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Is there still today any philosopher specialised in logic making any substantial argument against the notion that a material implication is a logical implication?

  • It's generally understood that material implication is different from logical implication--p logically implies q only if p->q is a tautology (as stated here for example), and certainly not all material implications are tautologies. These are just part of the standard definitions of material implication and logical implication, not sure what it would mean to make an "argument" for them. – Hypnosifl Aug 22 at 14:38
  • @Hypnosifl What difference is there between p → q as a tautology and p → q as a "tautology for all possible assignments of p and q"? If "not all implications are logical implications", can you give an example of an implication which is not a logical implication? – Speakpigeon Aug 22 at 18:28
  • Does "a logical implication" just mean an implication used in logic? Or something like modeling human reasoning? There is a consensus on (trivial) answers to both questions, yes and no. – Conifold Aug 22 at 19:26
  • @Conifold My question was in reference to the book linked by Hypnosifl. The author makes this distinction without justifying it. That being said, it is clear that a logical implication can only refer to some aspect of human reasoning, notwithstanding what mathematicians may want to say about that. I'm also not sure what's the value of a "consensus" in this context, since academics essentially learn the same fairy tale. – Speakpigeon Aug 22 at 19:49
  • In that book "logical implication" simply stands for tautologies of propositional logic that contain →, an example of how an expression can refer to whatever the author defines it to refer. – Conifold Aug 22 at 20:04

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