Questions tagged [set-theory]

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Can paraconsistent or other logics make the impossible happen?

A paraconsistent logic system it is defined as "a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that ...
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Selection of logical connectives {¬,∨,∧,⇒,⇔} in set theory?

Nearly every treatment of set theory, whether Paul Halmos' Naive Set Theory, Herbert Enderton's Elements of Set Theory, Patrick Suppes' Axiomatic Set Theory, etc. introduce a common set of logical ...
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Proof Universe Came From Nothing?

Consider the following proof: (1) Let the Universe be defined as the set of all things. (2) It is impossible for a thing to come from itself. (You can't be your own parent) (3) 2 implies a set of ...
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This is inspired by Russel's paradox stating there is not set of all sets. It uses the presupposition that set can contain itself. However, this already seems paradoxical. Suppose a set A = {}. Then ...
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Does Reflective Set Theory "RfST" fulfill the requirements of founding Category Theory and Mathematics?

On mathoverflow I've posed the question in the title in connection to Muller's 2001 criteria for a founding theory of mathematics, which largely raised in connection to Category theory [see here]. ...
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Do the set of "Concepts" contain itself?

So I gather that a set containing itself is not allowed. Yet it seems like a set of all concepts (Concepts) should contain an element denoting the idea of "concept". Is it that there is a ...
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Is there any logical system/method where impossible/illogical/inconsistent things can exist (like a solution to Russell's paradox that makes sense)? [duplicate]

Discussing with a philosopher about impossible things existing or being allowed within a particular logic system, he told me: "This is a funny thing about logically impossible things. You can prove ...
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What is a set? (Is it possible to define a set?)

I've recently been studying set theory from some introductory textbooks (like Steinhart's "More Precisely" or Open Logic Project's "Sets, Logic, Computation"). I'm interested in ...