All the books posted in The Logician Website are now on sale as quality hardbacks, paperbacks or eBooks in various outlets.

In the CreateSpace store , paperbacks, and in the Kindle store, the corresponding .mobi e-books. Or just go to, where there’s often a discount.

In store, hardbacks (for the six largest books), as well as paperbacks and .epub e-books.





of the works by Avi Sion

posted in The Logician website


All the books posted in The Logician Website are now on sale as quality hardbacks, paperbacks or eBooks in various outlets.

In the CreateSpace store , paperbacks, and in the Kindle store, the corresponding .mobi e-books. Or just go to, where there’s often a discount.

In store, hardbacks (for the six largest books), as well as paperbacks and .epub e-books.



Future Logic FUTURE LOGIC: Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional, and Logical Modalities. (1990, revised 1996)

Future Logic is an original, and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities. Traditional and Modern logic have covered in detail only formal deduction from actual categoricals, or from logical conditionals (conjunctives, hypotheticals, and disjunctives). Deduction from modal categoricals has also been considered, though very vaguely and roughly; whereas deduction from natural, temporal and extensional forms of conditioning has been all but totally ignored. As for induction, apart from the elucidation of adductive processes (the scientific method), almost no formal work has been done.

This is the first work ever to strictly formalize the inductive processes of generalization and particularization, through the novel methods of factorial analysis, factor selection and formula revision.  This is the first work ever to develop a formal logic of the natural, temporal and extensional types of conditioning (as distinct from logical conditioning), including their production from modal categorical premises.

Future Logic contains a great many other new discoveries, organized into a unified, consistent and empirical system, with precise definitions of the various categories and types of modality (including logical modality), and full awareness of the epistemological and ontological issues involved. Though strictly formal, it uses ordinary language, wherever symbols can be avoided. Among its other contributions:  a full list of the valid modal syllogisms (which is more restrictive than previous lists); the main formalities of the logic of change (which introduces a dynamic instead of merely static approach to classification); the first formal definitions of the modal types of causality; a new theory of class logic, free of the Russell Paradox; as well as a critical review of modern metalogic. But it is impossible to list briefly all the innovations in logical science — and therefore, epistemology and ontology — this book presents; it has to be read for its scope to be appreciated.


PhenomenologyPHENOMENOLOGY: Basing Knowledge On Appearance. (2003; expanded 2005)

Phenomenology is the study of appearance as such. It is a branch of both Ontology and Epistemology, since appearing is being known. By an ‘appearance’ is meant any existent which impinges on consciousness, anything cognized, irrespective of any judgment as to whether it be ‘real’ or ‘illusory.’ The evaluation of a particular appearance as a reality or an illusion is a complex process, involving inductive and deductive logical principles and activities. Opinion has to earn the status of strict knowledge.

Knowledge develops from appearances, which may be: (a) objects of perception, i.e. concrete phenomena in the physical or mental domains; (b) objects of intuition, i.e. one’s subjective self, cognitions, volitions and valuations (non-phenomenal concretes); and/or (c) objects of conception, i.e. simple or complex abstracts of preceding appearances. Abstraction relies on apprehensions of sameness and difference between appearances (including received or projected appearances, and projected negations of appearances). Coherence in knowledge (perceptual, intuitive and conceptual) is maintained by apprehensions of compatibility or incompatibility. Words facilitate our construction of conceptual knowledge, thanks to their intentionality. The abstract concepts most words intend are common characters or behaviors of particulars (concrete material, mental or subjective experiences). Granting everything in the world is reducible to waves, ‘universals’ would be equalities or proportionalities in the measures of the features, motions and interrelations of particular waves. Such a theory of universals would elucidate sensation and memory.

In attempting to retrace the development of conceptual knowledge from experience, we may refer to certain major organizing principles. It is also important to keep track of the order of things in such development, interrelating specific concepts and specific experiences. By proposing a precise sequence of events, we avoid certain logical fallacies and are challenged to try and answer certain crucial questions in more detail. Many more topics are discussed in the present collection of essays, including selfhood, adduction and other logical issues, the status of mathematical concepts and theology.


Judaic LogicJUDAIC LOGIC:  A Formal Analysis of Biblical, Talmudic and Rabbinic Logic. (1995, Slatkine 1997)

Judaic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician. Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books of the Bible, and analyzing the methodology of the Talmud and other Rabbinic literature by means of formal tools which make possible its objective evaluation with reference to scientific logic. The result is a highly innovative work – incisive and open, free of clichés or manipulation.

Judaic Logic succeeds in translating vague and confusing interpretative principles and examples into formulas with the clarity and precision of Aristotelean syllogism. Among the positive outcomes, for logic in general, are a thorough listing, analysis and validation of the various forms of a-fortiori argument, as well as a clarification of dialectic logic. However, on the negative side, this demystification of Talmudic/Rabbinic modes of thought (hermeneutic and heuristic) reveals most of them to be, contrary to the boasts of orthodox commentators, far from deductive and certain. They are often, legitimately enough, inductive. But they are also often unnatural and arbitrary constructs, supported by unverifiable claims and fallacious techniques.

Many other thought-processes, used but not noticed or discussed by the Rabbis, are identified in this treatise, and subjected to logical review. Various more or less explicit Rabbinic doctrines, which have logical significance, are also examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its universal aspects and its peculiarities. With regard to Biblical studies, one notable finding is an explicit formulation (which, however, the Rabbis failed to take note of and stress) of the principles of adduction[2] in the Torah, written long before the acknowledgement of these principles in Western philosophy and their assimilation in a developed theory of knowledge. Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish Bible) contains a lot more than ten instances of qal vachomer (a-fortiori) reasoning.

In sum, Judaic Logic elucidates and evaluates the epistemological assumptions which have generated the Halakhah (Jewish religious jurisprudence) and allied doctrines. Traditional justifications, or rationalizations, concerning Judaic law and belief, are carefully dissected and weighed at the level of logical process and structure, without concern for content. This foundational approach, devoid of any critical or supportive bias, clears the way for a timely reassessment of orthodox Judaism (and incidentally, other religious systems, by means of analogies or contrasts). Judaic Logic ought, therefore, to be read by all Halakhists, as well as Bible and Talmud scholars and students; and also by everyone interested in the theory, practise and history of logic.  


Buddhist IllogicBUDDHIST ILLOGIC: A Critical Analysis of Nagarjuna’s Arguments. (2002)

The 2nd Century CE Indian philosopher Nagarjuna founded the Madhyamika (Middle Way) school of Mahayana Buddhism, which strongly influenced Chinese, Korean and Japanese (Ch’an or Zen) Buddhism, as well as Tibetan Buddhism. Nagarjuna is regarded by many Buddhist writers to this day as a very important philosopher, who they claim definitively proved the futility of ordinary human cognitive means. His writings include a series of arguments purporting to show the illogic of logic, the absurdity of reason. He considers this the way to verbalize and justify the Buddhist doctrine of “emptiness” (Shunyata). These arguments attack some of the basic tenets and techniques of reasoning, such as the laws of thought (identity, non-contradiction and the excluded middle), conceptualization and predication, our common assumptions of self, entities and essences, as well as our beliefs in motion and causation.

The present essay demonstrates the many sophistries involved in Nagarjuna’s arguments. He uses double standards, applying or ignoring the laws of thought and other norms as convenient to his goals; he manipulates his readers, by giving seemingly logical form (like the dilemma) to his discourse, while in fact engaged in non-sequiturs or appealing to doubtful premises; he plays with words, relying on unclear terminology, misleading equivocations and unfair fixations of meaning; and he ‘steals concepts’, using them to deny the very percepts on which they are based. Although a critique of the Madhyamika philosophical interpretation and defense of “emptiness”, Buddhist Illogic is not intended to dissuade readers from Buddhism. On the contrary, its aim to enhance personal awareness of actual cognitive processes, and so improve meditation. It is also an excellent primer on phenomenological epistemology.


The Logic of CausationCausal Logic: THE LOGIC OF CAUSATION: Definition, Induction and Deduction of Deterministic Causality. (1st ed. 1999, 2nd ed. 2003, 3rd ed. 2010)

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) – but 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.


Volition and Allied Causal ConceptsCausal Logic: VOLITION AND ALLIED CAUSAL CONCEPTS. (2004

Volition and Allied Causal Concepts is a work of aetiology and metapsychology. Aetiology is the branch of philosophy and logic devoted to the study of causality (the cause-effect relation) in all its forms; and metapsychology is the study of the basic concepts common to all psychological discourse, most of which are causal.

Volition (or free will) is to be distinguished from causation and natural spontaneity. The latter categories, i.e. deterministic causality and its negation, have been treated in a separate work, The Logic of Causation. Volition may be characterized as personal causality, a relation between an agent (the self or soul) and his actions (acts of will). Unlike causation, this relation cannot be entirely defined using conditional (if–then) propositions. Although we can say that the agent is a sine qua non of his actions, we cannot say that the agent is invariably (in all or specific circumstances) followed by his actions. It appears that both an act of will and its negation remain possible to a soul in any given set of circumstances. This defines freedom of the will, and implies the responsibility of the agent for his actions. Introspection provides knowledge of particular acts of will.

The existence of freewill implies a distinction between necessary causation (determinism independent of volition) and inertial causation (determinism, except when some contrary will interferes). An act of will occurs on a spiritual plane. It may have natural (mental or physical) consequences; those that inevitably follow it may be regarded as directly willed, whereas those that vary according to circumstances must be considered indirectly willed. Volition presupposes some degree of consciousness. So-called involuntary acts of will involve a minimum of attention, whereas mindful acts are fully conscious. Even pure whim involves intention. Most volitions moreover involve valuation, some sort of projection of goals, deliberation on means, choice and decision. To judge responsibility, various distinctions are called for, like that between intentional, incidental and accidental consequences.

Volitional action can be affected through the terms and conditions of the world surrounding its agent, but also more intimately through the influence of concrete or abstract aspects of that world that the subject has cognized. The causal concept of influence, and its implication of cognition (of inner or outer information, including emotions), are crucial to measuring the effort involved in volition. Influences make willing easier or harder, yet do not curtail its essential freedom. All the causal concepts used in psychological explanation – affections, appetites, instincts, habits, obsessions, compulsions, urges and impulses – can be elucidated thanks to this important finding. Much of human (and animal) behavior can thus be both acknowledged as volitional and as variously influenced.

Volition and Allied Causal Concepts is a work of ambitious scope, intent on finally resolving philosophical and logical issues that have always impeded progress in psychology. It clarifies the structure and workings of the psyche, facilitating hygienic and therapeutic endeavors. The relation between volition and physical laws is discussed, as is the place of volition in biology. Concepts used in biology, analogous to that of purpose, are incidentally analyzed. Theological issues are also dealt with, as are some topics in ethics and law.


RuminationsRUMINATIONS: Sundry notes and essays on Logic. (2005)

Ruminations  is a collection of sundry notes and essays on Logic. These complement and enrich the author’s past writings, further analyzing or reviewing certain issues. Among the many topics covered are: the importance of the laws of thought, and how they are applied using the logic of paradox; details of formal logic, including some important new insights on the nesting, merger and splitting up of hypothetical propositions; details of causal logic, including analogical reasoning from cause to cause; a phenomenological analysis of negation

Additionally, this volume is used to publish a number of notes and essays previously only posted in the Internet site, including: a thoroughly revised version of an essay on J.S. Mill’s Methods; various addenda and diagrams for Judaic Logic, as well as a historical essay; a brief analysis of Islamic logic.


MeditationsMEDITATIONS: A Spiritual Logbook. (2006)

A meditation is a voluntary exercise intended to increase awareness, sustained over some time.  The main purpose of the present Meditations is to inspire and assist readers to practice meditation of some sort, and in particular ‘sitting meditation’. This includes practices such as: observing the mechanisms of one’s thinking, stopping unnecessary thought, forgetting things about one’s self and one’s life that are irrelevant to the current effort of meditation, dealing with distractions, becoming aware of one’s breath, being here and now. 

After such practice for some time, one gets to realize the value of meditation, and one’s commitment to it grows. The need for behavioral improvement becomes more and more obvious, and one finds it easy and natural to put more discipline into one’s life. Various recommendations are given in this regard.  Prior to such practical guidance, so as to prepare the reader for it, the book reviews the theoretical teachings relating to meditation in the main traditions of mankind. The ultimate goals of meditation, the various methods or techniques used to achieve them, the experiential results of meditation, and the interpretations given to them, are topics treated here.   


Logical and Spiritual ReflectionsLOGICAL AND SPIRITUAL REFLECTIONS. (2008)



A collection of shorter philosophical works, in two parts.  

The first part, consisting of Logical Reflections, includes:

Hume’s Problems with Induction, which is intended to describe and refute some of the main doubts and objections David Hume raised with regard to inductive reasoning. It replaces the so-called problem of induction with a principle of induction. David Hume’s notorious skepticism was based on errors of observation and reasoning, with regard to induction, causation, necessity, the self and freewill. These are here pointed out and critically analyzed in detail – and more accurate and logical theories are proposed. The present work also includes refutations of Hempel’s and Goodman’s alleged paradoxes of induction.

A Short Critique of Kant’s Unreason, which is a brief critical analysis of some of the salient epistemological and ontological ideas and theses in Immanuel Kant’s famous Critique of Pure Reason. It shows that Kant was in no position to criticize reason, because he neither sufficiently understood its workings nor had the logical tools needed for the task. Kant’s transcendental reality, his analytic-synthetic dichotomy, his views on experience and concept formation, and on the forms of sensibility (space and time) and understanding (his twelve categories), are here all subjected to rigorous logical evaluation and found deeply flawed – and more coherent theories are proposed in their stead.

In Defense of Aristotle’s Laws of Thought, which addresses, from a phenomenological standpoint, numerous modern and Buddhist objections and misconceptions regarding the basic principles of Aristotelian logic. Many people seem to be attacking Aristotle’s Laws of Thought nowadays, some coming from the West and some from the East. It is important to review and refute such ideas as they arise.

The second part, consisting of Spiritual Reflections, includes:

More Meditations, which is a sequel to the author’s earlier work, Meditations. It proposes additional practical methods and theoretical insights relating to meditation and Buddhism. It also discusses certain often glossed over issues relating to Buddhism – notably, historicity, idolatry, messianism, importation to the West.

Zen Judaism, which is a frank reflection on the tensions between reason and faith in today’s context of knowledge, and on the need to inject Zen-like meditation into Judaism. This work also treats some issues in ethics and theodicy.

No to Sodom, which is an essay against homosexuality, using biological, psychological, spiritual, ethical and political arguments.


A Fortiori Logic A Fortiori Logic: Innovations, History and Assessments. (2013)

A Fortiori Logic: Innovations, History and Assessments 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.


Other Writings


This module includes four ‘thematic compilations’ (2008-9). These bring together essays relevant to their title topic drawn from all of Avi Sion’s past works. They are:

The Laws of Thought is an exploration of the deductive and inductive foundations of rational thought. The author here clarifies and defends Aristotle’s Three Laws of Thought – and introduces a Fourth Law of Thought implicit in and crucial to them, viz. the Principle of Induction.

Ethics is a collection of thoughts on the method, form and content of Ethics.

The Self is an inquiry into the concepts of self, soul, person, ego, consciousness, psyche and mind – ranging over phenomenology, logic, epistemology, ontology, psychology, spirituality, meditation, ethics and metaphysics.

Theology is about God and Creation, or more precisely perhaps about our ideas of them, how they are formed and somewhat justified, although it is stressed that they can be neither proved nor disproved.

Also displayed here are various notes and essays in English and French. Previews and other temporary postings, .pdf files for download, etc.




All the books posted in The Logician Website are now on sale as quality hardbacks, paperbacks or eBooks in various outlets.

In the CreateSpace store , paperbacks, and in the Kindle store, the corresponding .mobi e-books. Or just go to, where there’s often a discount.

In store, hardbacks (for the six largest books), as well as paperbacks and .epub e-books.