Thursday, February 26, 2015


A Spiritual Logbook.

Avi Sion,  Ph. D.

First published, 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.

Buy it or read it online

All of Avi Sion’s published books can be purchased at (in paperback or kindle/.mobi form), and at (in hardcover, paperback or e-book/.epub form), as well as other online stores.

They can also be read online free of charge, chapter by chapter, at and, in '3D flipbook' format, at, as well as in Google Books and other Internet locations. They are also available in many university and public libraries.

Contents in brief

Part 1: Some Theoretical Considerations
Part 2: Understanding The Self
Part 3: Some Behavioral Disciplines
Part 4: Some Sitting Meditations

Contents in detail

  1. What is meditation?
  2. Thought and meditation
  3. The goals of meditation
  4. Theory and practice
  5. Interpretations
  6. The coexistence of the One and the many
  7. Methods and experiences

  1. The individual self in Monism
  2. The impression of self 
  3. Impermanence: the concept and the principle
  4. Not an essence, but an entity
  5. Distinguishing the ego
  6. Dismissing the ego
  7. Relief from suffering

  1. Taking up the challenge
  2. Face facts with equanimity
  3. Stop substance addictions
  4. Don’t stuff yourself silly
  5. Limit input from the media
  6. Forget your face
  7. Give up sensuality
  8. On “sexual liberation”
  9. Practice non-attachment

  1. Time, place and posture
  2. Observe the mechanisms of thought
  3. Stop unnecessary thinking
  4. Dealing with distractions
  5. Sitting forgetting
  6. Breath awareness
  7. Being here and now
  8. With or without a self
  9. Whether mind or matter
  10. Already there

(See also the sequel to this work: More Meditations)


Sundry notes and essays on Logic.

Avi Sion,  Ph. D.

First published, 2005. Expanded edition, same year.


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 cutting-edge phenomenological analysis of negation.
Additionally, this volume is used to publish a number of notes and essays previously only posted in the Internet site The Logician, including a history of Jewish logic and an analysis of Islamic logic.

Buy it or read it online

All of Avi Sion’s published books can be purchased at (in paperback or kindle/.mobi form), and at (in hardcover, paperback or e-book/.epub form), as well as other online stores.

They can also be read online free of charge, chapter by chapter, at and, in '3D flipbook' format, at, as well as in Google Books and other Internet locations. They are also available in many university and public libraries.

Contents in brief

1.     About the Laws of Thought
2.     About Induction
3.     About Words
4.     About Formal Logic
5.     About Paradoxes
6.     About “Modern Logic”
7.     About Cognitive Development
8.     About Causal Logic
9.     About Negation
10.  Jewish Logic: A Brief History and Evaluation
11.  Islamic Logic
12.  Logical Aspects of Foucault's "Archeology"
13.  Comments on 3 chapters of Foucault
14.  Bolzano's Semantics Concepts

Contents in detail

1.               ABOUT THE LAWS OF THOUGHT
1.               Dialectical Reasoning
2.               Genesis of Axioms
3.               Paradoxical Propositions
4.               Contradiction
5.               Varieties of Contradiction
6.               Double Standards
7.               Special Status of the Laws
8.               Motors of Rational Thought
9.               Cogito, Ergo Sum
10.            Concerning Identity

2.               ABOUT INDUCTION
1.     Critical thought
2.     Misappropriation
3.     Evidence
4.     Detail
5.     Seems and Is
6.     Adduction
7.     Pertinence
8.     Trial and Error
9.     Field Specific
10.  The Human Factor
11.  Theorizing
12.  Approaching Reality
13.  Experiment
14.  The Uncertainty Principle
15.  Epistemic Ethics
16.  Phenomenology
17.  Appearance, Reality and Illusion
18.  Existence and Non-existence
19.  Philosophy and Religion

3.               ABOUT WORDS
1.     Meaning
2.     Traditional Distinctions
3.     Logic and Linguistics
4.     Dialogue
5.     Poles of Duality

4.               ABOUT FORMAL LOGIC
1.     Form and Content
2.     Singular Subject
3.     Special Forms
4.     Fuzzy Logic
5.     Added Determinants
6.     Relational Expressions
7.     Disjunction
8.     Material and Strict Implication
9.     Nesting of Hypotheticals
10.  Compound Theses
11.  Validation of Nesting
12.  Brackets in Logic

5.               ABOUT PARADOXES
1.     On the Liar Paradox
2.     Making No Claim
3.     Nagarjuna’s Trickery
4.     Non-apprehension of Non-things
5.     A Formal Impossibility
6.     The Analytic/Synthetic Dichotomy
7.     On the Russell Paradox
8.     An Illustration of Russell’s
9.     On Grelling’s Paradox

6.               ABOUT “MODERN LOGIC”
1.     A School of Logicians
2.     Alleged New Methods
3.     Non-Aristotelian “Logic”
4.     Postmodern “Logic”
5.     Mere Manipulations
6.     Thinking Reflexively
7.     Conventional Logic
8.     Absolute Truths
9.     Untouched by Consciousness
10.  Logical Atomism
11.  Exclusive Judgments
12.  Empty Terms

1.     The Fourth R
2.     Empirical Studies
3.     Piaget’s Model
4.     Piaget’s Experiments
5.     Lines of Inquiry
6.     Experimental Techniques
7.     Private Languages

8.               ABOUT CAUSAL LOGIC
1.     Induction of Causatives
2.     True of All Opposites
3.     Extensional to Natural
4.     Hume’s Denials
5.     Hume’s Mentalism
6.     Constant Conjunction
7.     Billiard Balls
8.     Against Kant on Freewill
9.     Alleged Influences
10.  Analogical Inferences

9.               ABOUT NEGATION
1.     Negation in Adduction
2.     Positive and Negative Phenomena
3.     Positive Experience Precedes Negation
4.     Negation is an Intention
5.     Formal Consequences
6.     Negation and the Laws Of Thought
7.     Pure Experience
8.     Consistency is Natural
9.     Status of the Logic of Causation
10.  Zero, One and More
11.  Psychology of Negation
12.  Negation in Meditation

1.     Introduction
2.     Traditional Claims and Historical Record
3.     Comparisons and Assessments

11.            ISLAMIC LOGIC
1.     The Structure of Islamic Law
2.     Islamic Hermeneutics
3.     Interpreters

1.     Slippery
2.     Catch Him
3.     Healing

1.     Las Meninas
2.     The Prose of the World
3.     Representing

1.     “Propositions-in-Themselves”
2.     “Ideas-in-Themselves”
3.     The Issue of Time

(Note: As of 2008, the section headings in chapters 1-9 were added in for the reader’s convenience. Moreover, three essays originally included in this book were omitted from it, viz.: “J. S. Mill’s Methods” (2005), which was put with The Logic of Causation; and “Addenda to Judaic Logic” (1997-2005) and “Diagrams for Judaic Logic” (2005), which were put with Judaic Logic. The remaining few chapters were then renumbered 10-14.)

Wednesday, February 25, 2015



Avi Sion,  Ph. D.

First published, 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.

Buy it or read it online

All of Avi Sion’s published books can be purchased at (in paperback or kindle/.mobi form), and at (in hardcover, paperback or e-book/.epub form), as well as other online stores.

They can also be read online free of charge, chapter by chapter, at and, in '3D flipbook' format, at, as well as in Google Books and other Internet locations. They are also available in many university and public libraries.

Contents in brief

1.         Basic Causal Relations
2.         Interactions between Volition and Causation
3.         Further Analysis of Volition
4.         Consciousness and Responsibility
5.         Influence and Freedom
6.         Further Analysis of Influence
7.         The Workings of Volition
8.         Volition and the Special Sciences
9.         Will, Velleity and Whim
10.       Affections and Appetites
11.       Complications of Influence
12.       Urges and Impulses
13.       The Quasi-Purposive in Nature
14.       Concepts of Evolution
15.       More about Evolution
16.       The Self
17.       Some Topics in Deontology
18.       More Topics in Deontology

Contents in detail

  1. Causation and volition
  2. Causality and modality
  3. Spontaneity
  4. Relative vs. absolute contingency

  1. Necessity and inertia in causation
  2. Direct and indirect volition
  3. Matter-mind and spirit
  4. Conceiving Divine volition
  5. The study of volition

  1. Knowledge of volition
  2. Freedom of the will
  3. Decision and choice
  4. Goals and means

  1. The consciousness in volition
  2. The factors of responsibility
  3. Judging, and misjudging, people

  1. Influence occurs via consciousness
  2. Knowledge of effort, influence and freedom
  3. Formal analysis of influence
  4. Incitement

  1. Some features of influence
  2. Processes of influence
  3. Instincts in relation to freewill
  4. Liberation from unwanted influences
  5. Propositions about the future

  1. Cultural context and epistemological considerations
  2. Theoretical context
  3. Stages in the process of volition
  4. The scope of freewill

  1. Volition and the laws of physics
  2. Volition and biology
  3. Therapeutic psychology

  1. Cognition, volition and valuation
  2. Velleity
  3. Whim
  4. Inner divisions

  1. Valuation
  2. The main valuations
  3. Ethology

  1. Habits
  2. Obsessions and compulsions
  3. The ego abhors a vacuum

  1. Physical urges and impulses
  2. Mental urges and impulses
  3. Formal analysis of physical and mental urges
  4. Are there drives within the soul?
  5. Formal analysis of spiritual urges

  1. Purposiveness
  2. Organic functions
  3. The continuity of life

  1. The logical form of evolution
  2. Evidence for evolution
  3. Random mutation
  4. Natural selection

  1. Social Darwinism
  2. Spiritual Darwinism
  3. Theological perspectives

16.       THE SELF
  1. Ungluing the mind
  2. Abstract vs. concrete self
  3. Sundry reflections on the soul and God

  1. Founding ethics
  2. Ethics concerns the living, thinking, willing
  3. Conscience and conformism
  4. Tai Chi, karma yoga and faith

  1. Inducing ethics
  2. Ethical formulas
  3. Philosophy of law

  1. Some formal logic guidelines
  2. Aristotle’s four causes 



Basing Knowledge on Appearance

Avi Sion,  Ph. D.

First published, 2003. Expanded edition, 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.

Buy it or read it online

All of Avi Sion’s published books can be purchased at (in paperback or kindle/.mobi form), and at (in hardcover, paperback or e-book/.epub form), as well as other online stores.

They can also be read online free of charge, chapter by chapter, at and, in '3D flipbook' format, at, as well as in Google Books and other Internet locations. They are also available in many university and public libraries.

Contents in brief

1.         What, Why and How
2.         Organizing Principles
3.         Experiences and Abstractions
4.         Conceptualization
5.         The Self
6.         Additional Topics
7.         The Active Role of Logic
8.         Epistemological Issues in Mathematics
9.         Theology Without Prejudice

Contents in detail

1.         What, Why and How
  1. Phenomenology
  2. Knowledge is Based On Appearance
  3. To Be Or Not To Be
  4. The Phenomenological Approach

2.         Organizing Principles
  1. The Order of Things
  2. Appearance and Other Large Concepts
  3. Material, Mental, Intuitive, Abstract
  4. Number, Space and Time
  5. Modality and Causality

3.         Experiences and Abstractions
  1. The Objects of Perception
  2. The Objects of Intuition
  3. Correlations Between Experiences
  4. Conceptual Objects
  5. Degrees of Interiority

4.         Conceptualization
  1. Sameness and Difference
  2. Compatibility or Incompatibility
  3. Words and Intentions
  4. A Theory of Universals
  5. Unity In Plurality

5.         The Self
  1. The Self
  2. Factors of the “Self”
  3. Identification-With
  4. Ideal and Practical Concepts
  5. Fallacious Criticisms of Selfhood
  6. What “Emptiness” Might Be

6.         Additional Topics
  1. Present Appearances
  2. The Concepts of Space and Time
  3. Apprehension of the Four Dimensions
  4. Contents of Thought Processes
  5. Universals and Potentiality
  6. Social vs. Personal Knowledge

7.         The Active Role of Logic
  1. Principles of Adduction
  2. Generalization is Justifiable
  3. Logical Attitudes
  4. Syllogism Adds to Knowledge
  5. There is a Formal Logic of Change
  6. Concept Formation
  7. Empty Classes
  8. Context
  9. Communication
8.         Epistemological Issues in Mathematics
  1. Mathematics and Logic
  2. Geometrical Concepts have an Experiential Basis
  3. Geometry is a Phenomenological Science
  4. On “New Arithmetical Entities”
  5. Imagining a Thoroughly Empirical Arithmetic

9.         Theology Without Prejudice
  1. Applying Logical Standards to Theology
  2. Conceiving the Divine Attributes
  3. Analyzing Omniscience and Omnipotence
  4. Harmonizing Justice and Mercy
  5. The Formlessness of God

  1. Using Meditation
  2. Feelings of Emptiness

  1. Existence, appearance, and reality
  2. Assumed material, mental and spiritual domains
  3. A classification of appearances
  4. Three types of continuity



A Critical Analysis of Nagarjuna’s Arguments

Avi Sion,  Ph. D.

First published, 2002.


The 2nd Century CE Indian philosopher Nagarjuna founded the Madhyamika (Middle Way) school of Mahayana Buddhism, which strongly influenced Chinese (Ch’an), Korean (Sôn) and Japanese (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.

Buy it or read it online

All of Avi Sion’s published books can be purchased at (in paperback or kindle/.mobi form), and at (in hardcover, paperback or e-book/.epub form), as well as other online stores.

They can also be read online free of charge, chapter by chapter, at and, in '3D flipbook' format, at, as well as in GoogleBooks and other Internet locations. They are also available in many university and public libraries.



1.         The tetralemma
2.         Neither real nor unreal
3.         Nagarjuna’s use of dilemma
4.         The subject-predicate relation
5.         Percepts and concepts
6.         Motion and rest
7.         Causality
8.         Co-dependence
9.         Karmic law
10.       God and creation
11.       Self or soul
12.       Self-knowledge

Not ‘empty logic’, but empty of logic

1.     Fallacies in Nagarjuna’s work
2.      Brief glossary of some basic concepts

Further Description

This essay is a critical review of some of the main arguments proposed by the Indian Buddhist philosopher Nagarjuna (c. 113-213 CE), founder of the Madhyamika (Middle Way) school, one of the Mahayana streams, which strongly influenced Chinese (Ch’an), Korean (Sôn) and Japanese (Zen) Buddhism, as well as Tibetan Buddhism. Specifically, the text referred to here is Empty Logic - Madhyamika Buddhism from Chinese Sources (Delhi: Motilal Banarsidass, 1991) by Hsueh-li Cheng, of Hawaii University (Hilo). The main source-texts of this school of thought, to which Cheng of course often refers, are the “three treatises” – the Middle Treatise, the Twelve Gate Treatise and the Hundred Treatise.
The title Empty Logic was not intended pejoratively by its author, but simply to mean ‘logic of emptiness’, the term “emptiness” (Shunyata) referring to the Buddhist doctrine that (briefly put, very roughly) things have no abiding core, no essence, no fixed nature. Cheng’s work is a clear exposition of Madhyamika history and logical techniques, but it makes no attempt to criticize those techniques. All criticism of Madhyamika or Buddhist logic, here, is my own.
The present essay is not a religious tract and has no polemical intent. It is a work of philosophy, a fair-minded logical evaluation of certain propositions and arguments taken as philosophical positions open to discussion like any other. It examines and discusses a goodly array of Buddhist, and in particular Madhyamika, doctrines, but does not pretend to be an exhaustive treatment of all doctrines or of all aspects of those dealt with.
However, I do not attempt here to develop a historical perspective, or to list the various tendencies and their interrelations. Cheng’s book includes an interesting exposition of the development of Madhyamika philosophy, from Nagarjuna in the 2nd century CE through to the Yogachara school and on. However, he fails to investigate in sufficient detail the development of Buddhist philosophy prior to Nagarjuna, barely mentioning several centuries of earlier Theravada (Hinayana) philosophy and the early phases (starting 1st cent. CE, and before) of Mahayana reaction (e.g. the Mahasanghikas). To better understand Nagarjuna’s motives and goals, it would be well to be acquainted with this background.
My naming the present essay Buddhist Illogic should not be taken to imply that I consider all Buddhist philosophy or even all Madhyamika as illogical. It merely reflects my focus here on some of the (many) illogical arguments used in Nagarjuna’s discourse. Indeed, some of Nagarjuna’s arguments and beliefs have been refuted or rejected by other Buddhist philosophers. Buddhist philosophy is not monolithic, but a constellation of philosophies with as their common ground the (alleged) pronouncements of Buddhism’s founder. I do here challenge some underlying Buddhist doctrines, but only incidentally, not systematically.
I would have named this essay less pejoratively ‘Buddhist Logic’ if I had found some interesting new thought forms to report. Buddhism and Nagarjuna do indeed use valid as well as invalid forms of reasoning, but these forms (those I found so far) are all familiar to us today, and so not notable except for historical purposes (where we would try and determine whether Buddhist usage antedates usage in Greek or other writings). However, my main justification is that much of Buddhism itself, and particularly Nagarjuna’s version of it, cheerfully proclaims itself free of or beyond logic, or illogical and even anti-logical.
On a personal note, I want to stress my admiration for Buddhism in general, which has taught me much, both in the way of living skills and through its philosophical insights. So I cannot be accused of approaching this subject with any antagonistic prejudice. I read Empty Logic eager to learn from it, rather than to find fault with it. As a philosopher and logician I am however duty bound to analyze and judge philosophies dispassionately, and this is what I do here. Generally speaking, I have little interest in criticizing other people’s philosophical works, because I could write thick volumes doing so. Life is unfortunately too short for that, so I prefer to pass it developing a constructive statement. Nevertheless, one generally learns a lot through debate, and I can say that challenging Nagarjuna has helped me to clarify various philosophical problems and possible solutions.
Finally, let me say that the message of “Buddha” (the enlightened) Siddhartha Gautama (563-483 BCE), about “emptiness”, which as is well known is essentially non-verbal, should not be confused with Nagarjuna’s or any other writer’s attempted philosophical interpretation, explanation and justification of related ideas. Thus, to refute the latter does not necessarily deny the former.

Tuesday, February 24, 2015

JUDAIC LOGIC - by Avi Sion

A Formal Analysis of Biblical, Talmudic and Rabbinic Logic

Avi Sion,  Ph. D.

First published, 1995. Slatkine Edition, 1997.


Judaic logic: A Formal Analysis of Biblical, Talmudic and Rabbinic 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 Aristotelian 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 (the testing, and confirmation or rejection, of hypotheses - i.e. of beliefs, and equally of the reasons or explanations put forward in support of beliefs) 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, practice and history of logic.

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Contents in brief

1.         Introduction.
2.         Adductive Logic in the Torah.
3.         The Formalities of A-Fortiori Logic.
4.         Qal VaChomer.
5.         Revised List of Biblical  A-Fortiori.
6.         The Language of Biblical  A-Fortiori.
7.         Without Prejudice.
8.         Initial Impressions.
9.         Traditional Teachings.
10.       The Thirteen  Midot (I)
11.       The Thirteen  Midot (II)
12.       The Sinai Connection.
13.       On the Concept of Mitzvah.
14.       Logical Aspects of Emunah.
15.       Epilogue.

Contents in detail

1.         INTRODUCTION.
  1. The Development of Jewish Law.
  2. A Logic Primer.

  1. The Art of Knowing.
  2. Adduction in Western Philosophy.
  3. Adducing Prophecies and Prophethood.
  4. Logic and Mysticism.

  1. The Valid Moods.
  2. Validation Procedures.
  3. Additional Details.

4.         QAL VACHOMER.
  1. Background.
  2. Torah Samples.
  3. The Dayo Principle. 
  4. Objections!
  5. Rabbinic Formulations.

  1. Problems Encountered.
  2. The Solution Found. 
  3. The Data and their Analysis.
  4. Synthesis of Results.
  5. Talmudic/Rabbinic A-Fortiori.

  1. Torah Books.
  2. Historical Books.
  3. Other Books.
  4. Rejects.

  1. Taking a Dilemma by its Horns.
  2. About Revision.
  3. Changes in the Law.

  1. Methods and Contents. 
  2. Davqa or Lav Davqa? 
  3. Kushya and Terutz.
  4. Standards of Knowledge.

  1. Hermeneutics.
  2. Heuristics.     
  3. A Methodical Approach.

10.       THE THIRTEEN  MIDOT  (I).
  1. Exposition and Evaluation.
  2. Inference of Information.
  3. Scope of Terms.

  1. Harmonization.

  1. Verdict on Rabbinic Hermeneutics.
  2. Artificial Blocks to Natural Development of the Law.
  3. How "Tradition" Keeps Growing.

  1. Basic Properties.
  2. Complementary Factors.
  3. How to Count Mitzvot.
  4. Commanded  vs. Personal Morality.

  1. On Natural Proofs of Religion.
  2. Theodicy and the Believer's Wager.
  3. Faith and Justice.
  4. Legislated Belief.

15.       EPILOGUE.
  1. Motives of the Present Research.
  2. Conclusions of our Study.

Appendix 1.    Further Notes on A-Fortiori Argument.
Appendix 2.    Notions of Time.
Appendix 3.    Gematria.
Appendix 4.
  1. Feigenbaum's Understanding the Talmud.
  2. Rabinowich's Talmudic Terminology.
  3. The Ramchal's Ways of Reason.
Appendix 5.    The Hebrew Language.
Appendix 6.    Further Notes on Harmonization Rules.

  1. Concerning Adductive Reasoning Relative to Prophecy.
  2. A Note on Astronomy.
  3. An Example of Secondary A-Fortiori in the Talmud.
  4. One More Example of A-Fortiori in the Tanakh.
  5. A Note Concerning Anachronisms.
  6. Inferences from Context.
  7. Post Hoc Ergo Propter Hoc.
  8. Judgment-Calls.
  9. Tolerance of Contradictions.
  10. Proof of Gd by Analogy?
  11. Disproofs of Gd?
  12. Neither Certainty Nor Faith are Essential to Religious Ethics.
  13. The Rabbis' Antipathy to Philosophy.


Further Description

Judaic logic: A Formal Analysis of Biblical, Talmudic and Rabbinic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the objective perspective of a logician. The author's previous treatise, Future Logic: Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional and Logical Modalities, was a large-scale study of formal logic and epistemology; in the present work, his purpose is to consider the logic employed within his religion, Judaism, and honestly estimate the extent to which it fits into the general norms and whether it has any contributions to make to them. It covers a wide range of topics:

·       A brief overview of the sources of Jewish law (the Halakhah), and a quick introduction to generic logic theory (induction and deduction), for the uninitiated.
·       The new discovery of an explicit formulation of the principles of adduction in the Torah (the Pentateuch), written long before their acknowledgement in Western philosophy and their assimilation in a developed theory of knowledge (epistemology).
·       An original and thorough formal analysis of a-fortiori logic (the qal vachomer type of argument, the most deductive of Judaism's interpretative processes), together with a detailed investigation of its use in the Tanakh (the Jewish Bible) which reveals it to be much more widespread than traditionally supposed.
·       A reflection on the psychological and social factors affecting both religious and secular thought, which may cause people to deviate from openness and objectivity, whether within one of these domains or in relation to the other.
·       An examination of some of the main similarities and differences between the methods and databases of religious and secular pursuits of knowledge, which shows the overwhelmingly inductive (rather than, as traditionally assumed, deductive) methodology of Talmudic and Rabbinic thought.
·       A presentation, in considerable detail, of traditional teachings of Judaic logic, including principles of interpretation (hermeneutics) and organization (heuristics); and suggestions for methodical study.
·       A detailed and incisive formalization and evaluation of the 13 Midot of R. Ishmael and other fundamental principles of exegesis of Jewish law - a completely novel research effort (which may be considered as the central motive of the work), revealing impartially the strengths and weaknesses of Talmudic and Rabbinic modes of thought.
·       A formal study of the ethical logic (deontology) found in Jewish law, to elicit its universal aspects and its peculiarities.
·       Finally, an examination of possible bases and motives of belief in G-d, and, more broadly, in the religious tradition; and a critical assessment of some of the less formal legal generalities adopted by the Rabbinic tradition.

Judaic Logic is of both theoretical and practical value, to students of Bible and Talmud and to students of Logic and Philosophy alike. The work's universality lies in its efforts both (a) to bring Judaic logic into the general fold, demystifying it and showing the extent to which its processes are, or are not, commonplace; and (b) to draw from it any lessons of value to logic theory and practise in general. In fulfilling the first of those tasks, this work incidentally provides Bible and Talmud students, and more specifically the deciders of Jewish law, with wider methodological perspectives and powerful new technical tools. In fulfilling the second, it provides the secular layperson, the scientist or philosopher, and in particular the logician, with novel historical insights and formal instruments.