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How can we account for the differences between the conditional in truth-functional logic and the conditional in natural language?

Mark
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    I think I know what you're getting at but your question would be a lot easier to answer if you went into more detail about the specific differences you're looking at, preferably with examples. – Stephen Donovan Apr 19 '22 at 22:38
  • @StephenDonovan Thanks for the reply. I'm just looking for general differences and how to account for them. – Mark Apr 19 '22 at 22:39
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    See The Logic of Conditionals as well as Indicative Conditionals. – Mauro ALLEGRANZA Apr 20 '22 at 06:03
  • If you are talking about the state of world in the present, there is no difference AFAICT. There are features of classical material implication, e.g .vacuous truth, that are rarely if ever used in daily discourse. We don't usually care, for example, about the implications of something that is known to be false, but vacuous truth is often used in mathematical proofs. Also, "A implies B" is often confused with "A causes B." "A implies B" means only that, at present, it is not the case that both A is true and B is false. – Dan Christensen Apr 20 '22 at 15:02
  • Lacking context? – Hayatsu Sep 06 '23 at 01:29
  • This has been asked so many times here. Please do a search. – Karl Oct 09 '23 at 17:01

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The material conditional is a purely logical operator that returns a T/F output when given two arguments (‘if $A$ then $B$’ is a logically contingent material conditional). It underpins mathematical implication (implication under the assumption of mathematical axioms).

An everyday-language implication like “Susan is in a miniskirt if she is teaching” or “the banana is poisonous if it is green” (which aren't the same as “Susan is in a miniskirt every time she is teaching” and “every green banana is poisonous”) can reasonably be construed as asserting a material conditional.

On the other hand, the everyday-language implication “the sky is not green if bananas are not blue” feels like a false assertion of causation rather than a true assertion of a material conditional, due to its antecedent having only a tenuous apparent connection to its consequent and being neither blatantly false (e.g., “pigs fly”) nor true.

The everyday-language implications “I won't swim if I go to the beach” and “you may visit Jenny if you have time” express modality instead of asserting material conditionals.

Finally, the everyday-language counterfactual “Susan would have cried if she had fallen” can't even be rigorously formalised using the material conditional.

ryang
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  • Next time you are differentiating between if-then, the operator, and if-then, the natural language connective, try not to use symbolisms of the former for the latter. It complicates the issue even further. Also, your answer is a non-answer to begin with. – Bertrand Wittgenstein's Ghost Apr 21 '22 at 05:29
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    @BertrandWittgenstein'sGhost I have removed the two symbols so as not to obfuscate my explanation, which I agree is quite soft. P.S. To assert a sentence means to claim it to be true. – ryang Apr 21 '22 at 07:01
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    P.S. For whatever it's worth, chatGPT's reply to "Is if bananas are yellow, then the sky is blue true?" is this: "No, the statement if bananas are yellow, then the sky is blue is not true in a logical or factual sense. It is a statement that combines two unrelated concepts, the color of bananas and the color of the sky, with no logical or causal connection between them. In a conditional statement, the 'if' part should have a logical or causal relationship with the 'then' part to be considered true. In this case, there is no such relationship, so the statement is false." – ryang Oct 09 '23 at 16:58
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    @ryang Hey, one of the few times I agree with ChatGPT! :P – Bram28 Oct 10 '23 at 00:06
  • @ryang Well, sometimes we mean to express a logical implication with an English conditional, so I can live with ChatGPT's usage of logical here: the sky being blue is indeed not a logical consequence of bananas being yellow. – Bram28 Oct 10 '23 at 16:42
  • Yes, as a material conditional ... but what normal person uses an English if ... then ... to merely express a material conditional? Again, I am with ChatGPT – Bram28 Oct 10 '23 at 19:42
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    @Bram28 Right, so, in the above, chatGPT is disregarding the material conditional, so its reference to "truth in a factual sense" isn't about synthetic truth at all. I don't think that chatGPT's reference to an implication's "truth in a logical sense" is with reference to (genuine/strict) logical consequence either; the phrase "logically true" is frequently loosely used to simply mean "true (in the given context)" or, with reference to real-world implications, "causally true". – ryang Oct 16 '23 at 04:17
  • @ryang Yeah, I am with you on the ‘logical’ sense … people too use that word in all kinds of different ways, just like ‘valid’, ‘sound’, ‘follows’, ‘consequence,, etc. And ChatGPT has of course no meaning in mind at all! – Bram28 Oct 16 '23 at 12:07
  • @Bram28 Trying to delineate everyday-language conditionals (and how they depart from the material conditional) is trickier than I'd expected. In case relevant, am putting here this food for thought that you recently proferred: "the material conditional is the weakest reading of any conditional; you could think of it as 'playing it safe', or as mathematical logic only providing us with a first test: if a conditional has a true 'if' and a false 'then', then it is certainly false... otherwise we move on to the next test." – ryang Oct 17 '23 at 03:19