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Paradoxes and Their Resolutions

A Thematic Compilation by Avi Sion

Blog posts September 2017

Foreword and contents

 

A is A (and not-A is not.A);

nothing is both A and not-A;

nothing is neither A nor not-A.

(Aristotle’s three laws of thought.)

 

Foreword

Paradoxes and their Resolutions is a ‘thematic compilation’. It collects in one volume the essays that I have written in the past (…

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1. The vanity of the tetralemma

 

The most radical assault on reason consists in trying to put in doubt the laws of thought, for these are indeed the foundations of all rational discourse. First, the law of identity is denied by saying that things are never quite what they seem to be, or that what they are is closer to grey …

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2. Clarifying contradiction

 

1.    Dialectic

The three “Laws of Thought” may be briefly explicated as follows:

  1. Thesis: there are certain appearances; appearances appear.
  2. Antithesis: there are incompatibilities between certain of these appearances; in such cases, one or both of them must be false.
  3. Syn…

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3. Clarifying negation

 

1.    Negation in adduction

Concepts and theories are hypothetical constructs. They cannot (for the most part) be proven (definitely, once and for all), but only repeatedly confirmed by experience. This is the positive side of adduction, presenting evidence in support of rational constru…

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4. Clarifying paradox

 

A very important field of logic is that dealing with paradox, for it provides us with a powerful tool for establishing some of the most fundamental certainties of this science. It allows us to claim for epistemology and ontology the status of true sciences, instead of mere speculative digressi…

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5. The Liar paradox (early)

 

1.    Double paradox

We have seen that logical propositions of the form ‘if P, then nonP’ (which equals to ‘nonP’) or ‘if nonP, then P’ (which equals to ‘P’), are perfectly legal. They signify that the antecedent is self-contradictory and logically impossible, and that the consequent i…

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6. The Liar paradox (redux)

 

I dealt with the Liar paradox previously, in my Future Logic[1], but now realize that more needs to be said about it. This paradox is especially difficult to deal with because it resorts to several different discursive ‘tricks’ simultaneously.

1.    First approach

The statement …

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7. The Russell paradox (early)

 

1.    Self-membership

With regard to the issue of self-membership, more needs to be said. Intuitively, to me at least, the suggestion that something can be both container and contained is hard to swallow.

Now, self-membership signifies that a nominal is a member of an exactly identi…

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8. The Russell paradox (redux)

 

Logic is what helps us transmute scattered concrete perceptions into well-ordered abstract concepts. Human knowledge, or opinion, is based on experience, imagination and rational insight. The latter is a kind of ‘experience’ in the larger sense, a non-phenomenal sort of experience, call it l…

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9. More on the Russell paradox

 

1.    My resolution of the Russell paradox

My resolution of the Russel paradox is, simply put, that no class is, or can ever be, a member of itself. Self-membership is unconscionable. It is therefore no surprise that the unthinking adoption of the idea of self-membership by Russell led…

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10. Hempel's paradox of confirmation

 

1.    Traditional analysis

Carl Gustav Hempel[1] in the 1940s exposed an alleged “paradox of confirmation”, which suggested that a fully consistent formal inductive logic is impossible. This is commonly called “the raven paradox”, and may be described as follows:

  1. The obse…

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11. Goodman’s paradox of prediction

 

1.    The alleged problem

Nelson Goodman[1] proposed in 1955 a “riddle of induction” (as he called it[2]) or “paradox of prediction” (as others have characterized it), which seemed to demonstrate a formal difficulty in generalization. This may be stated as follows:

“Goodman …

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12. The Sorites paradox

 

1.    What’s a heap?

The Sorites paradox is not a paradox, in the strict sense of the term, but a question. The question is sometimes put in a sophistical manner, so as to make it seem paradoxical. But it can be put in a more straightforward manner, in which case it is seen to be sim…

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13. Protagoras vs. Euathlus

1.    An ancient paradox

One of the many alleged paradoxes that have come down to us from the Greeks is the dispute between Protagoras (of Abdera, ca. 480-410 BCE) and his student Euathlus (about whom nothing more is known). The story is told by Aulus Gellius (Roman, ca. 125-180 CE)[1], …

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14. Buddhist antinomic discourse

 

1.    The tetralemma

Western philosophical and scientific thought is based on Aristotelian logic, whose founding principles are the three “Laws of Thought”. These can be briefly stated as “A is A” (Identity), “Nothing is both A and non-A” (Non-contradiction) and “Nothing is neither A n…

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15. More Buddhist antinomic discourse

 

1.    The ‘I have no thesis’ thesis

a.         The Buddhist[1] philosopher Nagarjuna (India, c. 150-250 CE) attacked every thesis he regarded as rational by every means he regarded as logical, and declared his own discourse immune from scrutiny and criticism, by saying (accor…

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Main References

Main References

 

Cheng, Hsueh-li.  Empty Logic: Madhyamika Buddhism from Chinese Sources.  Delhi: Motilal Banarsidass, 1991.

Dawkins, Richard.  The Greatest Show on Earth: The Evidence for Evolution.  New York: Free Press, 2009.

Dhammapada, The.  Juan Mascaro, trans.  Harmondsworth…

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