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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
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
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
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
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.
To purchase the book, go to: http://stores.lulu.com/thelogicianbooks
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.
To purchase the book, go to: http://stores.lulu.com/thelogicianbooks
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.
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.
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).
Fourth post in the ongoing series on important innovations in logic theory to be found in my works.
“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.
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.
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.
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
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.
All M can be P (or nonP)
All/This/Some S can (or must) be M
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.
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.
Extract from VOLITION AND ALLIED CAUSAL CONCEPTS, CHAPTER 17.
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.
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.
Extract from VOLITION AND ALLIED CAUSAL CONCEPTS, CHAPTER 5.
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 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).
Extract from VOLITION AND ALLIED CAUSAL CONCEPTS, CHAPTER 2.
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
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.
Extract from BUDDHIST ILOGIC, CHAPTER 11.
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.
Extract from VOLITION AND ALLIED CAUSAL CONCEPTS, CHAPTER 7.
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.
Extract from: RUMINATIONS, CHAPTER 9.
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.
Extract from: HUME'S PROBLEMS WITH INDUCTION, CHAPTER 2.
There is an all-important principle of logic and more broadly of epistemology, which we may simply call the principle of induction (in opposition to the so-called problem of induction attributed to Hume) and formulate as follows: given any appearance, we may take it to be real, until and unless it is found to be illusory.
This is the fundamental principle of inductive logic, from which all others derive both their form and their content. And indeed, this is the way all human beings function in practice (with the rare exception of some people, like Hume, who want to seem cleverer than their peers). It is, together with Aristotle’s three laws of thought, the supreme principle of methodology, for both ordinary and scientific thought, whatever the domain under investigation.
Indeed, we could construe this principle of induction as the fourth law of thought. Just as the three laws proposed by Aristotle are really three facets of one and the same law, so also this fourth law should be viewed as implicit in the other three. Induction being the most pragmatic aspect of logic, this principle is the most practical of the foundations of rational discourse.
The principle of induction is a phenomenological truth, because it does not presume at the outset that the givens of appearance are real or illusory, material or mental, full or empty, or what have you. It is a perfectly neutral principle, without prejudice as to the eventual content of experience and rational knowledge. It is not a particular worldview, not an a priori assumption of content for knowledge.
However, in a second phase, upon reflection, the same principle favors the option of reality over that of illusion as a working hypothesis. This inbuilt bias is not only useful, but moreover (and that is very important for skeptics to realize) logically rock solid, as the following reasoning clearly shows:
This principle is self-evident, because its denial is self-contradictory. If someone says that all appearance is illusory, i.e. not real, which means that all our alleged knowledge is false, and not true, that person is laying claim to some knowledge of reality (viz. the knowledge that all is unreal, unknowable) – and thus contradicting himself. It follows that we can only be consistent by admitting that we are indeed capable of knowing some things (which does not mean everything).
It follows that the initial logical neutrality of appearance must be reinterpreted as in all cases an initial reality that may be demoted to the status of illusion if (and only if) specific reasons justify it. Reality is the default characterization, which is sometimes found illusory. Knowledge is essentially realistic, though in exceptional cases it is found to be unrealistic. Such occasional discoveries of error are also knowledge, note well; they are not over and above it.
If we did not adopt this position, that appearance is biased towards reality rather than illusion, we would be stuck in an inextricable agnosticism. Everything would be “maybe real, maybe illusory” without a way out. But such a problematic posture is itself a claim of knowledge, just like the claim that all is illusory, and so self-inconsistent too. It follows that the interpretation of appearance as reality until and unless otherwise proved is the only plausible alternative.
If appearance were not, ab initio at least, admitted as reality rather than as illusion or as problematic, we would be denying it or putting it in doubt without cause – and yet we would be granting this causeless denial or doubt the status of a primary truth that does not need to be justified. This would be an arbitrary and self-contradictory posture – an imposture posing as logical insight. All discourse must begin with some granted truth – and in that case, the most credible and consistent truth is the assumption of appearance as reality unless or until otherwise proved.
We may well later, ad terminatio (in the last analysis), conclude that our assumption that this appearance was real was erroneous, and reclassify it as illusory. This happens occasionally, when we come across conflicts between appearances (or our interpretations of them). In such cases, we have to review in detail the basis for each of the conflicting theses and then decide which of them is the most credible (in accord with numerous principles of adduction).
It should be stressed that this stage of reconciliation between conflicting appearances is not a consequence of adopting reality as the default value of appearances. It would occur even if we insisted on neutral appearances and refused all working hypotheses. Conflicts would still appear and we would still have to solve the problem they pose. In any case, never forget, the assumption of reality rather than illusion only occurs when and for so long as no contradiction results. Otherwise, contradictions would arise very frequently.
Extract from: A SHORT CRITIQUE OF KANT’S UNREASON, CHAPTER 4.
The phenomenological truth of human knowledge is exactly the reverse of how Kant views it: first we experience raw data, and then only do we mentally process the information so obtained. Raw experience is experience of the totality of the here and now within the immediate range of one’s consciousness. It is essentially pure of rational interference, though reason is quick to try sorting it out almost as soon as it occurs. Thus, experience is initially unitary and only in a second phase is it rationally made to explode into seeming multiplicity, with variations in space, time and circumstance.
This is a truth evident to anyone who has practiced meditation to the stage of contemplation. One is constantly in the here and now, even though the scenery around one changes continuously in various respects. In this cognitive posture, one is observing without comment of any sort (verbal or non-verbal). And indeed, even if thoughts do arise, they are viewed as just part of the scenery. The non-here and/or non-now are mental projections in the here and now; we here and now remember or imagine things beyond the here and now.
The self in fact always resides in the here and now, even if its attention is usually strongly drawn towards some place else and/or some other time. There seems to be a natural force (of varying intensity) pulling us away from the here and now, perhaps for biological reasons of survival. Nevertheless, through a contrary effort of stillness and silence, we can volitionally bring our awareness back in the here and now; and with much training this can become a habit.
Buddhist psychology has, in my view, well explained what it is that draws us out of the ‘here and now’ into the ‘there and/or then’. It is the pull and push of desire (and aversion). We cling to (or away from) some passing content of the ever unfolding here and now, and become absorbed by it. Our attention becomes locked onto it for a while, fed by and feeding memories and fantasies. To avoid this malady, it is necessary to practice non-attachment.
The content of raw experience is essentially a continuous field, not only at any given moment but also from moment to moment. The division of experience into moments is already a rational act; experience itself is one across time. More precisely, experience is only of the present, and any consideration of past (memory) or future (anticipation) is rational rather than experiential. We are always in the present, whose changing appearance is all part of the present. Mental impressions of memory or anticipation may float over more present-seeming appearances, but they must be regarded phenomenologically as in the present too, and only separated out of it by rational reflection.
Similarly, the imaginary cutting up of the visual and other phenomenal fields into distinct parts – and on a later, more abstract plane, the distinction between whole and parts of space as such – this is rational activity that comes after actual experience. Such rational acts presuppose phenomena to act on, and therefore must lag slightly behind the experiences they are applied to. Nevertheless, they do not necessarily rely on memory, because what we experience as “the present” is not an instant, but a moment of time – i.e. the present has a temporal extension, it is not a mere point in time.
Thus, it is we who mentally cut experience up and then bind it together, through various rational acts. These acts occur in the present, like all existing things and events. Before we can locate ‘parts’ of experience variously in space or time, or classify them together in any way, we must differentiate them from each other. For example, we may choose to consider visible blobs of colors as distinct things; thereafter we may regard these items as spatially or temporally separate, or this color and that one to be the same or at least similar (the same to some extent but differing in shade, say).
Extract from: HUME'S PROBLEMS WITH INDUCTION, CHAPTER 4.
The root of Hume’s problem with induction is perhaps his misconception as to what ideas are. I suggest that in his mind’s eye, ideas are clouds of ‘mental stuff’ produced by sensation. These perhaps very often look like the objects that generated our sensations, but we cannot be sure of that since we have no access to such objects other than through ideas. Thus, what we actually perceive and know are only ideas. Thus, ideas are veils that separate us from reality, rather than conduits to reality.
This view is, as already pointed out, self-defeating, since it accuses also itself of ignorance and error. However, the point I want to stress here is how ideas are reified in Hume’s discourse. Because he effectively visualized ideas as atoms of mental substance, his view of human knowledge as a whole was completely distorted.
In fact, an idea is something very abstract, an intention towards some object, a relation of pointing in a certain direction, directing our attention hither, rather than a substantial entity. An idea is an idea of an object. It has no existence apart from an object of some sort (although, of course, the object concerned need not be real, but may be illusory).
It is certainly true that the physical processes of sensation play a central role in our noetic relation to a domain beyond our apparent physical body. But it does not follow that what we perceive when we sense this ‘external world’ are sensations or even images of the world.
· The only coherent theory is that what we perceive is the world itself.
· The abstract concepts we form thereafter are not mere manipulations of concrete memories, but relations we intend to the objects initially perceived.
The fact that we perceive external objects, and not impressions or ideas of those objects, is certainly marvelous, so much so that we still cannot understand how that might happen. But our difficulty and failure to explain this marvel of nature is not a reason enough to deny its occurrence. That we perceive the world is obvious enough; how such a thing is possible is a distinct question, which we may never answer. Science does not normally deny the very existence of what it cannot thus far explain.
Note well, we can claim knowledge that we directly perceive the external world itself, without claiming to know yet just how we manage to do so. We know we can, because this is the only consistent theory we can posit, as already explained. But exactly what role the senses and brain play (other than memory production, storage and reactivation) in this evident direct perception is still an open question. The fact that a partial question remains does not invalidate the truth of the partial answer already obtained. There are many issues in the special sciences that remain unsolved to date – and we do not for that reason throw out the knowledge we already have.
It does not follow from such non-skeptical, objectivist theory of knowledge that perception or conception can never be erroneous. Errors in human knowledge are essentially conceptual, and it is the task of logic to minimize them. Perception sometimes seems wrong, after the fact, due to our noticing later percepts that seem to contradict the earlier. In such cases, we realize that in fact we drew some conceptual inference from the initial percepts, which the later percepts make clear was unjustified, and we correct our previous assumption. This is just an application of the laws of thought and the principle of induction to sorting out conflicting perceptions.
Once we comprehend human knowledge in this truly enlightened manner, it becomes clear why Hume was so confused and self-contradictory in his views of induction, and other logical and philosophical issues. If one starts with false premises, one is very likely to end up with false conclusions. He should have been more careful.
Philosophers like Hume have always found the idea that we might indeed be perceiving and conceiving the world out there, and not merely our impressions and ideas of it, difficult to comprehend or explain. This is understandable, because this seeming ability of ours (viz. external consciousness) is something truly surprising and, well, miraculous – no better word for it comes to mind.
But then these same philosophers take for granted that our inner perceptions and conceptions are valid and not in need of explanation. They apparently do not realize that this ability (viz. internal consciousness) is also miraculous – indeed, just as miraculous. For the difference between the two, after all, is just one of distance. And who is to say how big the soul (the subject of consciousness) is or where it is in fact located? Why do they assume that it is more ‘inside’ than ‘outside’ the apparent body?
In both cases, there is something marvelous, inexplicable – namely consciousness, a line of relation between an object and a subject. How can one existent (a soul, a spiritual entity) experience another (a mental or material phenomenon)? In the case of self-intuition, the subject and object are exceptionally one and the same. But even this is a marvelous event, that something can experience itself.
The mere fact of consciousness is the biggest mystery. In comparison to it, the issues of how far consciousness can go, and how in some instances it is aroused and made possible by sensation and yet the body does not block or distort our view – these are relatively minor issues.
Of course, a theory of the exact role of the senses remains highly desirable. Obviously, each sense organ (whether in humans or other animals) somehow gives the overall organism ‘access to’ a range of data of a specific sort, and no other: e.g. human eyes open the window to a range of light waves (the visible spectrum) but not to all frequencies (not to radio waves, ultraviolet rays or microwaves, for instances) and not to other modalities (such as sound or chemical signals). The different sense organs have evolved over millions of years (at different rates and in different directions in different organisms).
Without these sense organs, we would not (so it seems) be able to sense external reality. So their role is not only that of memory production, but they are somehow essential to the actual contact between the organism as Subject and material objects it perceives. Even so, to repeat, it cannot consistently be affirmed that what the Subject perceives are internal products of sensation. Nor is the explanation that sense organs serve to filter out some of external reality sufficient. The sense organs must have a more significant role in the Subject-Object interface. But what?