Thursday, February 26, 2015


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.)

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