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March 22, 2018

4:24 PM

27 books by AVI SION published to date

I have to date published 27 titles over a period of some 28 years. These are listed below (omitting subtitles).





Future Logic

1990; rev. 1996


Judaic Logic

1995; Slatkine 1997


Buddhist Illogic






Volition and Allied Causal Concepts









Hume’s Problems with Induction



A Short Critique of Kant’s Unreason



In Defense of Aristotle’s Laws of Thought



More Meditations



Zen Judaism



No to Sodom



Logical and Spiritual Reflections (compendium)

2008; rev. 2009


The Logic of Causation

I: 1999-2000; II: 2003-05; III 2008-10


A Fortiori Logic



Logical Philosophy (compendium)



The Self (compilation)



Ethics (compilation)



Theology (compilation)



The Laws of Thought (compilation)

2008; exp. 2014


Paradoxes and Their Resolutions (compilation)



Logical Criticism of Buddhist Doctrines (compilation)



Inductive Logic (compilation)



Logic in the Torah (compilation)


LTal Logic in the Talmud (compilation) 2018


Exposing Fake Logicians



Of these 27 books, the following 11 are primary works: FL, JL, BI, Phe, Vol, Rum, Med, LSR, LC, AFL, Exp (note that LC was published in three phases). The following 6 are components of LSR: Hume, Kant, Arist, MM, ZJ, NtS. LP is a compendium including 5 works: BI, Phe, Vol, Rum, Med. The following 9 books are thematic compilations drawn from several primary works: Self, Eth, Theo, LoT, P&R, Budoc, IndL, LTor, LTal, plus some previously unpublished material.

These 27 works may all be read online, in various locations indicated here: avisionlinks.bravesites.com.

The may all be purchased in print and e-book forms at major online outlets. Notably: Amazon.com, Lulu.com, and others. More specifically, they are all available in paperback and e-book forms in these sales channels. Additionally, the 6 largest books, namely: FL, JL, LSR, LC, AFL, LP, are available in hardback form through Lulu.com (only).

If you need further information, contact the author-publisher at: avi-sion@thelogician.net.

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November 24, 2013

1:03 AM

My new book: A Fortiori Logic

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

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

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

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

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

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

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

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October 10, 2010

2:30 AM

Causative Syllogism

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

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

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

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

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

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

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

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

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

Q is a complete and contingent cause of R

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

Positive conclusion(s): mq abs

P is a complete and contingent cause of R

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

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

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

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

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


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

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

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


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September 7, 2010

12:47 AM

About Laws of Causation

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

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

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

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

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

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

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

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

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

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

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


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

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

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


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