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2 votes

Which is better, an empirical basis for the meanings of the logical connectives or a relevance logic definition of them, and why?

You are oversimplifying. You cannot learn the meaning of logical connectives just from a couple of simple examples. So your question is a false dichotomy. Depending on your preferred understanding of ...
Bumble's user avatar
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5 votes
Accepted

Do the paradoxes of material implication in relevance logic, invalidate reductio ad absurdum?

You cannot prove P → (Q → P) from disjunctive addition alone, without other rules. Your proof using classical logic relies on the equivalence of ¬Q ∨ P with Q → P, which does not hold in general for ...
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2 votes

Do the paradoxes of material implication in relevance logic, invalidate reductio ad absurdum?

Note that (A->B):=(~A v B) doesn’t work for all logics, e.g. Intuitionistic Logic and relevance logics. The main thrust of (~P v Q)->(P->Q) is that Q->(P->Q) and ~P->(P->Q) are ...
PW_246's user avatar
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1 vote

What is the reason behind the fourth axiom in Gödel's ontological proof?

There are a couple of different versions of the proof. Wrt Wiki, we have that Axiom 4: "If a property is positive, then it is necessarily positive", is used in the proof of Theorem 3: "....
Mauro ALLEGRANZA's user avatar
1 vote

Can assumption in Hilbert style proof system be contradictory?

As Conifold points out, you can use contradictory assumptions in natural deduction proofs. You just have to discharge the assumptions in the usual way. But your question asks about a Hilbert style ...
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