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If people have a problem with conditionals with false antecedents and with true consequents always being true, why not just change it according to what is found to be more intuitive?

Regarding equivalence with some disjunctions, every explanation I hear seems to make sense prima facie, but I think ultimately they make sense merely because it makes the whole system simple and easy to work with. For instance, (p->q)->(~pVq) is not as intuitively necessarily true as maybe (pVq)->(~p->q). Simply changing how implications behave reflects that some of these disjunctions would cease to be equivalent.

So again, why do we stick with the material implication? Is it because in it, they're equivalent to some disjunctions and are therefore translatable by something like DeMorgan's Laws and provide for tidy simplifications?

Hircarra
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  • "We" don't stick with the material conditional, the [indicative conditional](https://en.wikipedia.org/wiki/Indicative_conditional) of ordinary language deviates from it. The main application of mathematical logic is to mathematics, where it matches the extensional semantics of set theory: validity = absence of counterexamples, p → q = ~(p∧~q). – Conifold Jan 04 '20 at 05:46
  • So you stick with it because no one has proven it wrong? – Hircarra Jan 04 '20 at 06:18
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    You stick with it because it does exactly what we want in math. And there is no proving a convention wrong, or right, it is either useful or not. – Conifold Jan 04 '20 at 06:34
  • I've voted to reopen because the material conditional isn't something that should only be discussed once; it's not an open or shut case. And it seems to me that almost all questions asked here will be similar to those asked before. Secondly, the question of this post is different to the one linked by the closer. Incidentally, my answer would have been that the material conditional is fine, the question is how far does it model what we want from indicative "if" conditionals? My personal opinion is that we confuse ourselves reading it as "if", it's actually a "whenever" conditional. – Daniel Prendergast Jan 04 '20 at 10:18
  • @Conifold "You stick with it because it does exactly what we want in math." This is entirely false. The material conditional isn't even relevant in math. Something like pVq is never even implicitly equivalent to ~p->q – Hircarra Jan 04 '20 at 19:16
  • @Daniel Prendergast He closed the question because he's butthurt at the implication: that there is no good reason. – Hircarra Jan 04 '20 at 19:22
  • You can prove some really useful things with material implication. it has its place and works for what it's intended for. – Daniel Prendergast Jan 04 '20 at 19:43
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    To the contrary, they are *always* equivalent in math by design, because ZFC explicitly adopts classical formal logic (unlike ordinary language). Even before ZFC and Russell, the practice of *reductios* and proving by cases in math effectively endorsed the material conditional in full, see [Azzouni, Is there still a Sense in which Mathematics can have Foundations? pp.37-39](https://as.tufts.edu/philosophy/sites/all/themes/asbase/assets/documents/azzouniStillASense.pdf) – Conifold Jan 05 '20 at 00:40

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