Questions tagged [symbolic-logic]

For questions related to symbolic logic, also known as mathematical logic. Topics might range from philosophical implications of metamathematical results to technical questions.

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Checking the validity of the logical conclusion gleaned from a heated conversation

I have two friends - call them John and Jane. I was recently privy to an argument concerning a book between John and Jane that went like this: John: This book did not make a single coherent, ...
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Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ ...
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Recommendation: Second Order Logic textbook

I'm looking into Universalist Realism, Nominalism, Trope theory and the application of Second Order logic to each of them, however I have little/no experience with Second Order logic. Please let me ...
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How did Fitch's opposition to the Russell-Whitehead theory of types turn out since the 1950's?

In a footnote to Appendix C of Frederic Fitch's Symbolic Logic (page 217), Fitch writes about his article, "Self-Reference in Philosophy": It is reprinted here in order to indicate more fully my ...
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Proof from tree to steps

I'm able to get the proof in a tree form (it's invalid). Is there a method where I can transform it to steps method indicating the rules of inference and replacement?
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Logical, semantic and self-referential paradoxes: The Truth teller and the Liar (draft) can an expert on the matter give feedback?

Title: Logical semantic and self-referential paradoxes: The Truthteller and the Liar (draft, informal) (major) assumption: A statement is either true or not true (law of excluded middle, classical ...
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How to define a new logical language

There are a number of logical languages defined that are so called flavors of a certain logic (for example, flavors of First Order Logic). Such new logical languages sometimes extend or restrict the ...
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Honestly have no Idea how to prove A v ¬¬B from A v B (LPL Q. 6.18)

Premise A v B Goal A v ¬¬B Please help. It seems so self evident but I don't know how to get there.
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A question about possibility

If A, then B ~ A So, possible that B Valid or not? My take: Not valid. Reason: Valid means if all the premises are true, the conclusion must be true That means adding new information should not ...