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Paradoxes and Their Resolutions

A Thematic Compilation by Avi Sion

Blog posts : "paradox"

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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