judge that Euathlus can lose the first round. This may be acceptable legally, but it is not acceptable logically – and our concern here is with logic. Logically, the idea that Euathlus can lose the first round is a non-starter, if we go by the explicit clause of the agreement. He might lose the first round only if the court grants the supposition that there was a tacit clause to the agreement, such as that he had to practice law sometime soon.

In any case, the verdict for the first round cannot be arbitrary – i.e. irrational, unjustified - but must directly relate to the agreement. This is equally true for the second round. So, no disconnect between verdict and agreement is logically permissible.

Interestingly, my first reaction to the paradox a few years ago[9] was very similar to Valla’s. But as soon as I set about seriously considering the issues for the present essay, I realized its weakness and uselessness. The paradox appears neutralized if we insert a distinction between ‘payment following court verdict’ and ‘payment following contract terms’ and assign different symbols to these two consequences, say C1 and C2. These two terms may or may not be quantitatively identical; but they anyway refer to distinct events. This measure seems to nullify the paradox, because the consequences of the first and second if-then statements would be different for each party. Thus:

a.     According to P: If P wins, then C1; but if P loses, then C2.

b.     According to Q: If Q wins, then not-C1; but if Q loses, then not-C2.

It follows that if P wins and Q loses, then C1 and not-C2 are true; and if P loses and Q wins, then not-C1 and C2 are true. Since C1 and C2 are different terms, even if they happen to refer to the same monetary amount, the consequents in each party’s argument are not formally contradictory (since the defining motive is different), so there is no paradox. But, to repeat, this approach does not explain why the court would give a verdict inconsistent with the agreement, so it is artificial. For a genuinely logical resolution, we must focus attention on the agreement, and not admit arbitrary verdicts. Arbitrary verdicts just muddy the waters.

Other attempted resolutions I have seen are also flawed, either because they similarly conflate legal and logical issues, or because they do not follow through on all the consequences of all the suppositions. In any case, either of my proposed two resolutions suffices to unravel the paradox; but the two together take care of all eventualities. Note that, in the first resolution, we not only resolve the paradox, but also incidentally decide the case (in favor of Protagoras); whereas in the second resolution, we are content as logicians to resolve the paradox, leaving the task of legal decision to the judge.

To conclude: the paradox of the court is due to a number of factors, which must be untangled and taken into consideration if it is to be resolved. (a) The terms ‘win/lose’ cannot refer to arbitrary judgments by the court; if they do, the paradox may be perpetuated. (b) It must be realized that the arguments put forward by the two parties imply that the process of resolution has two phases: a first trial followed by a second trial (or by a ready concession and settlement without need of a second trial); the appearance of paradox is partly due to overlooking this time factor. (c) There is some vagueness in what is meant by ‘the agreement’, and all possible interpretations must be taken into account: if the agreement is taken to refer exclusively to the explicit clause, then the first trial concerns that only and is easily decided; but if the agreement is claimed to involve a tacit understanding, then the first trial aims at a decision regarding that tacit clause and the second round deals with the explicit clause.



[1]              Some 550-600 years after the fact, in his Attic Nights (ca. 150 C.E.).

[2]              The contract in question was presumably verbal, rather than written, in those days; but we may take it that both parties agreed on its stated clause.

[3]              In The Paradox of Self-Amendment (Bern: Peter Lang, 1990). The section on the Protagoras v. Euathlus paradox can be read online; it is worth reading, including the notes, and not very long. See at: https://dash.harvard.edu/bitstream/handle/1/10288413/Peter%20Suber%2c%20Paradox%20of%20Self-Amendment%2c%20Section%2020.html?sequence=1#A.

[4]              Assuming this was possible in Athens in those days. This is a fair assumption (even if some commentators deny it) since, after all, Euathlus was apparently trained by Protagoras to be a lawyer himself.

[5]              Protagoras would also, of course, claim that the reasonable delay had expired. If the court agreed with the existence of a tacit clause but disagreed with the claim it was fulfilled, that would merely adjourn the case for a certain amount of time (of their estimate).

[6]              Needless to say, the present analysis is made entirely from a logical viewpoint, although a court of law might reason differently or even not reason at all (e.g. bribery, favoritism, pressure).

[7]              See Stanford Enc. of Phil., online at https://plato.stanford.edu/entries/lorenzo-valla/. This issue is apparently treated in Repastinatio dialectice et philosophie. The author of the article is apparently Lodi Nauta (2013).

[8]              I have not read Valla’s work. I have to assume that the author of the SEP article on Valla correctly presented Valla’s reasoning. I suspect he or she may not have, as the details given in the article are rather vague and inconclusive; they do not clarify exactly what resolution of the paradox Valla had in mind. Not everyone is good at logic. (Note that I did write to the author, asking him or her to please verify the summary of Valla’s view given in the SEP article, but I got no reply. That the author did not deign to respond confirmed my estimate that this is not a very reliable source: intelligent people confidently welcome reasonable queries.)

[9]              In 2009, in an e-mail to someone.

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November 16, 2016

11:18 AM

Critique of the Buddhist Five Skandhas Doctrine, sections 1 and 2

© Copyright Avi Sion, 2016. All rights reserved. This essay will be a chapter in my next book.


In this essay, I shall critically comment on the Buddhist ‘five skandhas’ doctrine. This doctrine is attributed to the Buddha himself and considered as a core belief of Buddhism[1]. However, in my humble opinion, in view of its evident intellectual limitations, this doctrine should not be given such elevated status. Buddhism and its founder have much more intelligent ideas to offer the world. That being the case, the present critique of the five skandhas doctrine should not be taken as a general critique of Buddhism or its founder.


Although often listed in the literature, the five skandhas are rarely clearly defined and expounded on. The Sanskrit word skandha (Pali: khanda) means ‘aggregate’ – and apparently refers to a building-block, of the mind or perhaps of the world. In Sanskrit, the five skandhas listed are: rupa, vedana, samjna, samskara, vijnana (in Pali: rupa, vedana, sanna, sankhara, vinnana). In the dozens of English texts that I have read over the years, I have seen these terms translated in various ways, and with rare exceptions barely explained. It is not made clear whether these terms are essentially phenomenological, psychological, metaphysical, ontological or epistemological. When interpretations are proposed, they differ considerably from one text to another. Nevertheless, this being an important doctrine in Buddhism, it is worth analyzing and evaluating.


1. My own phenomenological reading

Before studying the normative interpretations of these terms, permit me to present my own initial interpretations, even while admitting that they are largely inaccurate historically. That way, the reader will know where I am coming from, and will be better able to follow my thinking. When I first came across the five skandhas in Buddhist books, I took them to constitute a sort of phenomenology, i.e. a list of the different categories of being or appearance, one that suggests an ontological and epistemological theory insofar as the list distinguishes and interrelates the categories in certain ways. Consider the following reading:

  • Rupa, usually translated as ‘form’, could be taken to refer to the apparently external and material world, which contains the phenomena of all shapes and sizes in motion that we seem to witness through our senses, the senses of sight, hearing, smell, taste and touch. This field of experience is quantitatively overwhelming, and takes up most of our existence, but is of course not the whole story, not the whole of our world.
  • Vedana, usually translated as ‘sensation or feeling’, could be taken to refer more specifically to the phenomena we experience as within our personal body. In a sense, these are part of the external and material world, since our body is apparently part of it; but in another sense, they are closer to home (i.e. more internal) and less material (i.e. containing some phenomena notably different from those we experience further afield). In this context, our touch sensations of bodies beyond our own body are feelings, as are all the myriad physical sensations we experience within our bodies, such as sexual feelings (desire, satisfaction), digestive feelings (hunger, thirst, satiety, stomach aches, sensations when urinating or defecating, etc.), and feelings in other internal organs (headaches, heart beats, heartburn, muscular cramps, nerve pains, etc.). Here would also be included emotional reactions experienced within the body, such as love (a flutter or warmth in the heart region), fear (a flutter or warmth in the stomach region), etc. In short, all the pleasures and pains we may be subject to within our bodies, whether they stem from physical or mental causes. Also to be included under this heading would be our sensations of volition (acts of will), i.e. the sense we have that we move our body parts around and our whole body through space; and therefore also our sensations of velleity (pre-volitions, attitudes, intentions). Note however that, while volitions and intentions may have phenomenal aspects, they are largely non-phenomenal; i.e. they are intuited rather than perceived.
  • Samskara, usually translated as ‘mental formations’, and sometimes as ‘impulses to volition’, could be taken to refer to the inner phenomena we experience through our faculties of memory and imagination (the latter being voluntary or involuntary manipulation of memory items to produce somewhat new images, sounds, etc.). This includes the images of visualizations, the sounds of verbal thoughts, dreams (during sleep) and hallucinations (the latter being stronger projections, apparently into the space where matter resides, of imaginations). These phenomena resemble those experienced as external and material, in that they also have shape, color, sound, etc., and yet are experienced as substantially different, of a different ‘stuff’, so much so that we give them a different name (they are characterized as mental, as opposed to material), even if we do regard the mental phenomena, or phantasms, as derivatives of the material ones (through memory of experiences). Such mental phenomena obviously can and do condition (variously incite or otherwise affect) subsequent more overt actions.
  • Samjna, usually translated as ‘perception’, but often as ‘apperception’, ‘conception’ or ‘cognition’, could be taken to refer to our various objects of cognition, i.e. whatever we intuit (non-phenomenal concretes), whatever we perceive apparently through the physical senses or mentally through memory and imagination (phenomenal concretes), and all the abstractions and theories (based on the preceding items) that we construct through conceptual insight and reasoning (including negation, similarity, dissimilarity, etc.). Thus, samjna would include our non-phenomenal impressions (apperceptions), our phenomenal experiences (perceptions), and the concepts and thoughts (conceptions) emerging from the preceding through which we get, not merely to experience things, but also to order and interrelate them, and thus to understand them (or be confused by them) to various degrees. Thus, note well, samjna focuses on objects in the context of their being cognized, i.e. as contents of cognition (and not as objects apart from cognition).
  • Vijnana, usually translated as ‘consciousness’, could be taken to refer to the fact of cognition, the cognizing, as against its object (content), and its subject (the self apparently doing the cognizing). Consciousness has to be listed separately because it is substantially different from any of the other categories in our enumeration. Note well that, to assure a complete enumeration, this term in my view would have to include both the relation of cognition and the apparent self or soul which is related by it to the object. This refers to the self which we all routinely intuit – even though Buddhists deny the latter’s reality and consider it as illusory. This understanding is not entirely foreign to Buddhist practice, which tends to use the terms ‘consciousness’ and ‘mind’ in an ambiguous manner that sometimes really (though typically without frankly admitting it) intends the self (i.e. the one who is conscious)[2]. Moreover, it should be stressed that the self not only cognizes, but also wills and values – i.e. that volition and valuation are among its powers as well as cognition, and that these three faculties are interdependent and do not exist without each other.

That is to say in our present perspective: while rupa refers to external and material objects, vedana to more specifically bodily objects, and samskara to mental objects, and while samjna identifies these same categories of objects as contents of cognitive acts, vijnana refers to the implied knowing (and willing and valuing) acts and to the spiritual entities (ourselves) apparently engaged in them. From this we see that the various phenomenological categories here enumerated overlap somewhat: rupa includes at least part of vedana, samskara is a side-effect of rupa and vedana, samjna includes the preceding experiences and adds their more complex conceptual and rational products, while vijnana focuses on the subject and the relationship of consciousness (and volition and valuation) between it and these various concrete and abstract objects.[3]

The above phenomenological account is merely, to repeat, my personal projection: it is the way I have in the past tended to interpret the five skandhas doctrine in view of the terminology used for it in English. This is the way I, given my own philosophical background, would build a theory of knowledge and being if I was forced to use these five given terms, even while aware that such theory contains some non-orthodox perspectives.


2. A more orthodox psychological reading

However, Buddhists and other commentators present these terms in a rather different light. I will use as my springboard an interesting account I have seen on this topic by Caroline Brazier in Buddhist Psychology[4]. Let us first look at this psychological approach, which I think is close to the original intent of the five skandhas doctrine, given that Buddhism is concerned with ‘enlightening and liberating’ people rather than with merely informing them to satisfy their curiosity. She writes:

“The skandhas are the stages in a process whereby the self-prison is created and maintained. At each stage, perception is infiltrated by personal agendas that create distortion. Delusion predominates…. Each of us continually seeks affirmation that we are that person who we have assumed ourselves to be. Situations that disturb this process are avoided or reinterpreted, and the self appears to become more substantial” (pp. 92-93).

Her exposition of the stages is as follows (summarily put, paraphrasing her). The first stage is rupa, which is finding indications of self in everything we come in contact with; i.e. grasping onto all sorts of things because they reinforce our belief in having a self, and indeed one with a specific identity we are attached to. Next in the process comes vedana, which refers to our immediate value-judgments in relation to things that we come across (people, events, whatever); we may find them attractive, repulsive or confusing – but in any case, we have a visceral reaction to them that affects our subsequent responses to them. Thirdly comes samjna, which consists in spinning further fantasies and thoughts around the things we have already encountered and initially reacted to; due to this, we are unconsciously carried off into certain habitual behavior-patterns. Samskara refers to these action and thought responses which we have, through repetitive past choices, conditioned ourselves into doing almost automatically. Finally comes vijnana, which refers more broadly to the mentality (perspectives and policies) we adopt to ensure our self is well-endowed and protected in all circumstances.

These five stages constitute a vicious circle, in that the later stages affect and reinforce the earlier ones. They ensure that we enter and remain stuck in the cycle of birth, suffering and death. The important thing to note is that the purpose of this psychological description is to make us aware of the ways we ordinarily operate, so that we may over time learn to control and change those ways, and become enlightened and liberated. As Brazier puts it: “Buddhism is not a matter of just going with the flow. It is about changing course” (p. 95). In this approach, the skandhas doctrine is a practical rather than theoretical one. It is a ‘skillful means’, rather than an academic exposition. It is concerned with the ways we commonly form and maintain of our ‘self’.

Needless to say, this looks like a very penetrating and valuable teaching[5]. The question for us to ask at this point, however, is whether it is entirely correct. That is to say, assuming the above sketch is an accurate rendition of the Buddhist theory of human psychology, is this the way we ordinary (unenlightened, unliberated) human beings actually function? Brazier, being a committed Buddhist, takes this for granted rather uncritically. I would answer that though this theory seems partially correct, it is certainly not fully so. What we have here, at first sight, is a portrait of someone who is (very roughly put): very narrow-minded (rupa), instinctive (vedana), irrational (samjna), habitual (samskara), and selfish (vijnana). This may fully describe some people, and it may partly describe all of us, but it is certainly not a complete picture of the ordinary human psyche.

What is manifestly missing in this portrait are the higher faculties of human beings – their intelligence, their reason and their freewill. It could be argued that these higher faculties are present in the background, in the implication that people can (and occasionally do) become aware of their said lowly psychological behavior and make an effort to overcome it. But if so, this should be explicitly included in the description. That is to say, intelligence, reason and freewill should be presented as additional skandhas. But they are not so presented – it is not made clear that humans can function more wisely, and look at the facts of a situation objectively and intelligently, and decide through conscious reasoning how to best respond, and proceed with conscious volition to do so. In any case, these higher faculties are routinely used by most people, and not just used for the purpose of attaining enlightenment and liberation.

Why are these higher faculties, which are common enough, even if to varying degrees, not mentioned in the Buddhist account as integral factors of the human psyche? I would suggest that the main reason is that the self (or soul) has to be dogmatically kept out of it[6]. The central pillar of the Buddhist theory of enlightenment and liberation is that our belief that we have a self is the deep cause of all our suffering, because a self is necessarily attached to its own existence, and the way out of this suffering is to realize that we do not really have a self and so do not need to attach to anything. In such a context, the human psyche must necessarily be described as essentially reactive and stupid, like a ship without a helmsman, at the mercy of every wind and current. Buddhism does regard humans as able to transcend these limitations, by following the ways and means taught by the Buddha in the Dharma; but it does not (in my opinion) fully clarify the psychological processes involved in self-improvement, no doubt due to the impossibility of verbally describing them with precision and generality.

Brazier does go on to describe how Buddhist psychology conceives transcending of the skandhas. She does so in terms of the ‘five omnipresent factors’ being transformed into ‘five rare factors’ “through spiritual practice.” But of course, that account does not clearly say who is doing the spiritual practice, and what faculties are involved. It does not acknowledge that the individual person involved (the self) has to realize (through intelligence and reason) the need for and way to such transformation, and then proceed to bring it about (through complex volitional thoughts and actions). The self and its higher faculties are not given due recognition (because, as already explained, such recognition would go against the Buddhist dogma of no-self). This is not a fault found only in Brazier’s account, but in all orthodox Buddhist accounts.

Understandably, Buddhism, particularly its Zen branch, rejects excessive intellectualism. Admittedly, intelligence, reason and freewill are all very well in principle, as tools for human betterment; but used in excess – or simply misused or abused – they can also and often do exacerbate human delusion and suffering. The intellect can be compulsively used to weave complex webs that distance its victim from reality rather than bring him or her closer to it. We can by such excess become more and more artificial and divorced from our true nature. Of that danger there is no doubt; it is observable. But intellectualism is surely not the whole story concerning our said higher faculties. Surely, they play a big role in improving our understanding and behavior, both in everyday life and in longer-term more intentionally spiritual pursuits.

Moreover, we have to ask whether the five skandhas doctrine, even taken at face value, is truly consistent. We are told that rupa consists in viewing things in relation to self rather than objectively, that vedana consists in immediate likes or dislikes, that samjna consists in making up associations, that samskara consists in conditioning, and that vijnana consists in selfish mentality – and it is all made to seem simple and mechanical. But is it? The Buddhist account itself tells us that these events are interrelated, i.e. stages in a process. Therefore, beneath each of them there must be complex mechanisms at play. Rupa must involve a certain sense of self and of its identity, to be able to select information of interest. Vedana, however instantaneous it may seem, cannot be immediate since it must be filtered through the subconscious scale of values of the person concerned. Samjna presupposes that there are older mental contents to which it associates new mental contents. Samskara refers to habits, which imply programming by repetition. And vijnana in turn implies storage of information and of valuations.

Furthermore, even if we grant that the five skandhas reflect common tendencies within the human psyche, it is introspectively evident that normally the self can in fact, at every one of these stages, intervene through free will based on rational considerations and conscious valuations. That is to say, faced with the ego-centricity of rupa, we can still choose to view things more objectively; faced with thoughtless valuations of vedana, we can still choose to evaluate things in a more balanced manner; faced with wild associations of samjna, we can still choose to put things in context more accurately; faced with our bad samskara habits, we can still choose to resist temptations or overpower resistances; faced with native vijnana selfishness, we can still choose to act with larger perspectives in mind. The human psyche is not a mechanical doll, driven by forces beyond control – there is a responsible soul at its center, able (whether immediately or gradually) to impose its will on the rest of the psyche. Buddhists cannot consistently deny all this, since they do believe in and advocate self-improvement, as the Noble Eightfold Path makes clear.

This brings us to the crux of the matter, the determinism tacitly involved in the five skandhas doctrine. The skandhas are imagined by Buddhists as dharmas, i.e. as “a series of consecutive impersonal momentary events,” as Vasubandhu put it[7]. No one is making them happen, they just happen each one caused by the ones preceding it and causing the ones succeeding it. They do not happen to someone, either, even if they seem to. They are “linked to suffering,” but no one suffers them. Clearly, there is logically no room, in this conception of psychological processes, for a person actually cognizing, understanding, evaluating, reasoning, deciding, choosing and engaging in action. Not only is the person removed, but the acts of cognition, valuation and cognition are also removed. They are reduced to mere momentary electrical disturbances in the mental cloud[8], as it were. They are no longer special relations between a subject or author and other things in the mind or body. This doctrine is, really, crass reification of things that are definitely not entities.

The five skandhas is clearly a mechanistic thesis, even if it is mitigated in a subterranean manner by the Buddhist faith in the possibility of enlightenment and liberation. In this view, logically, such spiritual attainment is itself merely the product of a chain of impersonal mental events, with no one initiating them and no one profiting from them[9]. This state of affairs is claimed to be known by means ‘deep meditation’, although it is not made clear who is doing the meditating, nor by means of what faculties or for what useful purpose. Clearly, objectively, however deep such meditation it could not possibly guarantee the verity of the alleged insights, but must needs submit them to logical evaluation in accord with the laws of thought. Scientific thought cannot accept any deep insights, or any revelations based on them, at face value; it demands rational assessment of all claims.

In truth, granting that there is some truth to the psychological processes described by the skandhas doctrine, they must be viewed more restrictively as processes of ego-building, rather than so radically as processes of self-invention. They refer, not to ways that ‘we’ (a never explained yet still repeatedly used grammatical subject) imagine the self or soul to exist, but to ways that we (the truly existing self or soul, our real selves) constructs and maintains a particular self-image that we think flattering or securing. What is evident in honest, non-dogmatic meditation is that, while such processes can surely influence our mental and physical behavior, i.e. make things easier or more difficult for us, they do not normally determine it. An influence, however strong, can always (with the appropriate attitude and effort) be overcome. At almost every moment of our existence, we remain free to choose to resist these mental forces or to give in to them. If we but make the effort to be aware, to judge and to intervene as well as we can, we remain or become effective masters of our fate.

It is only because we indeed exist as individuals, and have these powers of cognition, valuation and volition, that we can observe, identify, understand and overcome the impersonal forces described by the five skandhas doctrine. Therefore, in fact, the said doctrine, far from constituting an exhaustive listing of the basic building blocks of the human psyche, at best depicts just some surface aspects of much more complicated events and structures. Not only is the list incomplete in that it lacks overt reference to the human self and its higher faculties, but additionally its presentation of the five lower faculties (even assuming that these five faculties indeed exist) is rather superficial. For all the above reasons, and yet others, I view the five skandhas account of human psychology as deficient.

As regards enlightenment, liberation and wisdom, these are impossible without a soul and its faculties of cognition, volition and valuation. Enlightenment means perfect cognition by the soul, i.e. a consciousness as high, wide and deep and accurate as can be for the person concerned. Liberation means perfect volition by the soul, i.e. a will as free of obstructions and as powerful as can be for the person concerned. Wisdom means perfect valuation by the soul, meaning full understanding of good and bad coupled with behavior that is accordingly fully virtuous and non-vicious. Enlightenment, liberation and wisdom are concepts only applicable to sentient beings (notably to humans and other animals, and perhaps in some sense to plants); they are irrelevant to non-spiritual entities (i.e. material and/or mental entities devoid of soul, such as skandhas, computers or fantasy creatures).


[1]              According to the Wikipedia article on this topic, the American Buddhist monk Thanissaro, in Handful of Leaves, Vol. 2, 2nd ed. 2006, p. 309, alleges that the Buddha “never defined a ‘person’ in terms of the aggregates” and that this doctrine is not pan-Buddhist. To my mind, if he said that (I have not seen it with my own eyes), he may well be right.

[2]              I have often in my past writings pointed out the vagueness of the terms mind and consciousness in the discourse of Buddhist philosophers, and explained there how it allows them to get away with much fallacious reasoning.

[3]              Note that in my listing, samjna is placed after samskara, which is not the usual order of listing. I could also have placed samjna after vijnana, since the latter category adds objects of cognition to be considered by the former. However, vijnana also has samjna as one of its objects, since the latter involves consciousness and a conscious subject; so the chosen order of presentation seems most logical.

[4]              London: Robinson, 2003.

[5]              One that could be, and no doubt is, used in meditation.

[6]              It is interesting to note in passing how modern physicists, biologist, psychologists and philosophers tend to similarly studiously ignore the human soul and its functions of cognition, volition and valuation, in their respective accounts of the world, life and humanity. But whereas Buddhism’s motive is to protect its dogma of no-self, the motive of modern ‘scientists’ is to protect their dogma of universal materialism and determinism. The intellectual sin involved in both cases is to deliberately make things look simpler than they are so as to make them fit more easily into one’s pet theory.

[7]              Quoted or paraphrased (not clear which) in Buddhist Scriptures (Harmondsworth, Middlesex: Penguin, 1959), edited by Edward Conze. Vasubandhu was a Buddhist monk and major philosopher, fl. 4th to 5th cent. CE in Ghandara (a kingdom located astride modern-day Pakistan and Afghanistan). His philosophical posture is today normative, at least among the Mahayana, but it was opposed by a Hinayana school called the Personalists, which lasted for many centuries as of 300 BCE and involved a good many monks (e.g. an estimated 30% of India’s 200,000 monks in the 7th cent.). See pp. 190-197.

[8]              Modern ‘scientists’ (I put the word in inverted commas deliberately, to signify criticism) would say much the same, but would place the electrical disturbances on the more physical plane of the brain and nervous system. The idea that the mind is a sort of very sophisticated computer is untenable, for exactly the same reasons that the idea of skandhas is untenable.

[9]              One Victoria Lavorerio, in a paper called “The self in Buddhism,” has written: “If following Descartes we say that where there is a thought there is a thinker, the Buddhist would respond ‘where there is a thought, there is a thought’.” While rather witty, this statement is of course inane, since its author does not grasp the logical absurdities of the Buddhist no-soul thesis (and that, even though she quotes a couple of arguments of mine regarding them), but merely seeks to position herself fashionably. See her essay here: http://www.academia.edu/1489808/The_self_in_Buddhism.

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November 16, 2016

10:50 AM

Critique of the Buddhist Five Skandhas Doctrine, sections 3 and 4

© Copyright Avi Sion, 2016. All rights reserved


3. The metaphysical aspects

The Encyclopaedia Britannica[1] defines the skandhas as “the five elements that sum up the whole of an individual’s mental and physical existence.” It lists them as “(1) matter, or body, the manifest form of the four elements—earth, air, fire, and water; (2) sensations, or feelings; (3) perceptions of sense objects; (4) mental formations; and (5) awareness, or consciousness, of the other three mental aggregates [i.e. items 2-4].”

In most accounts I have seen, this theory is presented as descriptive of what constitutes a person. Some accounts I have seen, however, apply it more broadly, viewing the five skandhas as the constituents of the phenomenal world. In any case, this theory clearly contains an ontological thesis, insofar as it acknowledges two kinds of phenomena, the material (the first skandha) and the mental (the other four skandhas)[2]. Moreover, note in passing, since the above definition mentions the ‘four elements’, it includes a physical theory, one admittedly very vague and by today’s standards rather useless[3]. Secondly, the skandhas doctrine has some epistemological implications, in that it identifies sensations or feelings, perception of sense objects, and so on – implying our ability to know of such things, presumably by introspection.

Furthermore, the said source (EB) explains that “The self (or soul) cannot be identified with any one of the parts, nor is it the total of the parts. All individuals are subject to constant change, as the elements of consciousness are never the same, and man may be compared to a river, which retains an identity, though the drops of water that make it up are different from one moment to the next.” This statement is the metaphysical element in the skandhas doctrine, since it involves important claims regarding the ultimate nature of individuals (i.e. persons, people).

This explanation reminds us that the philosophical motive of the skandhas doctrine is to buttress the Buddhist claim that we have no self or soul (anatta). According to this doctrine, we are only clusters of the listed five material and mental phenomena, which are in constant flux, unfolding as a succession of events, each new event being caused by those before it and causing those after it. It is stressed that none of the skandhas is the self, and neither is their sum the self. The self is not something apart from them, either. What we call the self is a mere illusion, due to our conflating these ongoing, causally-linked events and giving them a name.

The no-self idea is usually expressed by saying that the human being is ‘empty of self’. This is presented as one aspect of a wider metaphysical doctrine of ultimate ‘emptiness’ (shunyata), applicable to all things in the phenomenal world. Initially, I suggest, Buddhist thought sought to replace the self we all naturally assume we have with the five skandhas. Since the doctrine of ultimate emptiness needed to be applied to the apparent self, an explanation of apparent selfhood was provided through the doctrine of the five skandhas. The self does not really exist; it is only made to appear to exist due to the play and interplay of the five skandhas. However, consistency required that the five skandhas be empty too. This was later acknowledged, for instance, in The Heart of the Prajnaparamita Sutra, which stated:

“Form is emptiness, emptiness is form… The same is true with feelings, perceptions, mental formations, and consciousness.”[4]

Here, the five skandhas, thanks to which the self seems to us to exist even though it is in fact empty, are affirmed to be empty too, note well. All phenomenal existents are empty, and this includes the skandhas too. The question might then well be asked (by me, at least): if the skandhas are equally empty, what ideological need have we of them? Why can we not just as well admit the existence of the self or soul, and call it ‘empty’ too, directly? This is of course a significant flaw in the doctrine of the skandhas – it shows the idea of them to be logically redundant. If the motive behind it was to explain the emptiness of self, it was not only unnecessary but useless, since the emptiness of skandhas also had to be admitted! Logically, far from simplifying things, the skandhas hypothesis complicated them.

In other words, the Heart Sutra could equally well have stated: “self is emptiness, and emptiness is self;” or even: “soul is emptiness, and emptiness is soul.” And indeed, it could be argued that soul, being more insubstantial (less phenomenal) than the skandhas, is closer to emptiness than the skandhas are. There are obviously two concepts here to clarify – (a) soul and (b) emptiness. Additionally, we must (c) examine their interrelation.


(a) The term soul refers to an entity of spiritual substance, i.e. of a substance other than the substances that material or mental things seem to have. Soul has no phenomenal characteristics – no shape or color, no sound, no flavor, no odor, no hardness or softness, no heat or cold, etc. That is to say, it cannot be cognized by external perception (using the five sense organs) or by internal perception (using the proverbial mind’s eye, and its analogues, the mind’s ear, etc.). This does not mean it cannot be cognized by some other, appropriate means – which we can refer to as apperception or intuition.

Just because the soul is not phenomenal, it does not follow that it does not exist. Buddhists apparently cannot understand this line of reasoning. In the West, David Hume (Scotland, 1711-76) evidently had the same problem. Looking into himself, he could only perceive images and thoughts, but no soul. Obviously, if you look for something in the wrong place or in the wrong way, you won’t find it. If you look for something non-phenomenal in a field of phenomena, you won’t find it. If you look for color with your ears or for sound with your nose, you won’t find them. To look for the soul, you just need to be intuitively aware. All of us are constantly self-aware, even though we cannot precisely pinpoint where that self is. There is no need for advanced meditation methods to be aware of one’s soul – it is a common, routine occurrence.

Note well that I am not affirming like René Descartes (France, 1596-1650) that soul is known through some sort of inference, namely the famous cogito ergo sum, i.e. “I think therefore I am.” We obviously can and do know about the soul through such rational means, i.e. through abstract theorizing – but our primary and main source of knowledge of the soul is through direct personal experience, which may be referred to as apperception or intuition. So, my approach is not exclusively rationalist, but largely empiricist. In this, note well, my doctrine of the soul differs radically from the Cartesian – as well as from the Buddhist.

According to Buddhist dogma, one cannot perceive the soul in meditation; if one observes attentively one only finds various mental phenomena (the five skandhas, to be exact). But I reply that the soul is manifestly a non-phenomenal object and should not be conflated with such overt phenomena. We all have a more or less distinct ‘sense of self’ most if not all of the time, without need of meditation.

This is obvious from the very fact that everyone understands the word ‘self’. Buddhism admits this sense of self, but absurdly – quite dogmatically – takes it to be ‘illusory’. Having at the outset dismissed this significant ‘sense’ (intuition) as irrelevant, it is not surprising that it cannot find the soul (i.e. the human self) in the midst of the phenomena of mind (the five skandhas)! Note this well – Buddhism has no credible argument to back its no-soul thesis. It begs the question, calling the sense of self illusory because it believes there is no self, and claiming that it knows by introspection that there is no self while rejecting offhand the ordinary experience of self we all have. As a result of this manifest error of reasoning, if not outright doctrinaire dishonesty, Buddhism becomes embroiled in many logical absurdities.

To understand how the soul can exist apparently in midst of the body and mind (i.e. of bodily and mental phenomena) and yet be invisible, inaudible, etc. (i.e. non-phenomenal), just imagine a three-dimensional space (see illustration below). Say that two dimensions represent matter and mind and the third applies to spirit. Obviously, the phenomena of mind will not be found in the matter dimension, or vice versa. Similarly, the soul cannot be found in the dimensions of matter and/or mind, irrespective of how much you look for it there. Why? Simply because its place is elsewhere – in the spiritual dimension, which is perpendicular to the other two. Thus, it is quite legitimate to claim awareness of the soul even while admitting that it has no phenomenal (matter-mind) characteristics.

Note well that the above illustration of the spiritual as located in another dimension is intended as merely figurative, and not to be taken literally, because the concept of dimensions is itself a material-mental concept based on the perception of space. Even the idea of time as a fourth dimension relative to the three dimensions of space is mere analogy; all the more so, the idea of spirit as a further dimension (or maybe a set of dimensions) is somewhat artificial. The simple truth is that spirit cannot really or fully be expressed in material or mental terms, being so very different, truly sui generis. We might likewise object to the image of mind as a distinct dimension (or set of them) in comparison to matter, but mind does have some phenomenal characteristics in common with matter whereas spirit cannot be said to be at all phenomenal. So, to repeat, the above analysis of these three domains with reference to dimensions is merely a convenient metaphor.

Furthermore, it would be epistemologically quite legitimate to claim the existence of soul on purely abstract, conceptual grounds. This is justifiable with reference to the principles of adduction. One can hypothesize an entity, if such assumption serves to explain various observable concrete phenomena. In the case of soul, the ‘phenomena’ involved are our commonplace experiences of cognition, volition and valuation. These experiences are largely intuitive too, but they make their manifest mark in the fields of mind and body. We experience cognition whenever we perceive or conceive anything. We experience volition whenever we think or do anything. We experience valuation whenever we like or dislike anything. Soul explains all these experiences by means of a central entity. This is akin to, say, in astronomy, discovering a planet invisible to our telescopes by observing the displacement of other celestial bodies around it. This is inductive logic.

But in truth, soul is not a mere abstraction; it is a concrete (though spiritual) thing that can be cognized directly using our inner faculty of intuition, to repeat. One error Buddhists make is to confuse entity and essence. The claim of a soul is not a claim of essence, but of entity. The soul is not the essence of the body, or even of the body-mind complex – it is a distinct entity that resides, somehow, in the midst of these phenomena, and affects them and is influenced (and perhaps also affected) by them, but does not have the same nature as them. It is a substance, but a very different and insubstantial substance, as already pointed out. Indeed, to call soul an entity or substance is really just metaphor – analogical thinking. In truth, soul is so different from the other constituents of the world that it can only be described by means of analogy – it cannot really be reduced to anything else we know of.

We can see the said philosophical error made, for instance, in the Milinda-panha, a non-canonical but orthodox Theravada (Pali) text[5]. Here, Milinda questions Nagasena, after the latter claims not to really exist. He asks him very pertinent questions such as who, then, is it that eats, engages in spiritual practices, keeps morality, gains merit, etc. The latter replies by giving the example of a chariot, pointing out that no part of the chariot can be considered as the chariot, nor even the combination of all the parts. Milinda, whose questions were excellent, is very easily taken in by Nagasena’s answers. But (to my mind) we need not be.

For a start, a chariot cannot be considered as analogous to a person. We do not look upon a chariot as like a person, for the simple reason that it does not have capacities of cognition, volition and valuation. To look for the analogue of a soul in a chariot is to commit the red herring fallacy. Moreover, while it is true that a chariot contains no ‘core entity’ which can be so called, and it is true that no one part or combination of its parts can be used to define it, it still has an ‘essence’. A chariot, as a man-made object, is defined by means of its purpose or utility – as a horse-drawn carriage, used for transport and travel, especially in war or hunting or racing. Its essence is an abstraction, not a concrete entity. Certainly all the required parts must be there to form a functioning chariot, but these parts can be changed at will. The one constant in it is the said abstract purpose or utility.[6]

The same reasoning does not apply to persons, obviously. So, Nagasena’s argument was in fact beside the point. As already mentioned, a soul is not an essence, but a core (spiritual) entity. It therefore cannot be viewed as one of the five skandhas, nor as the sum of those skandhas, as the Buddhists rightly insist. It can, however, contrary to Buddhist dogma, be viewed as one of the parts of the complete person, namely the spiritual part; but more precisely, it should be viewed as the core entity, i.e. as the specific part that exclusively gives the whole a personality, or selfhood. This is especially true if we start wondering where our soul came from when we were born, whether it continues to exist after we die, where it goes if it does endure, whether it is perishable, and so forth.

This brings us to the question as to whether the soul is eternal or temporary, or (in more Western terminology) whether the soul is immortal or mortal. Eternal would mean that it has existed since the beginning of time and will exist till the end of time. Temporary would mean any shorter period of time, though it may be very long indeed. Temporary could mean as long as the current body lives, or it could mean for many lifetimes – and that with or without physical bodies.

It seems that Indian philosophy had no place for temporary souls, only eternal souls or no-souls – with regard to soul, it was all or nothing. However, this disjunction is philosophically untenable. It is conceivable that the soul is an epiphenomenon of the living human (and more broadly animal, or at least higher animal) body, which comes into existence with it and ceases to exist when it does. Or it may be that this temporary soul lasts longer, transmigrating from body to body or maybe existing without a body. We do not know (at least, I don’t); but what is sure is that these are conceptual possibilities that cannot be ignored. Certainly non-Buddhist humanity has found them conceivable, since many religions are based on such alternative beliefs.

As regards the eternal soul, the question is whether such a soul can or cannot be liberated from the (alleged) cycle of birth and death. Does eternity of the soul logically imply its eternal imprisonment in suffering? I do not see why. It is conceivable that the eternal soul was once happy, then somehow fell into suffering, but can still pull itself out of its predicament through spiritual practices. It may well be, even, that its liberation depends on a spiritual program like the Four Noble Truths of Buddhism; i.e. on realizing that it is in a vicious circle of suffering, that this suffering is caused by attachment and can be cured by non-attachment, and that such non-attachment can be cultivated through the Noble Eightfold Path. So, there is nothing inherently contradictory to Buddhism in the assertion of an eternal soul. I am not advocating this, only pointing out that it can consistently be advocated contrary to established dogma.

What is sure, in any case, is that the no-soul idea is logically untenable. Buddhists have never squarely faced the logical problems it raises and honestly tried to solve them. They are always inhibited by the fear of being regarded by their peers as heretical holders of ‘false views’; so they keep repeating the no-soul catechism and keep trying to justify it (using absurd means such as the tetralemma, which puts forward the nutty idea that something can both be and not-be, or that something can both not-be and not-not-be). The use of the five skandhas doctrine as an explanation of the (alleged) illusion of selfhood simply does not convince any honest observer, as above shown. Buddhist preachers say that individuals should not take Buddhism on faith, but try and think the issues through for themselves, and they will see the logic of it. But when someone does so, and comes to a different conclusion and rejects one of their clichés, they are nonplussed if not hostile.

The truth is that it is impossible to formulate a credible theory of the human psyche without admitting the existence of a soul at its center. Someone has to be suffering and wanting to escape from suffering. A machine-like entity cannot suffer and cannot engage in spiritual practices to overcome suffering. Spiritual practice means, and can only mean, practice by a spiritual entity, i.e. a soul with powers of cognition, volition and valuation. These powers cannot be equated electrical signals in the brain, or to events in the skandhas. They are sui generis, very miraculous and mysterious things, not reducible to mechanical processes. Cognition without consciousness by a subject (a cognizing entity) is a contradiction in terms; volition without a freely willing agent (an actor or doer) is a contradiction in terms; valuation without someone at risk (who stands to gain or lose something) is a contradiction in terms. This is not mere grammar; it is logic.

An important question as regards the soul is whether it is the same throughout its existence, or alternatively it spiritually changes (for better or worse) over time. This issue is important as it could affect responsibility, and reward or punishment (karma, in Buddhism). Granting that the soul is responsible for its acts of will at the time of such actions, is it just for the soul to receive the consequences of such actions at a later time? Should I pay in my old age for the vices of my youth that I no longer indulge in, or get the belated rewards for my youthful virtues even if I no longer have them? If the soul is unchanging through time, the answer would obviously be yes. But if the soul does evolve or devolve over time, the answer might at first sight seem negative. Can it still be said that the same person involved in such case?

Different solutions to this problem might be proposed. First, we should emphasize that much of the karmic load (for good or bad) of our lives is placed in our mental and bodily dimensions, our mind and body. The question here posed is whether some of the karmic load is placed in our spiritual dimension, our soul. If we say that the soul is constant, we must place all apparent spiritual changes related to it in its mental and physical environment. Thus, the same soul as a baby has more limited powers of walking, talking, etc.; as an adult, his intellectual and bodily powers reach their peak; in old age, they gradually deteriorate.

Moreover, if one thinks and acts in a saintly manner, one is likely to have a pleasant inner life and probably outer life too; whereas, if one thinks and acts in a depraved manner, one is likely to have an unpleasant inner life and probably outer life too. But what of in some supposed afterlife, when the soul is without body or mind? The choices a person makes at any given time reflect its total circumstances at that time. If I am the same across time, then in principle if I were put back in the same circumstances I would react the same way to them. This would seem contrary to the principle of free will, which is that whatever the surrounding influences the soul remains free to choose – and is therefore ultimately unpredictable. 

A better position to adopt may be that proposed by Buddhism in the context of the five skandhas doctrine. I am referring to ‘the Burden Sutra’ expounded by Vasubandhu[7]:

“The processes which have taken place in the past cause suffering in those which succeed them. The preceding Skandhas are therefore called the ‘burden’, the subsequent ones its ‘bearer’ [of the burden].”

We could adapt the same idea to the soul (instead of the skandhas), and say that since its present existence is caused by its past existence, it is in a real sense at all times a continuation of its past, carrying on not only its existence but also its good and bad karma. In this way, even if the soul (the ‘bearer’) has undergone inner changes, it remains responsible for its past deeds (the ‘burden’). The past becomes cumulatively imbedded in the present and future. In that case, we must ask the question: what changes are possible within a soul? Is it not a unitary thing? Can it conceivably have parts? This would seem to take us back full circle to a psychological description, such as the one proposed in the five skandhas theory!

However, I would suggest that such questions are not appropriate in the spiritual realm, which is not quite comparable to the material and mental realms. The soul, being non-phenomenal, cannot be thought of as having size or shape or even exact location, or as increasing or decreasing in content – these concepts and others like them being drawn from the phenomenal realms. We should rather accept that we cannot describe the soul, any more than we can truly fathom its ultimate workings. Just as cognition, volition and valuation are sui generis world-events, so is the soul too special to fit into any simplistic analogies.

It should be added that the view of the soul here proposed is not very far, in many respects, from the Buddhist notion of Buddha-nature. Consider the following statements by Son Master Chinul[8]:

“The material body is temporal, having birth and death. The real mind is like space, unending and unchanging….

The material body is a compound of four elements, earth water, fire, and air. Their substance is insentient; how can they perceive or cognize? That which can perceive and cognize has to be your Buddha-nature….

In the eyes, it is called seeing. In the ears, it is called hearing…. In the hands, it grabs and holds. In the feet, it walks and runs…. Perceptives [sic] know this is the Buddha-nature, the essence of enlightenment. Those who do not know call it the soul….

Since it has no form, could it have size? Since it has no size, could it have bounds? Because it has no bounds, it has no inside or outside. Having no inside or outside, it has no far or near. With no far or near, there is no there or here. Since there is no there or here, there is no going or coming. Because there is no going or coming, there is no birth or death. Having no birth or death, it has no past or present….”[9]

Clearly, the “real mind” which is “like space,” the “Buddha-nature” which alone can “perceive and cognize,” that which sees and hears and grabs and walks, i.e. that which is the Subject of acts of consciousness and the Author of volitional acts, corresponds to what we commonly call the soul, even if the said writer refuses to “call it the soul.” It is noteworthy that, despite the Buddhist dogma that cognitive and volitional acts do not imply a self, this writer seems to advocate that they do (even while virtuously denying selfhood). Is then the difference between these concepts merely verbal? I would say not. The idea of the soul suggests individuation (in some realistic sense), whereas that of Buddha-nature has a more universal connotation (with apparent individuality regarded as wholly illusory).


(b) Let us now examine the Buddhist concept of Emptiness. Note at the outset that I make no claim to higher consciousness, and have no interest in engaging in fanciful metaphysical speculations using big words. I write as a logical philosopher, an honest ordinary man intent on finding the truth without frills. By ‘emptiness’, most Buddhists do not mean literal vacuity, or a void (non-existence). It may be that some Hinayana thinkers understood the term that way, but I gather Mahayana thinkers viewed it more positively (or ambiguously) as referring to ‘neither existence nor non-existence’. The latter expression is meant to reject both excessive belief in the existence of the phenomenal world (Eternalism) and excessive belief in the non-existence of the phenomenal world (Nihilism). It is intended as a golden mean – a ‘middle way’.

However, as regards this concept of ‘middle way’, it is inaccurate (quite muddle-headed, in fact) to say, as Buddhists do, that this emptiness is ‘non-dualistic’, suggesting that it literally includes all opposites, i.e. allows of effective contradiction. All that can be said is that emptiness comprises everything that is positively actual, whether in the past, present or future. Just as actuals are never contradictory, i.e. just as contradiction never occurs in reality at any time or place (not even, upon reflection, in the mind), so emptiness does not admit of contradictions. Contradiction is certainly illusory, and any claim to it is necessarily false. ‘Non-dualistic’ must be taken to mean (more accurately) unitary, undifferentiated. It refers to the actual positive, not to any imagined negative.

Often, it is implied that Emptiness corresponds to the Absolute, the Infinite, Ultimate Reality, the Original ground of Being (or of Mind), the One, Nothingness, the Noumenon, and so forth. This concept, and some of the terminology used for it, are of course not entirely foreign to other philosophies and religions.

From its Pre-Socratic beginnings, Greek philosophy has sought for the underlying unity of the many, what lies beneath the variegated phenomenal world, the common ground of all things we commonly experience, from whence things presumably come and to which they presumably go (as it were). Comparable notions are also found in Judaism, Christianity and Islam, and of course in other Indian religions, notably Hinduism – especially in their respective more mystical undercurrents. Greek philosophy has of course influenced these various religions, and they have also demonstrably influenced each other, in this respect. There has also no doubt been influences from and to Buddhism, as the above mentioned Milinda-panha attests, being a dialogue between a Greek king and a Buddhist monk.

With regard to our bodies, or to matter in general, it is often argued that though they appear varyingly ‘substantial’ (including gases and liquids with solids), if we go deeper into their composition, as we nowadays can, we shall find mostly empty space, with only very rare particles of mass, which are just pockets of energy anyway, connected by insubstantial fields of force. But the obvious reply to that is that this would still not be total void; i.e. even if matter is not as full and substantial as it at first appears, that does not mean that there is nothing in it at all.

Nevertheless, I do not think that the Buddhist concept of emptiness applied to matter refers to this empty space with very rare substantiality. Rather, I think, that it refers to the assumed universal and unitary common ground of all things, which is conceivable as pure existence, prior to any differentiation into distinct entities, characteristics or events. This root existent cannot be described or localized, because to do so would be to ascribe to it some specific character or location to the exclusion of another.

With regard to mental phenomena, by which I mean the stuff of memories and derived phantasms, which apparently occur our heads, they seem much less substantial than material ones, but nevertheless they are phenomenal insofar as we perceive them as having colors, shapes, sounds, and perhaps also (though I can’t say I am sure of it) also odors, flavors and feelings of touch. We must also in this context pay attention to concrete feelings and emotions which appear to occur in our bodies or heads, which we would collectively classify as touch-sensations.

It is worth noting the importance touch-sensations play in our view of matter: the ‘solidity’ we ascribe to matter is defined in terms of the resistance we experience when we push it, pull it or squeeze it, as well as with regard to the evident relative duration of the object at hand. No matter how much empty interspace matter may in fact contain, the experience of solidity (to various degrees) remains, and strongly determines our sense of ‘materiality’. Mental phenomena, in this context, appear far less ‘solid’ than material ones, being able to dissolve more quickly and to be relatively more malleable (and in some respects less so). The Buddhist adjective ‘empty’ should not be taken to mean ‘devoid of solidity’, for solidity (as just explained) is a phenomenological given and therefore cannot be denied.

Additionally, in my view, we must take into consideration, as mental ‘phenomena’ in an expanded sense (more precisely, ‘appearances’), objects of intuition like self, consciousness, volition and valuation, even though they are quite non-phenomenal, i.e. devoid of color, shape, sound, etc. All these existents can also, and all the more so, be regarded as empty, if we understand the concept correctly as above suggested.

According to Buddhism, this root and foundation of all existence, which is somewhat immanent as well as transcendental, can be known through meditation, or at any rate when such meditation attains its goal of enlightenment. In this, Buddhism differs from Kantian philosophy, which views the noumenal realm as in principle unattainable by the human cognitive apparatus (even though Kant[10] evidently claimed, merely by formulating his theory, quite paradoxically, to at least know of it).

Nevertheless, the two agree on many points, such as the characterization of the phenomenal realm as illusory while the noumenal is real. What is clear is that emptiness refers to a universal and unitary substratum, which is eminently calm and quiet, and yet somehow houses and even produces all the multiplicity and motion we perceive on our superficial plane. The world of phenomena rides on the noumenal like ocean waves ride on the ocean. Water and waves are essentially one and the same, yet they are distinguishable by abstraction; likewise, with regard to the noumenal and phenomenal.

Mention should be made here of the Buddhist theory of the codependence or interdependence of all dharmas. According to this theory, everything is caused by everything else; nothing is capable of standing alone. That precisely is why everything (i.e. all things in the world of phenomena) may be said to be empty – because it has no ‘own being’ (svabhaha). This means that not only we humans, and all sentient beings, are empty of self, but even plants and inanimate entities are empty. This may sound conceivable at first blush, but the notion of interdependence does not stand serious logical scrutiny. The claim that everything is a cause of everything is a claim that there is at least a partial, contingent causative relation between literally any two things. But such causative relation must needs be somewhat exclusive to exist at all[11]. So the idea put forward by Buddhist philosophers is in fact fallacious, a ‘stolen concept’.

It should also be said that the term ‘emptiness’, insofar as it is intended negatively, i.e. as indicative of privation of existence, is necessarily conceptual. We can say that being comes from and returns to non-being, but it must be acknowledged that this is something that cannot be known by direct experience, whether ordinary or meditative, but only by conceptual insight. The simple reason for this is that negation cannot be an object of perception or intuition, but can only be known by inductive inference from an unsuccessful search for something positive[12]. Only positives can be experienced. All negative terms are, logically, necessarily conceptual; indeed, negation is one of the foundations of conceptual thought. Thus, any claim that one has purely experienced, in the most profound levels of contemplation, the Nothingness at the root of Existence, is not credible: reasoning (even if wordless) was surely involved.

For Buddhism, the original ground is something impersonal, though some might view it as a sort of pantheism. For the above mentioned major religions, the original ground is identified with God. In my opinion, such identification is more credible, because I do not see how the conscious, willful, and valuing individual soul could emerge from something greater that is not itself essentially conscious, willful, and valuing. These faculties being higher than impersonal nature, their ultimate source must potentially have them too. In Jewish kabbalah, for instance, the human soul is viewed as a spark of the Divine Soul (a chip off the old block as it were). We are in God’s image and likeness in that, like Him, we have soul, cognition, volition and valuation, although to an infinitesimal degree in comparison to His omniscience, omnipotence and all-goodness. But in any case, it is clear that there is some considerable agreement between the various philosophies and religions.


(c) Let us now consider soul in the context of emptiness. Is the concept of self or soul logically compatible, or (as the Buddhists claim) incompatible, with that of emptiness? Can a soul find liberation from its limitations and suffering, or is it necessarily stuck in eternal bondage to birth and death, deluded by endless grasping and clinging to things of naught? Is liberation only possible by giving up our belief the soul? If the answer to these questions is in accord with Buddhism, the five skandhas doctrine would seem to be useful; but if a soul can (through whatever heroic efforts of spiritual practice) extricate itself from the phenomenal and reach the noumenal, then that doctrine would seem to be, at best, redundant, if not ridiculous.

Consider, first, a temporary soul (whether its existence is limited to one lifetime or it spans several lifetimes, either in a body or disembodied). Such a soul, necessarily, like all other impermanent existents that have a beginning and an end, has come from emptiness and will return to emptiness; it is created and conditioned, by the uncreated and unconditioned One. Moreover, a temporary soul might even be regarded as eternal in the sense that it has a share in eternity, not only when it temporarily exists manifestly as a distinct entity, but even before its creation and after its apparent destruction, when it is still or again an undifferentiated part of the original ground. So, no problem there, other than finding out precisely how to indeed liberate it (no mean feat, of course).

A problem might rather be found with regard to an eternal soul, and this is no doubt what caused Buddhists to be leery of the very idea of self (which they regarded as necessarily eternal, remember). The problem is: if the individual soul (or anything else, for that matter) stands side by side with the ultimate reality throughout eternity, then how can it ever merge with it? No way to liberation would seem conceivable for a soul by definition eternally separate from emptiness. But even here, we could argue that the separation of the distinct soul from the universal unitary matrix is only illusory; i.e. that all through eternity this indestructible soul is in fact a constant emanation from the abyss and really always imbedded in it. What makes an illusion (e.g. a mirage or a reflection) illusory is not how long it lasts (a split second or a billion years), but its relativity (a mirage is due to refraction of light from an oasis, a mirror image of the moon is due to reflection of light from the moon). So, in truth, even an eternal soul can conceivably be reconciled with emptiness. I am not affirming the soul is necessarily eternal in that sense, but only pointing out that it conceivably could be so.

In conclusion, the skandhas idea serves no purpose with regard to the requirement of emptiness. Indeed, it is highly misleading, since it is based on false assumptions concerning other doctrinal possibilities. Buddhists cling to this idea for dear life, but without true justification. Clearly, the position taken here by me is that logically we can well claim that people have a soul, and reject the orthodox Buddhist belief that what we call our self is nothing but a cluster of passing impersonal events, without giving up on the more metaphysical doctrine that at the root of spiritual (i.e. every soul’s) existence there is ‘emptiness’ as here understood.

Just as we can say that apparently substantial material, or concrete mental, phenomena are ultimately empty, so we can say that the soul each of us consists of is ‘substantial’ in its own rarified, spiritual way and at the same time ultimately empty, i.e. at root just part of the universal and unitary ground of all being. In other words, contrary to what Buddhist philosophers imagined, it is not necessary to deny the existence of the soul in order to affirm its ‘emptiness’, any more than it is necessary to deny the existence of the body or mind in order to affirm their ‘emptiness’. That is to say, there is no logical necessity to adopt the five skandhas idea, if the purpose of such position is simply to affirm ‘emptiness’.


4. In conclusion

The fact of the matter is that the no-soul thesis is riddled with contradictions. We are told by Buddhists that we can find liberation, but at the same time that we don’t even exist. We are told to be conscious, but at the same time we are denied the power of cognition – i.e. that the soul is the subject of cognitive events. We are told to make the effort to find liberation, but at the same time we are denied possession of volition – i.e. that the soul is the free agent of acts of will. We are told to make the wise choices in life, but at the same time we are denied the privilege of value-judgment – i.e. that the soul is capable of independent and objective valuation.

The no-soul thesis is upheld in spite of these paradoxes, which were well-known to Buddhist philosophers from the start. What is the meaning of spirituality without a spirit (soul, self)? Who can be liberated if there is no one to liberate? Why and how engage in spiritual practice if we not only do not exist, but also have no power of consciousness, volition or valuation? Why bother to find release from suffering if we do not really suffer? Who is writing all this and who is reading it? The no-soul thesis simply cannot be upheld. The soul can well be claimed to be ultimately ‘empty’ in the aforesaid sense, but the thesis of five skandhas instead of a soul is logically untenable.

We have seen that the five skandhas doctrine cannot be regarded as an accurate description of the human psyche in its entirety. It is not a thorough phenomenological account, since it ignores mankind’s major higher faculties – intelligence, rationality and freewill. It focuses exclusively on some petty aspects of human psychology, the five skandhas, without openly acknowledging the more noble side of humanity, which makes liberation from such pettiness possible. It has metaphysical pretensions, with ontological and epistemological implications – notably, the idea that we are empty of soul, devoid of personality – but it turns out that this idea does not stand up to logical scrutiny, being based on circular arguments and foregone conclusions.

Thus, whereas the five skandhas thesis may have at first seemed like an important observation and idea, which applied and buttressed the more general Buddhist thesis of emptiness, and at the same time provided a spiritually useful description of human psychology, it turns out to be a rather limited and not very well thought-out creed. This does not mean that it has no worth at all, but it does mean that it is far less important than it is made out to be.

This being said, I hasten to add that the present criticism of this one doctrine within Buddhist psychology and philosophy is not intended as a blanket belittling or rejection of Buddhist psychology and philosophy. Certainly, Buddhist psychology and philosophy have a great deal more to offer the seeker after wisdom than this one doctrine. It is rich in profound insights into the human psyche and condition, which every human being can benefit from. This is evident already in the opening salvo of Buddhist thought, the Four Noble Truths, which acknowledge the human condition of suffering and identify the psychological source of such suffering in clinging to all sorts of vain things, and which declare the possibility of relief from suffering through a set program of spiritual practices.

In the Buddhist conception of human life, our minds are poisoned by numerous cognitive and volitional and emotional problems. At the root of human suffering lies a mass of ignorance and delusion about oneself and the world one suddenly and inexplicably finds oneself in. These give rise to all sorts of unwise desires, including greed (for food, for material possessions) and lust (for sexual gratification, for power), and aversions (fears, hatreds). The latter impel people to act with selfishness (in the more pathological sense of the term), and in some cases with dishonesty or even violence (coldness and cruelty), and generally with stupidity. But Buddhism proposes ways to cure these diseases, so its outlook is essentially positive.

Clearly, Buddhism has a particularly ‘psychological’ approach to life. It is also distinguished by its businesslike, ‘no blame’ approach to spirituality, which is no doubt why many people in the West nowadays are attracted to it. Unlike most of the other major religions, notably Judaism and its Christian and Islamic offshoots, it does not try to make people feel guilty for their sins, but rather encourages them to deal with their problems out of rational self-interest. It is thus less emotional and more rational in many ways.

Judaism too, for instance, includes psychological teachings, although perhaps to a lesser extent. One of the main features of Judaic psychology is the idea that humans have two innate tendencies – a good inclination (yetzer tov) and a bad inclination (yetzer ra’). These two inclinations influence a person for good or for bad in the course of life (physical life and spiritual life), but they never control one, for human beings are graced with freewill. This means that come what may, a man or woman is always (at least, once adult) responsible for his or her choices. This ethical belief is present in Judaism since its inception, as the following Biblical verse makes clear: “Sin coucheth at the door; and unto thee is its desire, but thou mayest rule over it” (Gen. 4:7). Knowing this, that one indeed has freedom of choice, one can overcome all bad influences and forge ahead towards the eternal life.

In Buddhism, we may discern a similar possibility of taking full responsibility for one’s life in the very first chapter of the Dhammapada (1:1-2). “If a man speaks or acts with an impure mind, suffering follows… If a man acts with a pure mind, joy follows.” Although the five skandhas doctrine gives people the impression (as shown above) that they are not responsible for their deeds, we see here that this is not really the message of Buddhism, which generally enjoins strong spiritual effort in the direction of self-liberation and thence of liberation for all sentient beings.



[1]              Deluxe Edition 2004 CD-Rom. Henceforth, EB.

[2]              I assume that the Yogacara, Mind-Only, school would advocate that matter is a sort of mental phenomenon. In that case, they would presumably advocate that the skandhas theory concerns not only personality but the whole phenomenal world.

[3]              It is worth noting, of course, that the fact that this simplistic, though ancient and widespread, theory of physics (with reference to the ‘elements’ of earth, air, fire and water, or similar concepts) is advocated by Buddhism is proof that this doctrine is not the product of any ‘omniscience’. If the Buddha indeed formulated it or accepted it, he cannot be said to have been ‘omniscient’ since this is not an accurate account of the physical world. This being the case, it is permitted to also doubt he was ‘omniscient’ in his understanding of the mental or spiritual world. Of course, it could be argued that he appealed to the four elements theory only because it was commonly accepted in his day, in the way of a ‘skillful means’, without intending to endorse it.

[4]              Given in full in Thich Nhat Hanh’s The Heart of Understanding (Berkeley, Ca.: Parallax Press, 1988).

[5]              See Conze, pp. 147-151. The dialogue is given in full here. Milinda (Gk. Menander) was the “Greek ruler of a large Indo-Greek empire [namely Bactria] in the late 2nd century BC.” Nagasena was a senior Buddhist monk. The text was, according to EB, “composed in northern India in perhaps the 1st or 2nd century AD (and p

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November 16, 2016

7:44 AM

The Sorites Paradox is Contrived

© Copyright Avi Sion, 2016. All rights reserved. This essay will be a chapter in my next book.


1. What's a heap?

The Sorites paradox is not a paradox, in the strict sense of the term, but a question. The question is sometimes put in a sophistical manner, so as to make it seem paradoxical. But it can be put in a more straightforward manner, in which case it is seen to be simple though not without importance. The term sorites is Latin, derived from the Greek sōros, meaning heap.

One way to express the Sorites paradox is: What is a ‘heap’ (of pebbles, say)? Or, how many pebbles (say) constitute a ‘heap’ of them? The obvious answer is there must surely be at least one pebble. If you have no pebbles, you do not have a heap, but a non-heap. But is one pebble enough? The obvious answer is: no, you need at least two pebbles to make a heap, since heap is a collective term, and one that additionally suggests that the pebbles are stacked one on top of the other (and you cannot stack a non-pebble on a pebble or a pebble on a non-pebble). A single pebble logically counts as a non-heap; heap is intrinsically plural.

Formulated like that, the question is not very problematic. But if it is formulated as follows, it becomes more complicated. If we have many pebbles (say, 100) piled up, we obviously have a heap. What happens if we remove one pebble, do we still have a heap? Yes, 99 make up a heap. What happens if we remove one more pebble, do we still have a heap? Yes, 98 make a heap. And so on, till we come to low numbers, at which stage the sophist wonders whether two pebbles constitute a heap, then one pebble, then no pebble. At this stage, the question appears paradoxical, rather artificially: should we conclude that no pebble makes a heap, or one pebble makes a heap? The sophist thinks we might; the real logician knows we cannot.


2. The use of vague terms

Clearly, the problem here, insofar as there is one, has to do with the exact formulation of initially vague terms. If we do not at the outset step back and think about the exact intent of a vague term, of this sort (a term suggesting quantity, as it happens) or any other, we may find ourselves in difficulty further on in our discourse. So we need to stop and think before use of such terms, and preempt any difficulties they might eventually create. In the present case, as we have seen, the term (heap) is inherently plural (and so inapplicable to less than two pebbles). A sophist prefers to complicate the matter, so as to put human reason and knowledge in doubt, as is his wont; but the matter is really simple enough.

In some cases, to be sure, there is a conventional element to the definition of a vague term. This can be illustrated with reference to another version of the so-called Sorites paradox: As of how many hairs is a man not bald? Obviously, a man with no hair at all is definitely bald. But would a man with only one hair, or a very small number of hairs, not be considered bald in ordinary discourse? Perhaps so – but only conventionally. If we define bald strictly, it implies zero hair; but if we define it loosely, it may include cases involving an arbitrary, though preferably small, number of hairs, determined by convention – for examples, five or twenty hairs[1]. Clearly, if we want to avoid confusion, nothing stops us from referring to this broadened sense of ‘bald’ as, more accurately, ‘bald or almost bald’.

This issue of vagueness is nothing special – it is not limited to terms giving rise to the Sorites paradox. For instance, a relative term like ‘small’ (or its relative, ‘large’) is inherently vague and can only be used with precision in specific situations by means of a conventional quantity. Again, when dealing with continua, we may need to set arbitrary dividing lines. For instance, there is no objective dividing line between one color and an adjacent color in the spectrum, and it may be necessary in some circumstances for us to imagine one (e.g. for legal or other practical purposes[2]). Conventional distinctions are part of human thought; but, it is important to stress, they are not all of human thought. There are always objective elements behind conventional ones. For example, the dividing line between blue and green would be somewhere in between what we see as clearly blue and what we see as clearly green – it would never be far on one side or the other, and much less between green and yellow or between blue and indigo or still further afield.

Returning to our alleged paradox, a few more comments are in order. As already stated, there is nothing paradoxical in the concept of a heap, if it is properly defined. Most simply, a heap can be defined as material items placed on top of each other in whatever way, implying that there must be two or more items. A more complex definition would assume that a heap must be pyramidal, i.e. requires at least four such items (three for the base and one on top); but this puts us in no difficulty, as it can be referred to more specifically as a pyramidal heap. Similarly, baldness stricto sensu refers to no hair at all; it is nevertheless applied to small quantities of hair, though only roughly-speaking.

There are many vague terms of this sort in our common discourse[3], some of which may require a conventional definition for pragmatic reasons. For example, the term ‘crowd’ might be taken to refer to a gathering of three or more people, on the basis of the popular saying that “two’s company, but three’s a crowd;” or we might, say in software used by the police to monitor large groups of people, opt for a larger minimum (say, 50 or 500), set arbitrarily as cause for alarm. The word ‘mob’ might be preferred when the latter crowd goes on a rampage.

But in any case, there is no real logical problem in such unspecific quantitative expressions. They do not constitute a defect in ordinary language, requiring us to construct an “ideal language” where all terms have single precise meanings[4]. Much less do they call for treatment by means of abstruse symbolic logics (dearly loved by many modern logicians). On the contrary, they demonstrate the versatility and flexibility of ordinary thought and speech; and they witness the fact that much of our linguistic communication has non-verbal undercurrents, which we mostly comprehend very ably. Most of our daily use of vague terms involves no need for more clear-cut definition. They are used to suggest things approximately, and are not intended as precise and true affirmations. If the need for precision and truth does arise, it is then addressed in a way that preserves consistency (by explicit convention if necessary).


3. Reasoning with vague terms

To be sure, vague terms can be perilous if we try to reason with them. But vague terms are often used without involving them in argumentative processes Moreover, reasoning with vague terms is not always invalid – there are contexts where the vagueness does not inhibit a reliable conclusion.


In categorical (or hypothetical) syllogism, the rule regarding vague terms (or theses) is the following: The middle item (term or thesis, as the case may be) cannot be vague, because it would provide no guarantee that its intent is the same in the two premises. If the middle item is vague, we cannot be sure of overlap and the conclusion is invalid. On the other hand, the major and minor items can be vague without affecting the argument, and that in all four figures. There is, however, an exception to this rule – when the middle term is vague, but not so vague that overlap is not guaranteed, a valid argument can still be made.

The latter is evident when we consider the following two arguments in the third figure, in which the middle term ensures overlap even though neither premise is universal. The expressions ‘most’ (more than half) and ‘few’ (less than half) are vague, insofar as they do not specify exact numbers. But notice the particularity (as against majority or minority) in the conclusion – i.e. the increased vagueness of the conclusion.


Most M are P

and Most M are S;

therefore, Some S are P


Few M are P (which implies that Most M are not P)

and Most M are S;

therefore, Some S are not P


In apodosis, the rules regarding vague terms or theses are the following:


Modus ponens:

If A is B, then C is D, and A is B (affirming the antecedent); then, C is D (consequent is affirmed).

The antecedent and the minor premise cannot be vague; else, the conclusion is invalid. However, the consequent could be vague, and the conclusion would still be valid (though also vague).


Modus tollens:

If A is B, then C is D, and C is not D (denying the consequent); then, A is not B (antecedent is denied).

The consequent and the minor premise cannot be vague; else, the conclusion is invalid. However, the antecedent could be vague, and the conclusion would still be valid (though also vague).


Here again, in both moods, exception is conceivable, if we know that the major and minor premises overlap, even if we don’t know precisely how much they overlap.


Similar rules may be formulated for other varieties of argument, such as dilemma or a fortiori.


The people who claim that vague terms are inherently paradoxical are dishonestly nitpicking, motivated by the desire to impress themselves or others by their ability to find and resolve (contrived) paradoxes, or (worse still) to demonstrate that human knowledge is inevitably paradoxical and therefore futile. Clearly, just as it is dishonest to call a single pebble or no pebble a heap, it is dishonest to call a person with one or more hairs bald[5]. If you indulge in such contradictions-in-terms to start with, you are bound to end up with paradoxes. People who behave thus are not real logicians but sophists. They spin and fabricate – they are not interested in finding ways to true knowledge.


4. Making up fake paradoxes

The original formulations of both the conundrums described above, relating to a heap and to baldness, are attributed to Eubulides of Miletus (fl. 4th Cent. BCE), the Megarian logician who also gave us the Liar paradox[6]. He was a student of Euclid, a teacher of Diodorus Cronus, and a contemporary and rival of Aristotle. These puzzles were perhaps not initially presented as paradoxes, but rather as illustrations of a question (viz. where should we draw the line?). This possibly reflected a dawning consciousness that there are vague terms that may require arbitrary definition in some circumstances. As above shown, this problem is solved easily enough. However, later thinkers tried to make a mountain out of a molehill, and presented the issue in the form of an argument-chain (or sorites, where the conclusion of the preceding argument serves as a premise for the next).

Thus, the bald man puzzle became, in its positive formulation: Surely, a man with one hair is about as bald as one with no hair; and if a man with only one hair can still be called bald, then a man with two hairs qualifies as bald; and if a man with two hairs is bald, then a man with three hairs is bald; etc.; therefore, a man with a thousand hairs can still be considered bald (paradox). Alternatively, the argument could be stated in negative form: if a man with a thousand hairs is not to be regarded as bald, then one with 999 hairs is not to be so regarded either; and if 999 does not qualify, then 998 does not either; and so on… whence, a man with one hair only is not bald; therefore, a man with no hair is not bald (paradox).

Clearly, these arguments are forced – they involve some very doubtful and misleading premises[7]. They do not pause and rationally reflect on the underlying issue (i.e. where is the dividing line?) before engaging in an apparent inference process, but instead attempt to bamboozle us into a paradoxical corner. The argument-chain proposed just serves as a smokescreen to conceal the crucial false claim being put over. They are the logical equivalents of pyramid sales, each sale supporting the next without solid foundation. People who are taken in by the tricky move are simply bad logicians, if not shamelessly dishonest. They then pretentiously weave massive and intricate theories around this phenomenon, untroubled by the initial error or lie in their discourse.

To those who argue that a single hair or pebble hardly makes any difference, I would suggest that they make the following simple physical experiment: take an accurate balance with the same weight on both sides, then add a single hair or pebble to one side and watch the scales tip! To those still unconvinced by this, because they dogmatically believe that logic is a matter of fancy and convention, I would suggest (tongue-in-cheek) that they place, under the heavier scale, a plunger connected to an explosive device strapped to their nose, and then watch Reality blow up in their face! That argument, I think, might finally convince them, if they survived.

As regards Eubulides, we might note in passing his other paradoxes. The most significant is of course the Liar paradox, which as I have shown in detail elsewhere[8] is exceptionally powerful due to the variety of difficulties it involves (but still quite resolvable). Another three paradoxes[9] deal with equivocations in the term ‘know’, specifically with failure to immediately recognize someone one normally recognizes immediately (such as a close relative or old friend), when the latter is masked or has been away too long or is not looked at attentively enough. Another, the Horns paradox claims that what you have not lost must be in your possession; whence, if you have not lost horns, you must have horns. This apodosis involves a false major premise, since something one has ‘never had’ may equally (as well as something one ‘still has’) be characterized as ‘not lost’ – so the consequent does not follow upon the antecedent; therefore, if one has not lost horns, one cannot be assumed to have horns (since one may well never have had any).

From this short list it can be seen that Eubulides’ queries all give rise to some sort of reflection on logic – reflections on vague terms, on conventional definitions, on equivocations, on term-negations, on self-reference, and various other difficulties that may arise in human discourse. It would be wrong, I think, to assume the motive of such queries to have been teasing or obfuscation (although, to be sure, later skeptics did use such conundrums malignantly, as already mentioned). Rather, I’d say, they served as springboards for earnest reflections and discussions on logic – because it seems unlikely that they were formulated without any attempt to solve the problems they engendered. In some cases, valid explanations or resolutions were no doubt proposed (even though they may not have come down to us), while in other cases the difficulties may have seemed insurmountable. In other words, I doubt that Eubulides was merely sophistical – I’d class him rather as a serious logician.



[1]              Or whatever minimal hairiness seems to us subjectively as so close to bald as to be effectively bald.

[2]              For example, in Jewish law (halakhah) much attention is given to quantitative definitions, notably to the maxima or minima of durations, times o’clock, distances, lengths, volumes, weights, temperatures, monetary values, etc. Initially, such measures were often expressed by the rabbis in vague terms (e.g. ‘the volume of an egg’), but later more precise formulations were called for (which different authorities might differently estimate). However, some measures remain subjective (e.g. the estimate of when one is full after eating). See for more details: http://halachipedia.com/index.php?title=Reference_of_Measurements_in_Halacha.

[3]              Indeed, this is inevitable on two counts. First, many concrete objects are impossible to precisely define. Where, for example, does an orange end precisely? Is the perfume or heat emanating from the fruit part of it or not? At what points in time and space may such emanations logically be regarded as separate from it? Second, human knowledge being inductive, we cannot always start a concept with a precise definition, but tend to leave it open, to be defined more and more precisely as experience unfolds. In this perspective, the majority of abstract terms we use are open, including terms that may be used to more precisely define other terms – so, here again, vagueness is inevitable. But such ontic and epistemic difficulties do not imply paradox; they simply call for philosophical reflection.

[4]              The resort to an “ideal language” by certain modern logicians to solve a problem of logic is futile. Unable to understand the actual way we real human beings logically deal with certain cognitive difficulties, they try to impose a superficial, artificial and impractical way of thinking on the rest of us. The role of the genuine logician is not to impose imaginary logics, but to understand our natural logical means and thence to perfect and reinforce them. Reasoning by humans should be the central concern of logicians. The natural language way to deal with Sorites paradoxes is to use words more precisely – e.g. instead of calling persons with very few hairs ‘bald’, to call them ‘almost bald’; or more accurately still, if necessary for some practical purpose, ‘having (say) one to ten hairs’.

[5]              As I explain in A Fortiori Logic, chapters 1.4 and 2.5, it is sometimes useful to formulate terms in a way so inclusive that positive, zero and negative values are all embraced by them. This is often done in scientific discourse because it facilitates some calculations and graphs. But it must be well understood that such inclusive terms are inherently undeniable – i.e. they already englobe both an affirmation and its denial. In the present context, we might choose to enlarge terms like heap or bald to include their opposites, for whatever reason; but when we do so we must remain keenly aware of what we are doing. If we do not treat such terms with appropriate care, we should not be surprised if we are forced into contradictions.

[6]              A couple of centuries earlier, Epimenides of Knossos declared: “Cretans, always liars,” though himself a Cretan, apparently unaware of the contradiction inherent such a statement. Eubulides may have noticed the paradox involved and sought to refine it and strengthen it, since it was not a double one but one easily resolved by saying that possibly not all Cretans are liars or that Cretans do not all always lie (Epimenides being a notable exception).

[7]              In the positive version, the false premise is that ‘a man with no hair can be called bald’ implies ‘a man with one hair can be called bald’. In the negative version, the false premise is that ‘a man with one hair cannot be called bald’ implies ‘a man with no hair cannot be called bald’. It is the same false claim of implication (in contraposite form). The paradox is created by the refusal to admit that ‘bald’, strictly-speaking, means ‘hairless’; which refusal is not based on honest logical insight, but on a willful act of illogic. Similarly, in the case of a heap, the trick consists in implying that a single pebble or even no pebble may be considered as a heap.

[8]              See my A Fortiori Logic, Appendix 7.4.

[9]              Namely, the Masked Man, Elektra and Overlooked Man paradoxes.

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November 24, 2013

1:03 AM

My new book: A Fortiori Logic

A Fortiori Logic: Innovations, History and Assessments, by Avi Sion, is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all dispel the many fallacious ideas circulating regarding the nature of a fortiori reasoning.

The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged.

The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah.

The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed.

This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox.

You can buy this book online at: http://www.lulu.com/spotlight/thelogicianbooks

You can read this book online at: http://www.thelogician.net/7_fortiori/7_afl_frame.htm

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October 10, 2010

2:30 AM

Causative Syllogism

Thirteenth post in the ongoing series on important innovations in logic theory to be found in my works. The present post continues and ends my brief account of causative logic started three or four posts ago.

My newly completed and published book, The Logic of Causation, is the proudest of my contributions to logic theory. Although I rank my work on factorial induction in Future Logic (briefly described in an earlier post) equally high in significance, the logic of causation was a more difficult achievement. The Logic of Causation had four major tasks: to define causation and its conceivable varieties; to describe how it is induced; to find ways to determine all the deductive properties of its forms, singly and in diverse combinations, and finally (only after having thus studied the matter in detail) to pass judgment on past ideas concerning causation.

The task of definition was relatively easy. It was largely fulfilled by proposing four generic forms (determinations) of causation (complete, necessary, partial and contingent). We found that only four specific combinations of these are logically possible (complete-necessary, complete-contingent, necessary-partial, and partial-contingent). Later, we distinguished ‘absolute’ partial and/or contingent causation, which make no mention of the complements involved in the causation, and ‘relative’ partial and/or contingent causation, which do specify the complements involved. Causation as a whole, then, could be defined as the applicability of any of its conceivable forms. At a much later stage, we were able to define causation as such in a more radical manner.

With regard to the induction of causation, the task was also relatively easy to fulfill. Having in our definitions of the forms of causation identified the conjunctive and conditional propositions jointly underlying each form, we could simply say that the induction of each causative proposition relied on the induction of its several logical constituents. Another way causative propositions could be induced was of course by adduction – that is, by hypothesizing such a proposition to be true and checking the evidence on behalf of it and counterevidence going against it.

But the most daunting task was the study of the deductive properties of causation. This seemed at first easy, in view of the reducibility of causative forms to sets of conjunctive and conditional propositions. And indeed, such reduction made readily possible certain immediate inferences (oppositions and eductions). However, to solve syllogistic problems involving causative propositions, we had to resort to matricial analysis. I had already used matrices in Future Logic to analyze disjunctions – but the job here was much more complex. Still, we succeeded by this means in evaluating (validating or invalidating) a large number of moods of the syllogism in the three main figures (Phase I).

However, this initial method of ‘macroanalysis’, as we later called it, was inadequate on three counts: it was very manual and time-consuming, it was not sure to be infallible or thorough, and it could not resolve all issues - in particular, it could not evaluate syllogisms with some negative premise(s) and/or conclusion. A more detailed sort of matricial analysis, which we called ‘microanalysis’, was seen to be sorely needed and gradually developed. The forms of causation were to begin with analyzed piecemeal, and thereafter more systematically (Phase II). This development allowed us to solve most problems relating to three-item syllogism, with considerably more certainty than previously.

However, this improved method too was open to criticism, again with reference to its dependence on human effort and especially because it could not deal with four-item syllogisms. To overcome these inadequacies, an enlarged perspective and a more mechanical approach were used (Phase III). The results of this last phase of the research were very satisfying. For the first time in history, we now have a means for resolving all three-item and four-item causative syllogisms, whether positive or negative, with whatever polarity of items, with utter conviction and thoroughness. This required the production of massive tables (with logical calculations from matrixes), some of which were 72,000 pages long.

Have a long look for instance at Table 24.3, which is posted online in pdf format at the following address: http://www.thelogician.net/4_logic_of_causation/4_phase3_pdf/4_table_24.3.pdf. The following is an example of its content:

Mood 122 (b) - premises: mq/mq (abs / rel S)

Q is a complete and contingent cause of R

P is a complete and (complemented by S) contingent cause of Q

Positive conclusion(s): mq abs

P is a complete and contingent cause of R

Negative conclusion(s): causative: not-q rel to notS; preventive: none

P (complemented by notS) is not a contingent cause of R

This summary table lists all valid and invalid positive causative syllogisms (144 moods in each of three figures). If we look at the statistics, 19% of the moods were found invalid, i.e. to yield no valid positive or negative causative or even preventive conclusion; the remaining moods yielded some sort of conclusion (of course, all conclusions not listed as valid are invalid). Some of these results are intuitively obvious; but many are clearly not (in particular, note the negative conclusions obtained in some cases). Yet we can now boast for them the precision and certainty of mathematical theorems.

Such lists and statistics go to show the importance of the whole enterprise. Without matricial analysis, we would not know how to reason correctly with causative propositions. And after all, what are we talking about, here? Causation! One of the supreme categories of rational thought! This is not about some obscure form of discourse hardly ever encountered in human reasoning, but concerns one of our main tools for understanding the world around us! Think about it, and you will hopefully be motivated to study the matter closely. Certainly, anyone claiming to be or wishing to be a logician should study it. But so should laypeople who care about fallacy-free reasoning.

To conclude, as I do in the book itself: This is the first time anyone has worked out and published these syllogisms, which are crucial to both ordinary and scientific thinking processes.


For more details on THE LOGIC OF CAUSATION, see: http://www.thelogician.net/4_logic_of_causation/4_lc_frame.htm

For the latest results and conclusions – Phase III – see: http://www.thelogician.net/4_logic_of_causation/4_lc_phase_three.htm

To purchase the book, go to: http://stores.lulu.com/thelogicianbooks


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September 7, 2010

12:47 AM

About Laws of Causation

Twelfth post in the ongoing series on important innovations in logic theory to be found in my works. In this and the next few posts, I will write about the logic of causation, which I have just finished researching over a period of 12 years on and off. The following is an extract from the last chapter of my newly published book The Logic of Causation.

We should also here mention the cognitive role of alleged laws of causation. We have already briefly discussed laws relating to space and time.

In times past, it seems that some degree of sameness between cause and effect was regarded as an important law of causation. Upon reflection, the proponents of this criterion for causation probably had in mind that offspring have common features with their parents. But apparently, some people took this idea further and supposed that the substance (and eventually some other characteristics) of cause and effect must be the same. But though this criterion may be applicable to biology or other specific domains (e.g. the law of conservation of matter and energy in physics could be so construed), it is not generally regarded as universal. Formally, I see no basis for it.

If we want to go more deeply in the history of ‘laws of causation’, we would have to mention, among others, the Hindu/Buddhist law of karma, according to which one’s good and bad deeds sooner or later have desirable or undesirable consequences, respectively, on oneself. It is the popular idea that ‘what goes round must come round’. Though I would agree this is sometimes, frequently or even usually empirically true, we must admit that it does not always seem confirmed by observation – so it is at best a hopeful generalization (to a life after this one) intended to have positive moral influence. In any case, I see no formal basis for it. The same can be said concerning reward or punishment by God – though it might well be true, it is not something that can readily be proved by observation or by formal means; an act of faith is required to believe in it (I do, on that basis). In any case, the latter can hardly be called a ‘law of causation’, since the free will of God is thought to be involved in bringing about the effect.

The law of causation most often appealed to (at least in Western thought) is that ‘everything has a cause’. But though it is evidently true of most things that they have causes, and the belief in this law often motivates us to look for or postulate causes (i.e. even if none is apparent, we may assume one to exist), we have not in our study found any formal grounds to affirm such a law as universal. Admitting the fact of causation does not logically force us to admit its universality. This does not prove that it is not empirically universal; and it does not prevent us from formulating such universality as an adductive hypothesis. In any case, today, as evidenced by quantum physics and big-bang cosmogony, it seems generally assumed by scientists that this law is indeed not universal (which does not mean it is not very widely applicable).

I wonder anyway if it was ever really regarded as universal. I would say that in the 19th Century, this law was assumed universal for physical phenomena – but not necessarily for mental phenomena; human volition was generally taken to be an exception to the rule, i.e. freedom of the will was acknowledged by most people. Paradoxically, in the iconoclastic 20th Century, while the said law of causation was denied universality for material things, every effort was made to affirm it as regards human beings and thus forcefully deny freedom of the will.

Actually, both these changes were (I suggest) consciously or subconsciously motivated by the same evil desire to incapacitate mankind. Their proponents effectively told people: “you cannot control matter (since it is ultimately not subject to law) and you cannot control yourself (since you have no freewill) – so give up trying”. People who believed this nonsense (including its advocates) were influenced by it to become weaker human beings. Virtue was derided and vice was promoted. We see the shameful results of this policy all around us today.

Intellectual fashions change, evidently. But as far as I am concerned, while I admit the possibility that this law [of causation] may not-be universally true of matter, I have no doubt that it is inapplicable to the human will.

I argue this issue elsewhere, in my Volition and Allied Causal Concepts. It should be mentioned that an analogue to the law of causation is often postulated, consciously or not, for the mind. We tend to think that every act of volition has a cause, in the sense of being influenced or motivated, by something or other. Though largely true, this assumption taken literally would exclude purely whimsical volitions; thus, I tend to doubt it, for reasons explained in my said book. In any case, do not confuse this ‘law of influence’ with the ‘law of causation’ here discussed. These are very distinct forms of causality, which cannot be lumped together.

Another alleged law of causation that should be mentioned here (because of the current interest in it, in some circles) is the Buddhist notion that ‘every thing is caused by everything’. As I have shown in The Logic of Causation (see chapters 16 and 19), this idea of universal ‘interdependence’ is logically untenable. It is formally nonsensical. Indeed, if you just think for a moment, you will realize (without need for complex formal analysis) that to affirm interdependence is to deny causation, or at least its knowability. Every concept relies on our ability to distinguish the presence and absence of the thing conceived; if it is everywhere the same, it cannot be discerned. I think the Buddhist philosopher Nagarjuna can be said to have realized that; and this would explain why he ultimately opted for a no-causation thesis. However, that does not mean that causation can logically be denied: as already explained earlier, it cannot.

Well, then. Are there any ‘laws of causation’? Of course there are, a great many! Every finding concerning the formal logic of causation in this volume is a law of causation, a proven law. For instance, the fact that not all positive causative syllogisms yield a positive conclusion of some sort is an important law of causation, teaching us that a cause of a cause of something is not necessarily itself a cause of that thing.


For more details on THE LOGIC OF CAUSATION, see: http://www.thelogician.net/4_logic_of_causation/4_lc_frame.htm

For the latest results and conclusions – Phase III – see: http://www.thelogician.net/4_logic_of_causation/4_lc_phase_three.htm

To purchase the book, go to: http://stores.lulu.com/thelogicianbooks


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August 22, 2010

11:22 PM

How is Causation Known?

Eleventh post in the ongoing series on important innovations in logic theory to be found in my works. In this and the next few posts, I will write about the logic of causation, which I have just finished researching over a period of 12 years on and off. The following is an extract from the last chapter of my newly published book The Logic of Causation.

We have in the previous post explained that causation is an ‘abstract fact’ and established that it is knowable by humans. Our definitions of the various types and degrees of causation provide us with formal criteria with which we are able to judge whether causation is or is not applicable in given cases. But to affirm that causation as such is definable and knowable does not tell us just how to know it in particular cases.

Can we perceive causation? Not exactly, since it is not itself a concrete phenomenon but an abstract relation between concrete phenomena (and more broadly, other abstractions). It has no visual appearance, no color, no shape, it makes no sound, and it cannot be felt or tasted or smelled. It is an object of conception.

Can it then be known by direct conceptual ‘insight’? This might seem to be the case, at first sight, before we are able to introspectively discern our actual mental processes clearly. But eventually it becomes evident that causation must be based on concrete experience and logical process. We cannot just accept our insights without testing them and checking all the thinking behind them. The foundation of causative knowledge – i.e. of knowledge about causation between actual things – is evidently induction.

That is to say, quite common and ordinary processes like generalization and particularization or, more broadly, adduction (the formulation and empirical testing of hypotheses). These processes are used by everyone, all the time, though with different degrees of awareness and carefulness. The bushman who identifies the footprints he sees as traces of passing buffalo is using causative logic. And the scientist who identifies the bandwidth of rays emanating from a certain star as signifying the presence of certain elements in it is using the same causative logic. The bushman is not different from or superior or inferior to the scientist. Both can make mistakes, if they are lazy or negligent; and both can be correct, if they are thorough and careful.

How is a given causative relation induced? Take for instance the form “X is a complete cause of Y”. This we define as: “If X, then Y; if not X, not-then Y; and X and Y is possible”. How can these propositions be established empirically? Well, as regards “X and Y is possible”, all we need is find one case of conjunction of X and Y and the job is done. Similarly for “if not X, not-then Y”; since this means “not-X and not-Y is possible”, all we need is find one case of conjunction of not-X and not-Y and the job is done.

This leaves us with “If X, then Y” to explain. This proposition means “X and not-Y is impossible”, and we cannot by mere observation know for sure that the conjunction of X and not-Y never occurs (unless we are dealing with enumerable items, which is rarely the case). We must obviously usually resort to generalization: having searched for and never found such conjunction, we may reasonably – until and unless later discoveries suggest the contrary – assume that such conjunction is in fact impossible. If later experience belies our generalization, we must of course particularize and then make sure the causative proposition is revised accordingly.

Another way we might get such knowledge is more indirectly, by adduction. The assumption that “X and not-Y is impossible” might be made as a consequence of a larger hypothesis from which this impossibility may be inferred. Or we may directly postulate the overall proposition that ‘X is a complete cause of Y’ and see how that goes. Such assumptions remain valid so long as they are confirmed and not belied by empirical evidence, and so long as they constitute the most probable of existing hypotheses. If contrary evidence is found, they are of course naturally dropped, for they cannot logically continue to be claimed true as they stand.

Another way is with reference to deductive logic. We may simply have the logical insight that the items X and not-Y are incompatible. Or, more commonly, we may infer the impossibility of conjunction – or indeed, the whole causative proposition – from previously established propositions; by eduction or syllogism or hypothetical argument or whatever. It is with this most ‘deductive’ source of knowledge in mind that the complex, elaborate field of causative logic, and in particular of causative syllogism, is developed. This field is also essential to ensure the internal consistency of our body of knowledge as a whole, note well.

Additional criteria. It should be added that though causation is defined mainly by referring to various possibilities and impossibilities of conjunctions – there are often additional criteria. Space and time are two notable ones. Two events far apart in space and time may indeed be causatively related – for example, an explosion in the Sun and minutes later a bright light on Earth. But very often, causation concerns close events – for instance, my eating some food and having a certain sensation in my digestive system. In the both these cases, the effect is temporally after the cause. In the latter case, unlike the former, the cause and effect are both ‘in my body’.

Between the Sun’s emission of light and its arrival on Earth, there is continuity: the energy is conserved and travels through all the space from there to here, never faster than the speed of light, according to the theory of relativity. But what of recent discoveries (by Nicolas Gisin, 1997), which seem to suggest that elementary particles can affect each other instantly and at a large distance without apparent intermediary physical motion? Clearly, we cannot generalize in advance concerning such issues, but must keep an open mind – and an open logic theory. Still, we can say that in most cases the rule seems to be continuity. When we say ‘bad food causes indigestion’, we usually mean that it does so ‘within one and the same body’ (i.e. not that my eating bad food causes you indigestion).

As regards natural causation, we can formulate the additional criterion that the cause must in fact precede or be simultaneous with the effect. But this is not a universal law of causation, in that it is not essential in logical and extensional causation. In the latter modes, the causative sequence may be reversed, if it happens that the observer infers the cause from the effect. Although, we might in such cases point out another temporal factor: when we infer (even in cases of ‘foregone conclusion’), we think of the premises before we think of the conclusions. That is to say, there are two temporal sequences to consider, either or both of which may be involved in a causal proposition: the factual sequence of events, and the sequence of our knowledge of these events.

Similarly, quantitative proportionality is often indicative of causation; but sometimes not. Although it is true that if the quantity of one phenomenon varies with the quantity of another phenomenon, we can induce a causative relation between them; it does not follow that where no such concomitant variation (to use J. S. Mill’s term) is perceived, there is not causation. In any case, the curve quantatively relating cause and effect may be very crooked; ‘proportionality’ here does not refer only to simple equations, but even to very complicated equations involving many variables. In the limit, we may even admit as causative a relation for which no mathematical expression is apparent. An example of the latter situation is perhaps the quantum mechanics finding that the position and velocity of a particle cannot both be determined with great precision: though the particle as such persists, the separate quantities p and v are unpredictable (not merely epistemologically, but ontologically, according to some scientists) – which suggests some degree of natural spontaneity, in the midst of some causative continuity.

Thus, we must stick to the most general formulations of causation in our basic definitions, even as we admit there may be additional criteria to take into consideration in specific contexts. It follows from this necessity that we can expect the logic of causation certain inferences (like conversion, or those in second and third syllogism) where what is initially labeled a cause becomes an effect and vice versa. Keep this in mind. (It is interesting to note here that J. S. Mill’s definitions of causation use the expression: “is the effect, or the cause,… ” – meaning he had in mind the general forms.)


For more details on THE LOGIC OF CAUSATION, see: http://www.thelogician.net/4_logic_of_causation/4_lc_frame.htm

For the latest results and conclusions – Phase III – see: http://www.thelogician.net/4_logic_of_causation/4_lc_phase_three.htm

To purchase the book, go to: http://stores.lulu.com/thelogicianbooks


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August 1, 2010

12:00 AM

What is Causation?

Tenth post in the ongoing series on important innovations in logic theory to be found in my works. In this and the next few posts, I will write about the logic of causation, which I have just finished researching over a period of 12 years on and off. The following is an extract from the last chapter of my newly published book The Logic of Causation.

What is causation? This term refers to a concept – an abstraction through which we can order empirical facts in a way that makes them more comprehensible to us and helps us makes predictions. Like every reasonable concept, causation does indeed signify an existing fact – namely the fact that sets of two or more facts are often evidently related in the ways we call causation. Causation refers to certain observable or induced or deduced regularities in conjunction or non-conjunction between two or more things. By ‘things’ (or preferably, henceforth, ‘items’) here, understand any domain of existence: material, physical, bodily, mental, abstract, spiritual; any category of existent: substance, entity, characteristic, quality, change, motion, event, action, passion, dynamic, static, etc. – anything whatever.

As with all concepts, the concept of causation varies somewhat from person to person, and over time in each person. At one end of the spectrum, there are people for whom the concept of causation is a vague, subconscious notion, which often produces erroneous judgments. At the other extreme, there are those who clearly understand causation and use it correctly in their thinking. The purpose of causative logic, i.e. of the present detailed theory of causation and its relevance to thought, is to improve people’s understanding and practice.

Causation can thus be defined, broadly – and more and more precisely, as our study of it proceeds. But can causation as such be ‘proved’ to exist? Yes, indeed. Causation relies first of all on the admission that there are kinds of things. For, generally, we establish causation (as distinct from volition, which is indeterministic causality) not for individual items, but for ‘kinds’, i.e. for sets of things that resemble each other in some way. When we say that X causes Y, we mean that instances of the kind X are related in a certain way to instances of the kind Y.

Now note this first argument well: if there were no kinds, there would be no causation. That is, if nothing could be said to be ‘the same’ as anything else, kinds would not exist and causation could not be established. But if we claim “Nothing is the same as anything else in any respect”, we are engaged in an inextricable self-contradiction, for that very statement is full of assumption regarding the existence of kinds. Therefore, such a claim is logically untenable, and we must admit that kinds exist, i.e. that our concepts have some empirical basis.

Now, causation refers to the possibility or impossibility of various combinations of things (or their negations). For example, to say that X is never found in conjunction with not-Y and that not-X is never found in conjunction with Y, is a statement of ‘complete necessary’ type of causation. We can certainly argue, regarding a particular pair of items X and Y (e.g. irrational behavior and mental suffering), as to whether or not they indeed fit in this relational format; merely asserting it as fact does not of course make it fact.

But no one can logically deny that there exist some pairs of things in this world that do indeed fit this pattern of relation. It would mean that we deny that there are possibilities and impossibilities of conjunction. Note this second argument well: if we claim “No conjunction of things is possible”, we are saying that the conjunctions implied by this very statement are impossible; and if we claim “No conjunction of things is impossible” we are saying that contradictions are possible. All the more so, if we claim that nothing is possible or that nothing is impossible, we are involved in logically unacceptable self-contradictions. When a thesis is self-contradictory it must be abandoned, and replaced by its contradictory thesis.

Therefore, the definitional bases of causation as such – i.e. the fact that there exists the modalities of possibility and impossibility, and thence of necessity and unnecessity – and the fact that some conjunctions in the world are bound to be related by one or the other of these modalities (nothing else is even conceivable) – are indubitable. Thus, causation, which refers to different combinations and permutations of such modalities of conjunctions, is indubitable. There are no ifs and buts about it.

Why, then, you may ask, are the likes of David Hume or Nagarjuna, and all their modern followers and imitators, so convinced of the illusoriness of causation? The answer is that they are clearly not committed to reason or logic, but merely express their cognitive or psychological problems; or they are not very intelligent. Nagarjuna relied heavily on fallacious reasoning to support his alleged critique of causation. Hume’s search for an empirically observable phenomenon of ‘connection’ or ‘bond’ was a red herring; it implied that causation is something concrete, i.e. tangible or otherwise materially detectable. No wonder he could not find it! No: to repeat, causation is an abstraction, through which we order our empirical observations and predict similar events of the same sort.

Hume admits as much when he defines causation as ‘constant conjunction’ between things. However, that definition is flawed inasmuch as it draws attention to only the positive side of causation; it ignores the crucial negative side (the constant conjunction between the negations of the things). Hume also ignores the different determinations or degrees of causation. And in attempting to ‘explain away’ causation by referring it to habitual associations of ideas, he contradicts himself – since such explanation is itself an appeal to causality; i.e. it purports to tell us ‘why’ we assume causation. Causation is formally the same whether it is assumed to occur in the material surrounds or in the mind, i.e. whether it correlates things or ideas. The fact that causation is usually induced by means of generalizations does not allow us to equate it to association of ideas. And anyway, association of ideas can occur even where causation is doubted; so these concepts cannot be the same in our minds.

As shown above, the concept of causation rests on two pillars, two fundamentals of human knowledge. The one is the fact of similarity and the other is the fact that conjunctions may be possible or impossible.

You can deny that two or more particular objects are similar, but you cannot deny that there are somewhere similar objects and that we are able to identify them in principle. You can deny that two or more particular objects are sometimes or never conjoined, but you cannot deny that there are somewhere objects that are sometimes or never conjoined and that we are able to identify them in principle. When I say “you cannot deny”, I mean you cannot do so without self-contradiction – i.e. you cannot do so with the sanction of logic, i.e. you do so against logic.

Ontologically, causation occurs because not everything is possible in the world. If nothing was impossible, everything could proceed every which way. The limitations that exist in Nature constitute obstacles in its free flow, and ‘force’ it to flow along specific routes. Nature’s course is determined by where it cannot go, rather than by where it must go. The stream of events follows the groove formed by the limits set.

There are as many modes of causation as there are modes of modality. Rational argument refers to the logical (de dicta) mode of causation. Extensional causation is based on extensional modality. Natural, temporal and spatial causation likewise are based on these (de re) modes of modality. It is logically inconsistent to admit one mode of causation (e.g. the logical) and refuse to admit the others (e.g. the natural mode). There is formally no reason to discriminate between them.

In conclusion, causation is a mental overlay through which we order observed reality. But this overlay does not force reality into any arbitrary patterns; it is not an invention of ours. It is merely an acknowledgement that certain patterns do observably occur, and our task in causative reasoning is to identify when they do occur as well as possible. The overlay is not a distortive filter or a hindrance to knowledge. It is based on experience of the world and helps us to more correctly and profoundly discern and understand the world, and thus also to better predict and deal with it.

The concept of causation has no doubt a long history, dating from the beginnings of humanity, if not earlier still in its wordless animal ancestors. Certainly, the moment our ancestors thought or said “because…” or “therefore…” they displayed their belief in or knowledge of causation. The study of the concept is a much later development, of course, which coincides no doubt with the dawning of philosophy, especially in ancient Greece. But it is, I think, in modern times that people began to look for applications of causation in a very conscious manner. I refer of course to the advent of modern experimental science in Europe.

Two important philosophical figures in this context were Francis Bacon and John Stuart Mill. Not because they discovered causation theoretically or the ways to find it in practice, but because they sought to verbalize causative logic. However, neither of these thinkers asked all the right questions or gave all the right answers. Surprisingly, no one made a big effort to follow up on their work, discouraged perhaps by the skepticism instilled by David Hume. It is not until the present study of causation that we have a full analysis and practical guide to causative reasoning, a truly formal logic of causation. This is really a historic breakthrough.


For more details on THE LOGIC OF CAUSATION, see: http://www.thelogician.net/4_logic_of_causation/4_lc_frame.htm

For the latest results and conclusions – Phase III – see: http://www.thelogician.net/4_logic_of_causation/4_lc_phase_three.htm

To purchase the book, go to: http://stores.lulu.com/thelogicianbooks


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July 23, 2010

1:36 AM

The Logic of Causation: abstract

Ninth post in the ongoing series on important innovations in logic theory to be found in my works. In this and the next few posts, I will write about the logic of causation, which I have just finished researching over a period of 12 years on and off. The following, to begin with, is the abstract to my book of that name.

The Logic of Causation is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004).

The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts).

Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians.

The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction.

Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses.

This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation.

Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – and also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated.

In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions.

This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed.


For more details on THE LOGIC OF CAUSATION, see: http://www.thelogician.net/4_logic_of_causation/4_lc_frame.htm

For the latest results and conclusions – Phase III – see: http://www.thelogician.net/4_logic_of_causation/4_lc_phase_three.htm

To purchase the book, go to: http://stores.lulu.com/thelogicianbooks


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April 9, 2010

2:52 AM

Introduction to the theory of induction: about generalization and particularization

Eighth post in the ongoing series on important innovations in logic theory to be found in my works. First, let me apologize again to readers for not posting new blogs more often, but I am at this time very busy with new research and writing. In the present posting, I will present to you the major advance in induction theory published in my book Future Logic 20 years ago, called “factorial induction”. Readers are referred to my previous post on adduction for introductory comments.

The problem of formalizing generalization and particularization using actual/non-modal categorical propositions is simple enough (though some logicians and philosophers seem to have a lot of trouble with it still today). Before we can generalize, we need a particular proposition to generalize. Particulars can be known through direct observation, or less directly through adductive means or by deduction from other propositions so obtained. Note that we do not just assume a positive particular “some X are Y” to be true without reason: we need at least one case to convince us of it; for example, we would not accept that “some humans are blue-skinned” without empirical evidence. On the other hand, negative particulars – and indeed generalities – are often assumed when positive information was sought and not found; for example, “no humans are blue-skinned”.

Having in some way established that “some X are Y”, and not having found any reason to believe that “some X are not Y”, we can readily generalize and say that “all X are Y”. Why is that logically allowed and indeed recommended? Because whereas we do have evidence for the positive case, we have no evidence for the negative case. This is the basis for generalization that many logicians and philosophers have failed to understand. They think that generalization is an arbitrary act based only on particular evidence, not realizing the crucial role played by the absence of contrary evidence. Moreover, they forget that generalization is an inductive process – i.e. one subject to revision if further research uncovers contrary evidence. That is, having generalized from “some X are Y” to “all X are Y”, we are not stuck there for evermore; if we discover later on that “some X are not Y” – or even that assuming “all X are Y” leads us to some contradiction – we may and must particularize “all X are Y” to “only some X are Y” (i.e. some X are Y and some other X are not Y).

Needless to say, all this can in principle function the other way, starting from “some Y are not Y”, generalizing to “no X are Y”, then particularizing to “only some X are not Y”. Obviously, if we already know that “some X are Y” and “some X are not Y”, we would not bother generalizing either way, but would from the start adopt a contingent viewpoint. Generalization is not a must, but a rational option, to be exercised when appropriate; and it remains always tentative to some degree, with an open mind to retreat from it should new evidence or insight justify and demand particularization. Of course, in accord with the principles of adduction, the longer and more often the initial particular is confirmed by experience, and evidence is sought and not found for the subcontrary particular, the less tentative and uncertain does our generalization get. But it may still in principle be overturned at any time by means of just one contrary case, remember. All this is simple enough, as already said, when we are dealing with a ‘bestiary’ of only four actual forms, viz. “some X are Y”, “some X are not Y”, “all X are Y” and “no X are Y”.

However, when we start dealing with a larger bestiary of propositions, including notably de re modal propositions, first categorical and then more broadly conditional, we find the said simple approach no longer adequate as it stands. The question then arises: how far up the scale of generality (in the various modes of modality) can we rise, and how far back must we retreat if contrary evidence is found? For when dealing with more numerous propositions of various sorts, generalization and particularization depend not on one or two simple conditions, but on a variety of complex conditions; and we must be prepared to efficiently logically adapt to constant flux in our data base and reasoning processes.

This is where the processes of factorial induction come into play. This theory constitutes a sophisticated formal logic of induction, which foresees all possible permutations and combinations of categorical (and more broadly, conditional) propositions, in various modes of modality, singly and jointly, and by means of clear and persuasive principles foretells the valid inductive (and sometimes deductive) conclusion(s) to be drawn from them. No one has done this work before, or even thought that it ought to be done and tried to do it.

To start with, the ‘elementary’ propositions are identified and listed. Then all their ‘gross compounds’ (that is to say, their consistent combinations in twos, threes, or fours – including elements of either or both polarities) are identified and listed. The oppositions and eductions from these are considered, because these demonstrate that there are sometimes many possible paths of generalization or particularization from a given point of departure. In view of this, the need becomes evident to identify and list all possible ‘integers’ of propositions and their constituent ‘fractions’. The fractions refer to a subset of the subject-class concern, and the integers to the conjunction of such fractions. The advantage of integral formulae over gross compounds being that in the latter overlaps between different subsets cannot be handled, whereas the former leave no ambiguity in the distribution of cases.

Once this preparatory work is done, the ‘factorial analysis’ or ‘factorization’ of gross compounds can be pursued; i.e. we can identify and list the various alternative integers – now called ‘factors’ – that each gross compound can become in different contexts of knowledge. Some gross compounds have only one factor – one possible outcome in terms of integers (sometimes quite unexpectedly) – whereas most gross compounds have many factors. Induction – i.e. here understood in the sense of generalization and particularization processes – is now viewed as a pursuit of integers, consisting of ‘factor selection’ sometimes later corrected by means of ‘formula revision’.

These processes are guided and controlled by a single, universal law of generalization, which states: “in any factor selection, the strongest factor is the one to prefer”. The reason why this law is universal is that when new data appears, the resultant gross compound is changed, and therefore we refer to another row on the table of all possible factorizations to determine the appropriate strongest factor. When for some reason we know more directly that the previous strongest factor is inappropriate – for instance, if it leads to some contradiction – we can simply select the next available factor, since they are classed in order of their ‘strength’, that is how high they go on the scale of generalization. Precise rules of generalization, and thereafter of particularization, can thus be developed. The result is a precise list of valid moods of inductive argument.

This is work as original and revolutionary today as Aristotle’s formalization of the syllogism was in his day. No one claiming to be a logician can reasonably ignore this work and continue business as usual without reference to it. Once one has studied and understood it fully, one’s outlook on human knowledge changes entirely. Its essentially inductive nature is brought home forcefully and irreversibly. It is shocking to observe just how widespread still today is the ‘deductive’ approach to knowledge among logicians and epistemologists. The theory of factorial induction is designed to shatter this mind-set once and for all, and institute a truly ‘inductive’ approach to knowledge.


For more details on factorial induction, see FUTURE LOGIC, PART VI (CHAPTERS 50-59),


See also: FUTURE LOGIC, part VII, Chapter 67, about inductive logic.

And RUMINATIONS, part I, chapter 9, about negation.


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February 18, 2010

1:11 AM

Introduction to the theory of induction: about adduction

Seventh post in the ongoing series on important innovations in logic theory to be found in my works. First, let me apologize to readers for not posting new blogs more often, but I am at this time very busy with new research and writing. As of the present posting, I will begin presenting to you the major advance in induction theory published in my book Future Logic 20 years ago. I skip (at least for now) other matters covered in that work, so as to maintain the continuity of the narrative here.

Before presenting (hopefully in my next posting) “factorial induction”, however, I must for the sake of some readers explain certain traditional notions and processes underlying induction. We all at any given time have a mass of experiences and ideas, which are constantly in flux. At each moment, we regard this sum of concrete and abstract information as our “world”. Most of us are aware that this punctual information may not all be reliable, since we remember that parts of it were different at earlier times. That is, though we trust our faculties of knowledge for the most part, we are also well aware that we are neither omniscient nor infallible.

Although the human way of acquiring and verifying knowledge has no doubt not changed very much in its essentials since mankind arose on earth, it is only in relatively modern times that the theoretical understanding of the crucial mental/logical process of induction has crystallized. The equally important process of deduction (inferring particulars or narrower universals from larger universals) has been an object of study since antiquity, but it was not then very clear that or how universals emerged out of particulars (inductive inference). We only began to realize the nature of induction by observing modern scientists like Galileo or Newton at work.

It then became evident that the “scientific method” for acquiring knowledge is “hypothetico-deductive”. That is, modern thinkers realized that their ideas were hypotheses related to their experiences in the way that an antecedent is related to a consequent in a hypothetical proposition. The bond between the two aspects of knowledge, i.e. between the abstract/universal aspect and the concrete/particular one, was to be established through deductive reasoning. But the essentially inductive nature of knowledge was that theories were imaginary constructs deeply dependent on empirical evidence for their credibility.

Our ideas are attempts to explain experiences, and thus our theories have to logically imply the evidence at hand. But even so, it is the empirical data that justifies the theory, not the other way round. The way this occurs is through adduction. The term adduction refers to the adducing of empirical evidence in support of an idea or theory. An adductive argument is a deductively invalid apodosis. In deductive reasoning, given that a proposition P implies another proposition Q, we can when we find P to be true infer Q to be also true, but we cannot proceed in reverse fashion and infer P from Q (unless, of course, we have established that ‘if Q then P’ is also true, as occasionally happens).

However, in inductive reasoning, we do consider the reverse argument as having some value (i.e. even though Q does not imply P). Given that ‘if P then Q’ is true, we regard the empirical occurrence of Q as slightly strengthening the probability that the theory P is also true. Probability is not proof in the strict sense of the term, but it adds credibility, and many such small additions of credibility proportionally increase our trust in the theory. But this is not the only basis for induction. Early on, Francis Bacon realized the crucial importance of the negative instance in the rejection of theories. A theory may be supported by a mass of positive indices like that, but all it takes is one erroneous prediction from it for it to lose all credibility (at least as it stands, without modifications). This is simple deduction, the argument being: “given ‘if P then Q’ and finding that Q is false, it follows that P is false”. This means that the credibility of a theory depends not only on the positive evidence going for it, but also on the absence of any damning negative evidence, note well.

There are many other issues in inductive logic that we won’t go into here. But one more issue must be mentioned here: induction rarely occurs with reference to one hypothesis – it is usually, implicitly or explicitly, a contest between two or more alternative theories, so that we cannot evaluate a theory in isolation, merely with reference to the positive and negative evidence, but must compare the success or failure of competing theories at explaining or predicting the same data.

Anyway, as the above described inductive understanding of scientific knowledge developed, it became obvious to scientists, philosophers, logicians and psychologists that these patterns of thinking did not merely concern science – but were descriptive of all human thought. Everyone functions in this trial and error manner: acknowledging empirical data; formulating some imaginary proposition concerning it; testing that proposition as time goes on and new related evidence makes its appearance; and eventually, if contrary information happens to be found, realistically abandoning it. This is valid for any kind of information – not just information about the external material world seemingly perceived by the senses, but also information about our inner life manifested in our intuitions, feelings and mental projections.

Of course, we do not all always proceed so rationally and carefully in practice, so our thought is not always so ‘scientific’, so rigorous. We may, for instances, fail to show a strong logical connection between our idea and the empirical data it is conventionally attached to, or we may fail to consider competing ideas, or again we may simply disregard counter-evidence for emotional reasons. Nevertheless, what has become clear is that the methodology of human acquisition of knowledge is essentially inductive (deduction being, in the last analysis, just a tool of induction, albeit a crucial one).

One of the most important processes of induction is generalization and particularization. It is necessary to realize that this two-sided process fits into the pattern of induction above described. A general proposition is related to particular data in the way that a hypothesis is related to empirical evidence supporting it. So long as a generalization continues to be supported by the particular facts that gave rise to it in our minds, it is to that extent trustworthy; but the moment some contrary evidence comes to our attention, we must obviously particularize, i.e. retreat from our attempted generalization. This will be dealt with in more detail in the next posting, where factorial analysis will be introduced.

For more details on induction in general, see FUTURE LOGIC, PART V (only CHAPTERS 46-49), on adduction.


See also: PHENOMENOLOGY, chapter 7.1, on the principles of adduction; and RUMINATIONS, chapter 2 sections 1-13, for more details on induction.

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January 21, 2010

4:07 AM

So-called material implication cannot adequately do the job of ‘de re’ conditionals

Sixth post in the ongoing series on important innovations in logic theory to be found in my works. The present post is intended as a continuation of the preceding one regarding ‘de re’ conditioning. Although it presents no major innovation, it is needed here to put some novel order in the concept of conditioning, and thus to highlight certain failures of understanding displayed by many logicians since the late 19th Century.

Of course, implication in various guises was used in human discourse long before it was discussed by philosophers. But so far as we know, according to logic historians, the notion of implication was first elucidated by Diodorus (Cronus of Megara, d. circa 307 BCE), who defined it as a sequence of events (or concepts or propositions) such that the first (the antecedent) is always followed by the second (the consequent). Soon after, his disciple Philo (known as the Megarian, though his origin is not sure) advocated a simpler definition of implication, which eschewed the specification ‘always’. For the former, implication (the hypothetical form ‘If P, then Q’) was a modal relation, meaning that the conjunction ‘P and not-Q’ never occurs; whereas for the latter, it sufficed to simply deny that conjunction (effectively, at a given point in time). As closer scrutiny makes clear, Philo was a bad student who should have listened more carefully to his teacher, Diodorus.

Nevertheless, modern logicians (at least those mathematically inclined) considered implication as referring to Philo’s form of implication (later called material implication). This was the situation at least until Clarence I. Lewis revived Diodorus’ form of implication (now called strict implication), in 1918 and more forcefully in 1932. Even after this, many logicians have continued to formulate logic theories or teachings with reference to implication as mere negation of conjunction instead of as impossibility of conjunction (of P and not-Q, given ‘If P, then Q’). They do not yet realize that without appeal to strict implication, we would be hard put to express the difference between disproof (‘proving the contradictory’) and non-sequitur (‘showing the conclusion does not follow from the premises’). Such refinement of discourse is impossible using material implication.

If we compare the ‘truth-tables’ for strict and material implication, they would seem superficially the same as regards the positive aspect ‘if P, then Q’. The truth of P implies that of Q and the falsehood of Q implies that of P. But when we look at the negative aspect, their difference becomes glaring. In strict implication, the negation of ‘if P, then Q’ is ‘if P, not-then Q’, which leaves the respective truths and falsehoods of P and Q open and does not allow us to infer from P the truth or falsehood of Q or from Q the truth or falsehood of P. Whereas in material implication, the negation of ‘if P, then Q’ is simply ‘P and nonQ’, i.e. it tells us categorically that P is true and Q is false!

However, this is only half the story. Already in antiquity to some extent (if only implicitly), and especially since the Scholastics (who seem to have coined the terms), a distinction was made between ‘de dicta’ (or de dicto) and ‘de re’ modalities. The former related to the states of our knowledge (including speculations and hypotheses) about things, whereas the latter concerned the things themselves. That is, more specifically in the present context, the former concerned the logical mode of modality (epistemology), while the latter was about natural, temporal, extensional or similar ontological modes (notably that related to volition, the personal mode).

Many modern logicians after Lewis, whether out of ignorance or naivety, or a stubborn desire to simplify complex issues, have tended to conflate de dicta conditioning with strict implication and de re conditioning with material implication. That is evident in the terminology used – strict means formal, in accordance with logical discourse (i.e. de dicta), and material means contentual, relating to things (i.e. de re); and in the kind of examples they give to illustrate material implication (e.g. ‘if it rains, the match will be called off’). But of course this is quite wrong. Both strict and material implication are (stronger and weaker) forms of logical conditioning. Material implication cannot adequately do the job of ‘de re’ forms of conditioning. This is made evident in Future Logic, part IV, where the latter are examined in detail.

The poverty of modern assumptions in this respect is evident as soon as we try using them to interpret or explain commonly used expressions like ‘when and if’, for example. If ‘when’ and ‘if’ both belong to the logical mode of modality, their conjunction is incomprehensible. Whereas, when we understand the difference between modes of conditioning and between connection and basis of conditioning, such conjunction becomes clear. The ‘when’ tells us that a natural or temporal modality of connection between the theses applies, while the ‘if’ tells us that the base of the antecedent is uncertain, i.e. is merely a logical possibility (and not a de re one). The formal possibilities of material implication cannot be compared to the precision and complexity of discourse made possible by ‘de re’ conditioning. That our practice is more in accord with the latter is easily demonstrated by examples.

Much of this confusion has remained hidden from public view, and to the logicians themselves, due to excessive reliance on symbolic logic.

For more details on this topic, see FUTURE LOGIC, PART III (CHAPTERS 20-32), on logical conditioning. Note in particular chapter 24.3, regarding the strict-material implication distinction.


See also: RUMINATIONS, chapter 4.8, on the strict-material implication distinction; and VOLITION AND ALLIED CAUSAL CONCEPTS, chapter 6.5, regarding ‘personal conditioning’.

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January 5, 2010

1:07 AM

Distinguishing the modes of conditioning

Fifth post in the ongoing series on important innovations in logic theory to be found in my works.

One of the most striking demonstrations of the importance of distinguishing between the different types (or modes) of modality is the way this makes possible more accurate reasoning using conditional propositions. For each type of modality gives rise to a different type of conditioning; and though these various types are analogous in many respects, if we treat them in an undifferentiated manner in our reasoning processes we are bound to make very serious errors.

We must first distinguish between ‘de dicta’, i.e. logical, conditioning – and various forms of ‘de re’ conditioning, notably the natural, the temporal and the extensional. The ‘de dicta’ versus ‘de re’ distinction between modalities, signifying a difference between epistemological and ontological modes of thought, was (as the Latin names we use suggest) known since antiquity, and to a lesser extent so were the varieties of ‘de re’ modality.

However, while logical conditioning has been extensively studied (especially in modern times), the natural, temporal and extensional forms of conditioning have received little attention. Logicians have tended to look upon the logical ‘if--then—’ form as one applicable to all conditioning. But this is far from true or wise, though in practice we often do use this as an undifferentiated form. Logical conditioning in truth relates primarily to states of knowledge.

In Future Logic, I develop a detailed analysis of ‘de re’ types of conditioning, how they are produced and the arguments we can form with them. It soon becomes obvious that, despite the analogies or parallelisms between them, their distinction cannot be ignored. Natural or temporal conditioning concerns states of being of individual things, whereas extensional conditioning concerns instances of a kind of thing. This is evident to us in everyday discourse, and we are quite able to express the differences in meaning linguistically when we feel the need to be precise.

Thus, when we mean natural or temporal conditioning we tend to say “When any X is Y, it is Z”, whereas we mean extensional conditioning we tend to say “In such cases as an X is Y, it is Z”. What do we mean here? In the former statement, we mean that all X are potentially or sometimes Y, and for each X the Y predicate is by natural necessity or always accompanied by the Z predicate. In the latter statement, we mean that some X are Y, and all those instances of X that are Y are also Z. These are just two examples, of course; there are many other forms of each type.

We notice that ‘de re’ conditioning involves a ‘base’ and a ‘connection’. In natural or temporal conditioning, the base is the implied modal statement that “All X can be or sometimes are Y” and the connection is the necessity that ties the actualization of this potentiality or temporal possibility with the consequent predicate Z. In extensional conditioning, the base is the particular proposition that “Some X are Y” and the connection is the universality that ties the instantiation of this particularity with the consequent Z.

In logical conditioning, too, we have a base as well as a connection, but we avoid the restriction implied by a base because it would straitjacket our discourse excessively, because it would make dealing with logical paradoxes a very complicated matter. More precisely put, a peculiarity of logical modality is that logical possibility may always be assumed to be true until and unless it is found, through some implied breach of the laws of thought, to be false. For this reason, logical conditioning may always be assumed to have an appropriate base, except when it is proven to lack one.

Such assumption of possibility until impossibility is proved is not applicable to the 'de re' types of modality, which are subject to more stringent inductive rules. This implies, for instance, that 'de re' necessary conditional propositions cannot automatically be contraposed. This is all said in passing – what I want to stress here is the importance of distinguishing the various ‘de re’ forms of conditioning, of understanding their implicit base and connection. For, once we do this, we realize how different reasoning in each of these modes really is.

One important effect of the study of conditioning in its various ‘de re’ modes is the realization of the logical continuity between categorical and conditional propositions; they are not two opposed forms of expression but greater or lesser degrees of relation. This insight becomes essential when we get into the formal logic of induction. Another important result of the study of the modes of conditioning is the deeper understanding of causation that it makes possible.

For more details on this topic, see FUTURE LOGIC, PART IV (CHAPTERS 33-40).


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December 10, 2009

1:19 AM

Logic depends for its full development on identifying the various categories and types of modality

Fourth post in the ongoing series on important innovations in logic theory to be found in my works.                                                                

On the back cover of the 1996 edition of Future Logic, I wrote the following (among other things) concerning modality:

“What do we mean when we say that something is 'necessarily', 'actually' or 'possibly' so and so? These so-called 'modalities' are attributes of relations, and they vary in meaning. For each category of modality (like necessity or possibility), there are several types of modality (the natural, the temporal, the extensional, the logical, and others), and each of these modalities serves a distinct purpose, expressing some aspect of reality or the state of our knowledge about it. Each category and type of modality has its own peculiar logical properties, and a host of relations to the various others.

“Future Logic demonstrates the centrality of modal concepts in human knowledge and in the processes leading to it. Starting with precise definitions of the various categories and types of modality, it develops a systematic study of reasoning processes involving them, which not only retraces past achievements in the field but also enables a great many new discoveries.

“Modality is significant not only in the study of categorical propositions, but also in that of conditional propositions. There are as many forms of conditioning as there are categories and types of modality; and while some of their logical properties are similar, many are quite different. What this means in practice, is that we cannot reason properly without awareness of these differences. The study of conditioning is of fundamental importance to an understanding of causal relations.

“Future Logic is the first work ever to develop a thorough formal study of the natural, temporal and extensional types of conditioning (as well as logical conditioning), including their production from modal categorical premises.”

While the categories of modality are well known since antiquity and to a lesser extent so is the notion that there are different types (or modes) of modality, Future Logic breaks new ground in its systematic treatment of this field.

Most modern logicians have often left the categories undefined, arguing between them only as to whether to use necessity or possibility as the starting notion. Some have begun with the Liebniz-like definition of necessity as “true in all possible worlds” – ignoring the circularity of such definition (using the yet-undefined term possible) and its pretentiousness (we have a hard time enough to know this world, let alone “all possible worlds”!) And moreover, most modern logicians have concentrated all their efforts on extensional and logical modality, although the natural and temporal modes have been debated by philosophers since antiquity.

One of the important novelties in Future Logic is the analogous definition of categories of modality in the different modes – for instance, the category of ‘necessity’ is defined as occurrence in all instances in the ‘extensional’ mode, in all circumstances in the ‘natural’ mode, at all times in the ‘temporal’ mode and in all contexts of knowledge in the ‘logical’ mode (similarly, for ‘possibility’, saying ‘some’ instead of all, and for actuality saying ‘this one’). This uniformity of structure of the modalities does not however imply that they can be treated collectively, without regard to their basic differences.

Each mode has a specific utility for us. The extensional mode (concerning instances of a kind) is basic to class logic. The natural mode (circumstances surrounding the existence of something) is basic to causal logic. The temporal mode (times in the existence of something) is somewhere in between those two ‘de re’ (or ontal) modes. The logical mode (contexts) concerns our knowledge as such – it is ‘de dicta’ (or epistemic). The ‘de re’ modes are also ‘de dicta’ in a way, but only indirectly.

Future Logic is unprecedented in the history of logic in its transparent and thoroughgoing development of the logics of these various categories and types of modality. Within deductive logic, as already pointed out, its complete and reasoned listing of all modal syllogisms is quite novel. This in itself shows the need for the distinctions made. But their importance becomes crucial and ineluctable when we consider their impact on conditional statements and inferences relating to them. This will be dealt with in my next post.

For more details on this topic, see FUTURE LOGIC, PART II (CHAPTERS 11-13).


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November 29, 2009

3:14 AM

A systematic listing and validation of modal syllogisms

Third post in the ongoing series on important innovations in logic theory to be found in my works.

There is so much to say, I hardly know where to start. Perhaps I had best go back a little and draw your attention to the extensive work done in Future Logic in listing syllogisms.

Following Aristotle and his successors (notably his disciple Theophrastus on the 4th figure), with respect to actual categorical propositions (those of the form “S is P”), I have there listed and validated 19 primary moods and 25 secondary moods in the four figures. I point out incidentally that these 44 valid moods out of a conceivable number of 864 (i.e. a mere 5% validity rate) clearly demonstrate the need to study logic if we want to make sure we reason correctly.

Thereafter, after discussing the various types and categories of modality, I did a similar treatment with respect to modal categorical propositions – meaning primarily for natural modality. Aristotle (and others) had indeed done considerable work in this field, but as I have pointed out in a previous blog, his understanding of modality there (though not in his philosophical discussions, note well) seems to have been limited to the logical mode of modality (or perhaps, I sometimes speculate, some sort of generic mode, underlying all the others) – and this led him to make some serious errors in his list of modal syllogisms.

Moreover, Aristotle’s listing of modal syllogisms was not as thorough and systematic as his listing of actual syllogisms; and so far as I know no one after him has managed an exhaustive and reasoned listing. In Future Logic, I do just that. I begin, as already said, by analyzing and explaining the main varieties of modality. Then, focusing on the crucial “de re” modes (as against the “de dicta” or logical mode, which is the usual object of study of modern logicians), I develop a full list of propositions, examine their oppositions and eductions (i.e. immediate inferences) and then their deductions (i.e. syllogisms, mediate inferences).

One novelty that greatly facilitated my inventory of the various possibilities was the introduction of the symbols n, a, and p for natural necessity, actuality and potentiality, respectively – which notation could be used either independently or as suffices to the traditional A, E, I, O symbols (for plural propositions – to which I added R and G for singulars). Another novelty in this context was to formulate general principles for quantification and modalization of oppositions as well as for intermodal oppositions – expressed in rectangular and three-dimensional ‘figures of opposition’ derived from the traditional ‘square of opposition’.

Finally, I systematically develop a list of valid modal syllogisms, including tables with the valid modes of quantity (all, some, this one), polarity (i.e. positive or negative – what is traditionally but misleadingly called ‘quality’), and modality (mainly of the natural type, and by analogy of the temporal type). The results obtained are sobering. Out of a total 108,000 theoretical combinations of modal and non-modal premises and conclusions, including mixtures of natural and temporal modalities, and including the earlier mentioned wholly actual syllogisms, only 1486 (1.4%) were found valid – and of these, only 93 (6.3%) were primary and the rest (93.7%) were secondary (i.e. implied in the main 93, and relatively less used though not never used).

Validations were of course done using the traditional methods of exposition, direct reduction and reduction ad absurdum (indirect reduction), as appropriate to each figure and mood. The results obtained for modal syllogism demonstrate again that reasoning cannot be left to “instinct” but requires serious investigation – not only to avoid invalid forms of reasoning, but to be made aware of valid forms that are not immediately obvious. The practical value of such knowledge is incalculable. Many more discoveries and insights are to be found in these chapters.


For more details on this topic, see FUTURE LOGIC, PART II (CHAPTERS 11-16).


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November 15, 2009

2:08 AM

Evolving from the traditional static formal deductive logic to a more dynamic treatment of classification

Second post in the series on important innovations in logic theory to be found in my works.                                               

In my previous post I highlighted two important innovations in formal deductive logic, presented in Future Logic, chapters 15 and 17, namely: a) a first figure syllogism consisting of attributive propositions (of the form “S is P”) that draws a possible conclusion from a possible major premise is invalid, but (b) we can however from such premises (and others like them) draw a disjunctive conclusion of the form “S can get to be or become P” (i.e. a disjunction of alterative and mutative propositions). In the present post, I wish to explain the larger significance of these two related findings.

The first finding is of course significant in itself in that wrong reasoning has wide repercussions on all knowledge, and past logicians of the highest caliber have till now (so far as I know) failed to notice the error made by Aristotle and his successors. Aristotle may be excused somewhat because in his mind “possibility” here meant uncertainty one way or the other; thus, he reasoned: if the major and minor premises are both uncertain, so must the conclusion be. But of course, even this intuitive argument is upon reflection untenable, for the two premises may well be uncertain while the conclusion is quite certain for other reasons – so one cannot infer uncertainty for it from the premises, i.e. the syllogism adds nothing to the status of the conclusion.

The second finding is of course significant in itself in that it opens the door to a formal logic concerning change, which here again (to my knowledge) has received no systematic treatment till now.  Aristotle’s deductive logic dealt with attributive propositions, but virtually ignored transitive (alterative or mutative) ones, even though in his general discussions concerning nature and knowledge he was very conscious of the fact of change and had many important insights concerning it. This second finding is also significant in that it was not made independently of the first, but from the beginning was closely tied with it, constituting a solution to the problem it raised.

This brings us to the combined significance of these findings. It is this: whereas till now formal deductive logic has seemed to be a description of essentially static interrelations between individual objects and concepts about them and between concepts, it can henceforth be viewed in a much more dynamic light. This concerns specifically the logic of classification, or class logic. Till now, based on Aristotle’s syllogistic theory, which encompassed only attributive propositions, we could only tell us how things are classified in our minds at a specific time. This expansion of syllogistic theory to include propositions about change allows us at last to see our knowledge in motion, with things changing classes over time. Till now, such changes in classification were intuitively obvious enough, but they were not formally taken into account.

More broadly still, this expanded view of the possibilities of syllogistic reasoning was made possible through the full integration of natural modality in the Aristotelian scheme. Whereas Aristotle had developed modal syllogism rather intuitively in relation to what seems to be an epistemic type of modality, in Future Logic I have managed to systematically insert natural modality and show that its behavior is similar to Aristotle’s quantity (i.e. to extensional modality). Natural modality being inherently a reflection of natural change, this study was bound to lead to a consideration of transitive propositions and of their relations to attributive ones.

Furthermore, the discovery of dynamic formal deductive logic opened the door to my later treatment of the dynamics of induction, i.e. to formal inductive logic, including factorial analysis, factor selection and formula revision. More will be said on this and other consequences in later posts.

All these developments hugely enlarge the scope of formal logic. And of course they reflect more precisely the actual ways human thought is formed and progresses. They are not artificial contraptions externally imposed on people by narrow-minded logicians.


For more details on this topic, see PHENOMENOLOGY, CHAPTER 7, SECTION 5.


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November 9, 2009

1:35 AM

The conclusion of a modal syllogism does not always just follow the modality of the weakest premise

In my first ten blog posts, I have endeavored to give readers a quick cross-section of my philosophy, ranging over a variety of subjects. In the present posting, and the next few ones, I aim to showcase some of the important discoveries in logic theory to be found in my works.

In chapter 63, section 2 of Future Logic, discussing modal syllogism, I point out that Aristotle apparently allowed 'drawing a possible conclusion from a possible major premise in the first figure'. This is suggested, for instance, in his Prior Analytics, book I, chapter 14, where he says: "Whenever A may possibly belong to all B, and B to all C, there will be a perfect syllogism to prove that A may possibly belong to all C". (Actually, he has previously defined "possibility" as what we would call contingency, i.e. as including possibility-not, but the result is the same.) Likewise, Theophrastus of Eresus, Aristotle’s successor as head of the Lyceum, is reported to have taught that “the conclusion follows the modality of the weakest premise” as a general principle. This was a serious error of logic on their part (that to my knowledge no one has since corrected).

In chapter 15 of Future Logic, I on the contrary class as logically invalid to first figure syllogisms of the form:

All M can be P (or nonP)

All/This/Some S can (or must) be M

ergo, All/This/Some S can be P (or nonP)

I expose this invalidity in section 3 of that chapter, saying that we cannot be sure that the circumstances referred to by the major premise include those referred to by the minor premise. The rule for modality here is similar to the rule for quantity that the middle term must be distributive. (This is said by me with regard to the ‘circumstances’ underlying natural modality, but the same applies equally well to the ‘contexts of knowledge’ underlying logical modality, which is seemingly more the intent of Aristotle’s discourse.)

I further explain this in chapter 17 of the same book, where I deal with “transitive categorical propositions”, which concern change either in the sense of alteration, e.g. “This egg has hardened (gotten to be hard)” or in the sense of mutation, e.g. “This soft egg has become hard (or a hard egg)”, as against attributive propositions such as “This egg is soft (or is hard)”. The following is an extract from section 4 of that chapter.

a. When both premises are attributive, an attributive conclusion can only be drawn (if at all) from a necessary major premise; if the major is potential, we cannot draw an attributive conclusion. However, a transitive conclusion can be drawn, showing that the modality may have an impact on the copula. The following moods are valid:

All M can be P (or nonP)

All/This/Some S can (or must) be M

ergo, All/This/Some S can get to be or become P (or nonP)

We know from the premises that what started as S, will in some circumstances be S and M; and that whatever is M, will in some further circumstances be M and P (or nonP); but be cannot predict whether the end result of this process includes or excludes S. It is conceivable that S stays on with P (or nonP), but it is also conceivable that S disappears prior to the arrival at P (or nonP). For this reason, our conclusion cannot be merely 'S can be P (or nonP), but must be open to the 'S can become P (or nonP)' outcome.

b. The same can be argued with a mutative major premise, whatever the modalities involved. Thus, the following are valid:

All M can (or must) become P (or nonP)

All/This/Some S can (or must) be M

ergo, All/This/Some S can get to be or become P (or nonP)

If one or both premises are potential, so is the conclusion, as above; but if both premises are necessary, a necessary conclusion can be drawn, as below:

All M must become P (or nonP)

All/This/Some S must be M

ergo, All/This/Some S must get to be or become P (or nonP)

c. In cases where the minor premise is mutative, whether the major is attributive or mutative, similarly disjunctive conclusions may be drawn. We know from the minor premise that S will disappear to become M, but we cannot be sure whether, in the circumstances when M is or becomes P, S reappears or stays away.

Note that in all the cases so far considered, we could view the conclusion as a logical disjunction as we did, or we could say that a more specific conclusion can be drawn if we know one or the other alternative to be excluded. This would be equivalent to having a third premise, viz. 'S cannot get to be P' or 'S cannot become P'. But formally speaking, this constitutes an additional argument (apodosis) after the syllogism as such.

d. All the above only concerns cases with both premises affirmative (whether the predicate be P or nonP). Now, the minor cannot be negative in the first figure, but what if the major premise is negative (in the sense of negating the copula, not merely the predicate)? In such case, we cannot draw a likewise negative conclusion, because we can construct a syllogism with compatible affirmative premises yielding a conflicting affirmative conclusion. Thus, for example, the following mood is invalid:

No M can become P

This S must be M

ergo, This S cannot get to be or become P

This is invalid, because it is conceivable that, though no M can become P, all M can nonetheless be P, in which case the following syllogism could be constructed, as earlier established:

All M can be P

This S must be M

ergo, This S can get to be or become P

We could interpret this to mean that, a (compound) negative conclusion is possible, if the negative major is compound, as in the following mood. Note that major premise and conclusion are conjunctions, not disjunctions, of negatives. The result is due to the attachment of S to M.

No M can be or become P

This S must be M

ergo, This S cannot get to be or become P

If either or both of these premises were potential instead of necessary, a potential conclusion would be drawn.

For more details on this topic, see FUTURE LOGIC, CHAPTER 17.


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October 12, 2009

2:08 AM

Two basic meditations: breath awareness and thought awareness



To meditate is to make a sustained effort to increase one’s awareness, or at least to prevent it from decreasing from a certain level; this defines what constitutes meditation. This is to be distinguished from contemplation, which is steady, effortless, stable awareness (or increased awareness, in comparison with some previous state). Contemplation is a goal of meditation. At some stage, meditation (an effort of awareness) becomes contemplation (effortless awareness).

There are many ways and means of meditation, of which two may be mentioned here.

In breath awareness meditation, we make an effort to watch the breath entering and leaving the body, patiently, without interfering in its speed or trajectory. Calmly and single-mindedly, fix your attention on the sensory receptors inside your nostrils (which are static relative to the movements of breath); and persevere in this attentiveness for a long time. At the same time, be mindful (from the inside, if only peripherally) of the rise and fall of your belly with every incoming and outgoing breath.

Experience one breath at a time. You cannot achieve mindfulness of breath in a mechanical manner, merely by initially deciding to watch your breath and then doing so for a couple of breaths. You cannot just launch breath awareness – or any other sort of meditation, for that matter – and expect it to carry on by itself. Your attention will in such case naturally float away at the first opportunity. Awareness is not something inertial – it demands effort.

Thus, to sustain your interest in the breath, engage one breath at a time. At the end of the first in and out breath, remember to make a new decision and effort to attentively follow the trajectory of next breath, and so on – one step at a time. This principle is applicable to all sorts of meditation (e.g. to walking meditation or to calligraphy). Even when one reaches the level of free-wheeling contemplation of one’s breathing, feeling the emptiness within, one has to remain focused and not take things for granted.

In the words of Zen master Dogen: “the breath that comes in does not anticipate the breath that goes out”. You remain mindful of things as they are, at their own pace. This mental will (or more precisely, spiritual will) must be distinguished from the effort of breath control, which involves physical will (on the muscles of the nostrils, the diaphragm or whatever). It is more akin to the “presence of mind” (or again, more precisely put: presence of spirit, or spiritual presence) used in Tai Chi or Yoga.

If your breath is irregular in some way (whether ragged, uneven or however uncomfortable), the simplest way to calm it is to wait for it patiently to do so by itself (as it is bound to do eventually). If such waiting results in your forgetting to watch the breath, no matter – when you become aware of your loss of attention, just return to breath awareness. If you lack the patience to wait but want to do something about it, then count the breaths as they occur (whatever their speed and shape). But abandon words again as soon as possible, for they are ultimately a hindrance to progress.

In thought awareness meditation, we make an effort to watch our thoughts come, play out and go. This is again essentially a spiritual act, a willing of attention – to be distinguished from the effort of thought control, which involves willing one’s thoughts to take shape, to go in a certain direction, or to stop. It takes a lot of practice to get to the point where one can sit back and watch one’s thoughts flow without getting caught up in them and carried away by them; but, although the brain seems programmed to hinder it, such detachment is indeed possible.

Thought awareness is facilitated by body awareness, breath awareness and awareness of one’s surroundings. When thoughts run wild, you can rein them in more readily if you increase awareness of the here and now. The thinker is suspended in a cloud, unaware of his physical existence or his surrounds: return him to earth. If the thoughts are overwhelming, ask them only for a little room in a corner of your mind – a place for monitoring thought. Then slowly expand this observatory’s portion of the mind.

It would not be quite correct to say that one should just sit back and watch one’s thoughts, as one watches one’s breath. Breathing is not expected to stop (but only to calm down), whereas thoughts ought to eventually stop. Therefore, one has to use a certain amount of thought control, even while avoiding crude force. Paradoxically, true thought control is not possible without thought awareness; you cannot precisely influence what you are not sufficiently conscious of. That is to say, to succeed at fine-tuned control, one needs proportionate attentiveness. Therefore, meditation on thought is a cunning mélange of awareness and control, in measured succession, until awareness and control both reach their peak level.

At that stage, it is possible, not only to instantly stop thought by an act of will, but to sustain this interdiction for a long time. Eventually, even this act of will becomes unnecessary or unconscious, because we come to reside comfortably in inner stillness and silence. This is not the final goal of meditation, but merely an intermediate stage. Until now, thoughts were a distraction from deeper meditation; now, it becomes possible to contemplate the non-phenomenal self and its relation to phenomenal experience more precisely.

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October 5, 2009

3:50 AM

Mental health can be equated mainly to self-knowledge, self-control and self-value



Just as our physical health is defined with reference to the human body, and its various members, organs and systems, as the optimum condition and function of that body – so in the case of mental health. Mental health is the optimum condition and functioning of the psyche.

The psyche, the subject-matter of psychology, is of course a very large concept. It includes to some extent the body, since our mental life is largely psychosomatic, and since the body is the substratum of the so-called mind; especially, our mental health depends on the healthy condition and functioning of our nervous system, including the brain and the sense organs. On a less physical level, the psyche has two main domains, the spiritual and the mental (in a narrow sense of the term).

By the spiritual domain, I mean the soul, and by the (narrow) mind I mean the mental phenomena that occur (as it were) around the soul. With regard to those mental phenomena, they are perceptible (to various degrees) things or events, like thoughts, dreams and emotions. They are, strictly speaking, outside the soul. They can be experienced and manipulated by the soul, but their existence depends on the nervous system too; and indeed, sometimes they are entirely products of the nervous system.

The soul is the true self, that which constitutes a person within us. The soul may be active or passive relative to mental phenomena and relative the physical aspects of the psyche (i.e. the nervous system). The soul itself has three obvious faculties or powers, namely cognition (intuitive, perceptual, logical and conceptual), volition (our will) and valuation (our values). (The term ‘faculties’ should not be taken to imply that the soul contains entities or departments – it merely refers to capabilities to cognize, to will and to value.) The core issue in mental health is the health of the soul, although the issue is wider than that.

Mental health refers mainly to the correct functioning of the three faculties of the soul. It has three components, corresponding to these three faculties. These are of course closely interrelated, each requiring both the others to function. Mental health has degrees. The degree of overall mental health is proportional to the degrees and combinations of degrees of health in these three areas of human endeavor.

Ø  The faculty of cognition is at its best when it is well prepared and trained to know the surrounding world and how to deal with it. That is certainly true and important, but the main cognitive health issue is self-knowledge. This is achieved by introspection and self-observation in action. Without a lucid, profound and extensive knowledge of one’s own inner workings (motives, desires, fears, emotions, capabilities, etc.) and outer behavior, one is bound to feel imprisoned or lost in strange territory.

Ø  The faculty of volition, likewise, has to be maintained for maximum efficiency in dealing with mental and physical phenomena. But the essence of health in relation to it is self-control (in the best sense of the term, not implying oppression), i.e. getting into the habit of doing what needs to be done (energy) or not-doing what needs to be avoided (restraint). This is essential to self-trust and self-confidence. For it is clear that if one allows oneself to be at the mercy of every passing fancy, impulse, urge, obsession, compulsion, bad habit, one will soon experience great anxiety, for anything might happen anytime. Without discipline one becomes one’s own worst enemy.

Ø  The faculty of valuation is properly used when or insofar as one’s values are conducive to life, to self-knowledge and to self-control. This may be called self-value (in the best sense of the term, not implying egoism or egotism, selfishness or vanity). Clearly, if one has twisted values, contradictory values, an inclination to perversion of some sort, and so forth, one will soon become confused and ultimately bring about one’s own self-destruction.

Thus, briefly put, the three most spiritual aspects of mental health are self-knowledge, self-control and self-value. These are spiritual, because they concern the soul (or spirit or self), the core of our psyche or mental existence. When the Subject of cognitions, the Author of volitions and the Valuer of valuations is appropriately looked after, he or she is healthy and the rest follows. If the self’s faculties are on the contrary neglected, the opposite occurs. We may thus speak of spiritual health – or in the opposite case, of a sick soul.

This is one aspect of mental health, its most intimate aspect. Of course, mental health does not only refer to how we take care of our soul, but to the full range of survival conditions and tasks. We need to improve our general cognitive abilities, e.g. by studying inductive and deductive logic, by being attentive, by remaining sober, and so on. Our capabilities of action will be improved by controlling our diet and our sex life, by staying physically fit, and so forth.

In short, without going into details, mental health relates to a wide range of inner and outer behavior patterns. It is therefore closely related to what we call ethics, the study of what is conducive to life. A person who cultivates mental health gets inner equilibrium and self-respect as reward, and achieves happiness, or at least basic contentment. Whereas the opposite person, sentences himself or herself to much inner conflict and self-contempt, and ends up suffering considerably.

Moreover, although the primary task of mental hygiene relates to oneself, this has a strong impact one one’s social relations. That is to say, a mentally healthy person will naturally treat other people with respect and consideration, since that is the way he or she is used to dealing with himself or herself. On the contrary, a mentally unhealthy person will have many inter-personal conflicts, and suffer fear, anger, hatred, and similar negative emotions as a consequence.

Thus, mental health begets both dignity and decency. And inversely, mental sickness spoils life for self and others. Mental health is ennobling; mental sickness is debasing.

When one has mental health, the ongoing task is to maintain it and increase it. When one lacks it, the first task is to obtain it, i.e. to cure oneself of mental sickness. A very powerful way to obtain, maintain and improve mental health is meditation. Through meditation, one gets to really know oneself, gets to really take charge of oneself, and gets to really see for oneself what is good and what is bad in life, right and wrong in behavior.


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September 28, 2009

9:41 PM

The concepts of life, consciousness and volition are central to any ethical claim or system



The term ‘deontology’ may be taken to refer to the theoretical study and foundation of ethics, without initial preference for any particular ethical system; another term for this is ‘meta-ethics’. This philosophical discipline is concerned with the form, rather than the content of ethics – how ethical systems are structured, the logical forms and arguments used in them, how standards or norms might be first established (‘axiology’), and indeed all ontological and epistemological issues relative to ethical judgment.

Deontology will, for instance, emphasize that the concepts of life, consciousness and volition are central to any ethical claim or system.

  • Ethical discourse can only concern living beings. Inanimate entities (e.g. a table or a molecule) have nothing to lose – for their defining boundaries are fluid and arbitrarily set. We may break a diamond or disintegrate it – but ‘it’ has lost nothing. Living beings, on the other hand, have things to lose – their limb and life, which may be harmed or destroyed. A microbe is not just a mix of matter; kill it, and the matter remains but it no longer behaves as a living cell.
  • Ethical discourse is of no use to unconscious organisms, since they have no way to gain knowledge of it. We do consider that some things are conducive and others are detrimental to plants or microbes – but knowledge of such things concerns us, not the plants or microbes. Such knowledge tells us humans how to cultivate them, presumably so as to eat them or otherwise use them – so it is really a subset of human ethics. Animals can acquire knowledge of sorts, and so may conceivably learn facts or behavior (e.g. from their parents) that protects and furthers their life.
  • Ethical discourse presupposes volition. If the conscious organism has no volition, no ethical proposition concerning it is meaningful – since it can do nothing other than whatever it happens to be doing in the circumstances concerned anyway! Ethics is for organisms with freewill, meaning humans and higher animals.

Ultimately, of course, ethics is the prerogative of humans – who are not only alive and conscious and volitional, but moreover able to reason about ethics in general, to formulate and understand particular ethical propositions, and to monitor and manage their own behavior systematically. There is no point researching and writing an ethics, if the subject of it is unable to read it or follow it.

Imperatives, prohibitions, permissions and exemptions – all such statements, whatever their specific contents, logically presuppose an acceptance that the subject has some rationality and free will . It is absurd (self-contradictory) to make or imply statements like: “don’t refer to the concepts of consciousness or volition in your discourse” – since to say “do not” implies one has awareness and choice.

Of course, volition is something very hard to fully define and prove, because it is – like consciousness and like feelings – a primary object of experience. It is not like something else, to which it might be compared and reduced; it is something sui generis, a basic building block of experience. There is no logical basis for excluding volition from the realm of existence, just because it cannot be entirely described in terms of material or mental phenomena. It suffices to point out that it is something we experience distinctively (through ‘self-knowledge’, ‘introspective intuition’ or ‘apperception’ – however we choose to call it). We do not, note well, merely conceive it as a generality – but distinctly experience particular acts of volition within us.

Most human propositions and reasoning about causality are really about volition and allied concepts. Although the world of nature, or causation, is of course of great daily concern to us – we are also all the time greatly involved in thinking about our place in that world and in society, as well as our inner world, and all such thought is essentially to do with volition and allied causal concepts, including ethical concepts.

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September 21, 2009

12:35 AM

Human will is free and yet capable of being influenced - that is, conditioned through consciousness



An important and complex concept in causal logic, and specifically in the logic of volition, is that of influence. This refers to the impact on one’s volitional act, before or while it occurs, of some cognized natural event(s) and/or other volition(s) by oneself or other agent(s). Note well, the agent of volition concerned must have cognized the natural event(s) and/or other volition(s) in question, for the latter to count as ‘influences’. The distinguishing characteristic of influence, compared to other ‘conditions’ surrounding volition, is the intermediary of consciousness.

The philosophical importance of this concept is due to the confusion of most people relative to the concept of freedom of the will. On the one hand, most people in practice believe the will is free somehow; on the other hand, they realize it is varyingly affected by surrounding natural events and persons. These givens seem theoretically irreconcilable because the latter is mistaken for conditioning or partial causation, whereas it is influence, a different, subtler sort of causality.

For example: a man’s muscles are conditions affecting his volitions, in that he can in fact lift a certain weight with them and also in that he cannot lift more weight than they physically make possible; these same muscles however become influences on his volitions, only when thinking of their supposed limited strength he chooses another course than he would if they seemed stronger or weaker. Note well the subtle difference. Conditions and influences both affect actions, but not in comparable ways.

Influence is a special kind of conditioning, differing from an ordinary condition in that it operates specifically through the medium of consciousness, i.e. of any kind of cognitive process. The influencing object is one that has been sensed or imagined, perceived or conceived, remembered or projected, found evident or inferred, induced or deduced, or in any way thought about. What it influences, strictly speaking, is the Subject of such cognitions or thoughts, i.e. the eventual Agent of volition. When the agent finally ‘makes up his mind’ and wills something, he does so either in the direction of or against the tendency implied by the influence at hand.

Thus, influences imply positive or negative tendencies, temptations or spurs to voluntary action. If such tendency was in the direction of the eventual will, the will was facilitated by it; if such tendency was against the eventual will, the will had to overcome it.  The agent is always free to accept or refuse to ‘follow’ a given influence, i.e. to ‘yield’ to its weight or ‘resist’ it.

The concept of effort refers to a degree of will. Volition is not an either-or proposition, something one switches on or off; it has degrees. Powerful will is required to overcome strong opposing influences; a weak agent is easily influenced to go against his will. Thus, we may speak of amount of effort involved in an act of will. If influences are favorable, the effort required to complete them is comparatively minimal. If influences are counteractive, the agent must pump proportionately more effort to get his way.

We may also view effort as a measure of the agent’s responsibility, his causal contribution or ownership of the action and its outcomes. The more effort he requires, the more wholly ‘his own’ they are. The less effort he requires, the greater the part played in them by surrounding influences.

The postulate of freedom of the will is that an influence is never alone sufficient to produce some effect, irrespective of the will of the agent concerned. Granting surrounding conditions allow the power of will in a given case, the agent always has ‘final say’ to resist the tendency implied by the influence, though such resistance might require a maximum of effort. As of when conditioning occurs via consciousness, i.e. in the way of influence, necessity does not apply, though the effort required to overcome influence may be daunting. Wherever necessity does apply, one cannot say that there was possibility of will, nor therefore speak of influence. The subject was simply overwhelmed, proving in this case to be not an agent but a mere patient. He may have been an observer of the events, but he was in this case a passive recipient of natural forces.

If this postulate is correct, it means that consciousness of an object cannot by itself move a spiritual entity (soul, subject) to action, by way of complete causation. Though such consciousness may play a major causative part in the action, approaching one hundred percent, still the action cannot effectively occur without the final approval and participation of the spiritual entity concerned. If necessity is indeed observed occurring, then the conditioning involved was not via consciousness of the object but directly due to the object.

Note that not only an influence cannot by itself ever move an agent into action, but also – granting the possibility of pure whim – the agent can well move himself in the absence of any influences. Therefore, influence is neither sufficient nor necessary for volition.

Thus, note well, we are not here involved in verbal manipulations. Freedom of the will is a thesis, a hypothesis, concerning the causal relations possible in the domain of the spirit. Consciousness may well occur in cases where there is no volition, i.e. where causation (necessity) takes over; but when this happens, consciousness has played no part in the effect. Consciousness becomes a condition only as of when causation recedes, and a space is leftover for volition to intervene; in that event, consciousness (or its objects, through it) becomes influential, and the will remains free (to at least some extent).

All volition seems subject to some influences to some degree. This seems evident of human volition, which usually occurs in response to an apparent mental and material context, though it could be argued to be at times indifferent to all influences. Other animals, likewise, and perhaps much more so, have powers of volition subject to influence.
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September 11, 2009

3:18 AM

Clarifying the relation between the concepts of necessary causation, inertial causation and volition




In natural causality or determinism, we must distinguish between necessary causation and inertial causation.

Our understanding of the term ‘nature’ refers primarily to necessary relations, such that no matter what else happens in the world, that particular sequence of two things is bound to happen, i.e. once the one arises, the other is bound to also arise. The specifics may vary from case to case, with regard to time (the sequence may be simultaneous or at a set time after or some time later), place (here, there) and other respects; but the correlation is inflexible. Most of the causative events in the world proceed thus, relentlessly, as inevitable and invariable courses of events that no other natural event and all the more no volition (or at least no human or animal volition) can prevent or in any way deviate. For example, the Sun’s evolution and trajectory are de facto out of our power to interfere with.

On the other hand, it seems, some causative sequences are avoidable or subject to volitional manipulation. Such natural courses of events may be characterized as inertial. They are strictly speaking conditional causation, i.e. sequences that are bound to occur provided no volitional (human or animal – or eventually Divine) intervention occurs. For example, the river Nile would have continued to flood over yearly, had people not built a dam at Aswan. Or again, closer to home, my breath continues rhythmically, if I do not willfully hold it or change its rhythm.

Thus, whereas the concept of necessary nature concerns causation alone, the concept of inertial nature refers to an interface between causation and volition. When volition does intervene in the course of nature, we say that an artificial event has replaced the inertial event. The artificial event is of course ‘natural’ in a larger sense – a natural potential; but it is a potential that will never actualize without volitional intervention. For example, a piece of clay will never become a pot by mere erosion.

We would express causation in formal terms as (in its strongest determination): “If X occurs, then Y occurs; and if X does not occur, then Y does not occur”. Weaker relations are definable with reference to compounds, replacing ‘X’ by ‘X1 and X2 and X3...’ and ‘Y’ by ‘Y1 or Y2 or Y3...’ as the case may be.

When volition interferes, simply one of the causal factors – be it the whole ‘X’ (as rarely happens) or a part ‘X1’ – refers to the volitional act, and the rest ‘X2’, ‘X3’, etc. (if any) constitutes natural ingredients and forces, and the effect is an artificial event ‘Y’. In such cases, the conditional “if X, then Y” or “if X1, plus X2 etc., then Y” is operative.

When volition abstains, the preceding volitional causal factor is negated, i.e. ‘not X’ or ‘not X1’ is true, and natural causal factors come to the fore, i.e. ‘X2’ etc., resulting in an inertial event, ‘not Y’. In such case, the conditional “if not X, then not Y” or “if notX1, plus X2 etc., then not Y” is operative.

Thus, there is nothing antinomian about causative relations involving volition at some stage. The event willed, once willed, acts like any other causative, complete or partial, necessary or contingent, within the causative complex concerned. The only difference being that this causative did not emerge from natural processes, but from volition.

It should be noted that volition, unlike causation, is not (or rather, not entirely) formally definable with reference to conditional propositions. That is the main difficulty in the concept of volition, which has baffled so many philosophers.

Note that the dividing line between necessity and inertia may shift over time. Some feats are de facto out of our power one day, and later become feasible (for example, walking on the moon was until recently in fact impossible). Or the opposite may occur: something at first possible to us becomes impossible at a later time (for example, certain damages to the brain make the victim lose many cognitive and motor powers). Necessity may be permanent or temporary, acquired or lost; and so with inertia.

The ‘not yet possible’ is so due to time-constraints: there may be physical, psychological or cognitive/intellectual impediments to overcome before the necessary factors can be lined up; once it occurs or is brought about, we admit it as having always been possible ‘in principle’ though not immediately. The ‘no longer possible’ is so due to the irreversible destruction of some faculty or the erection of some impassable barrier, or to lost opportunity; what was previously possible, since the beginning of or during the existence of the entity or entities concerned, has become impossible. Thus, what is causative necessity at one time may be mere inertia at another, and vice versa.

Also, of course, the powers of different individuals of a given species, or of different species, differ. Consequently, what is necessity relative to one individual or species, is mere inertia to another; and vice versa. Nevertheless, at any given time and place, we can state as absolute principle either that no human or animal is in fact capable of affecting a certain natural course of events (so that that course is necessary), or that some specified individuals of some specified group have the volitional power to do so if they so choose (so that the course is inertial). The same distinction between necessity and inertia can be used to harmonize our assumptions of God’s all-powerful volition and of causation in nature.

With regard to the epistemological underpinning of the above ontological statements, it should be stressed that our knowledge of causation is inductively acquired.


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August 30, 2009

8:03 AM

Two important criticisms of the Buddhist notion of non-self



I think it is very important to realize that all Buddhist accounts (at least all those I have encountered) of how an illusion of selfhood might conceivably be constructed by a non-person fail to avoid begging the question. A theory is required, which answers all possible questions, before such a revolutionary idea as that of denial of real self in man can be posited with confidence; and no theory without holes or inconsistencies has to my knowledge been proposed. We may readily admit the existence of an illusory self (or ‘ego’), constructed and suffered by a stupid or misguided real self. But an aberration or delusion with no one constructing it or subject to it, seems like an absurd concept to me. It implies mere happenstance, determinism, without any consciousness, volition, values or responsibility.

Indeed, if you examine attempted such theories they always (overtly or covertly) describe an effective person (the pronoun ‘he’) constructing a false self. They never manage to escape from the sentence structure with a personal subject; typically: ‘he gradually deludes himself into thinking he has a self’. They do not provide a credibly detailed and consistent scenario of how unconscious and impersonal elements and processes (Nagarjuna’s “characteristics”) could possibly aggregate into something that has the impression (however false) it is someone! A machine (or robot with artificial intelligence) may ‘detect’ things (for us) but it has no consciousness; it may ‘do’ things (for us) but it has no volition; it may loudly proclaim ‘I’ but it has no soul.

There is also to consider the reverse process of deconstruction, how an ultimately impersonal artificial self (non-self) would or could go about freeing itself from illusion. Why would a non-self have any problem with remaining deluded (assuming it could be), and how if it has no personal powers would it intelligently choose to put in motion the prescribed process of liberation from delusion. A simple sentence like ‘to realize you have no self, make an effort to meditate daily’ is already a contradiction in terms, in my view.




With regard to the identification of the self with an illusion of consciousness, which is found in some Buddhist texts and becoming more popular in the West today, it seems to me that a misuse of the term ‘consciousness’ is involved. Consciousness is not, as they seem to suggest, a sort of stuff, which can become ‘delusive’. The substance of ‘mind’ (in a large sense, i.e. all of the psyche) is two-fold, in my view, comprising the stuff of soul (spirit) and that of mental projections (memories, imaginations, and the like – the ‘mind’ in a more restricted sense). As for consciousness, it is a relation, between two terms, one called the subject (any soul) and the other called the object (be it spirit, mind or matter).

Consciousness has no consciousness of its own. The relation it constitutes is unequal, involving at one end something cognized and at the other end something cognizing. The former exists at least as appearance; the latter ‘apprehends’ or ‘comprehends’ this appearance as an ‘experience’ or an ‘abstraction from experience’. Consciousness is never the subject of the relation of consciousness; it is usually the relation, and occasionally (in the case ‘self-consciousness’, which is a misnomer because it is the soul that is conscious of its consciousness; i.e. one instance of consciousness by the soul turned on another instance of consciousness by the soul) additionally the object. Consciousness or awareness is a function of the soul (subject), and not identical with it. Consciousness may have as its object contents of mind, but that does not make the two the same.

Buddhist philosophers and their modern imitators tend to blur the distinction between the three terms: soul, consciousness and mind. This tacit equation or ambiguity serves to give certain of their pronouncements a semblance of psychological and philosophical depth and consistency. For it allows us to assume one meaning or the other as convenient to the context, without having to systematically harmonize the different meanings. From a formal logic point of view, this is a common expedient to conceal a breach of syllogistic rules – in particular the ‘fallacy of four terms’. Thanks to an ambiguity, predicates applicable to one subject are illicitly passed over to another. Such a ‘fuzzy logic’ approach is lazy (if not dishonest), and in the long run obstructs knowledge development in this field. We must admit that three terms are used because we are dealing with three distinct objects. It is not arbitrary hair-splitting, but objective precision. 

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August 23, 2009

12:53 PM

We cannot experience something negative without first thinking about the corresponding positive



Negation is a pillar of both deductive and inductive logic, and requires careful analysis. We have to realize that negative terms are fundamentally distinct from positive ones, if we are to begin fathoming the nature of logic. The following observation seems to me crucial for such an analysis:

We can experience something positive without having first experienced (or thought about) its negation, but we cannot experience something negative without first thinking about (and therefore previously having somewhat experienced) the corresponding positive.

a.         Cognition at its simplest is perception. Our perceptions are always of positive particulars. The contents of our most basic cognitions are phenomenal sights, sounds, smells, tastes, and touch and other bodily sensations that seemingly arise through our sense organs interactions with matter – or mental equivalents of these phenomena that seemingly arise through memory of sensory experiences, or in imaginary recombinations of such supposed memories.

A positive particular can be experienced directly and passively. We can just sit back, as it were, and receptively observe whatever happens to come in our field of vision or hearing, etc. This is what we do in meditation. We do not have to actively think of (remember or visualize or conceptualize) something else in order to have such a positive experience. Of course, such observation may well in practice be complicated by thoughts (preverbal or verbal) – but it is possible in some cases to have a pure experience. This must logically be admitted, if concepts are to be based on percepts.

b.         In the case of negative particulars, the situation is radically different. A negative particular has no specific phenomenal content, but is entirely defined by the ‘absence’ of the phenomenal contents that constitute some positive particular. If I look into my material or mental surroundings, I will always see present phenomena. The absence of some phenomenon is only noticeable if we first think of that positive phenomenon, and wonder whether it is present.

It is accurate to say that our finding it absent reflects an empirical truth or fact – but it is a fact that we simply would not notice the negative without having first thought of the positive. Negative knowledge is thus necessarily (by logical necessity) more indirect and active. It remains (at its best) perfectly grounded in experience – but such negative experience requires a rational process (whether verbal or otherwise).

To experience a negative, I must first imagine (remember or invent) a certain positive experience; then I must look out and see (or hear or whatever) whether or not this image matches my current experience; and only then (if it indeed happens not to) can I conclude to have “experienced” a negative.

Thinking about X may be considered as positioning oneself into a vantage point from which one can (in a manner of speaking) experience not-X. If one does not first place one’s attention on X, one cannot possibly experience the negation of X. One may well experience all sorts of weird and wonderful things, but not specifically not-X.

From this reflection, we may say that whereas affirmatives can be experienced, negatives are inherently rational acts (involving imagination, experience and intention). A negative necessarily involves thought: the thought of the corresponding positive (the imaginative element), the testing of its presence or absence (the experiential element) and the rational conclusion of “negation” (the intentional element).

c.         The negation process may involve words, though it does not have to.

Suppose I have some momentary experience of sights, sounds, etc. and label this positive particular “X”. The content of consciousness on which I base the term X is a specific set of positive phenomenal experiences, i.e. physical and/or mental percepts. Whenever I can speak of this X, I mentally intend an object of a certain color and shape that moves around in certain ways, emitting certain sounds, etc.

Quite different is the negation of such a simple term, “not X”. The latter is not definable by any specific percepts – it refers to no perceptible qualities. It cannot be identified with the positive phenomena that happen to be present in the absence of those constituting X. Thus, strictly speaking, not-X is only definable by ‘negation’ of X.

Note well, it would not be accurate to say (except ex post facto) that not-X refers to all experiences other than X (such as Y, Z, A, B, etc.), because when I look for X here and now and fail to find it, I am only referring to present experience within my current range and not to all possible such experiences. We would not label a situation devoid of X as “not X” without thinking of X; instead, we would label that situation in a positive manner (as “Y”, or “Z”, or whatever).

Thus, we can name (or wordlessly think of) something concrete “X”, after experiencing phenomena that constitute it; but in the case of “not-X”, we necessarily conjure the name (or a wordless thought) of it before we experience it.

“Not-X” is thus already a concept rather than a percept, even in cases where “X” refers to a mere percept (and all the more so when “X” itself involves some abstraction – as it usually does). The concept “not X” is hypothetically constructed first and then confirmed by the attempted and failed re-experience of X.

In short, negation – even at the most perceptual level – involves an adductive process. It is never a mere experience. A negative term never intends the simple perception of some negative thing, but consists of a hypothesis with some perceptual confirmation. Negation is always conceptual as well as perceptual in status.

A theory cannot be refuted before it is formulated – similarly, X cannot be found absent unless we first think of X.


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