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Would you agree with the following proposition: “if all of my unicorns fly, then some of my unicorns fly”?
by LudwigNagasena 2y ago
Would you agree with the following proposition: “if all of my unicorns fly, then some of my unicorns fly”?
- Supermancho 2y agoYes
- LudwigNagasena 2y agoSo if “all my hats” doesn’t imply that I have at least one hat, “some of my hats” doesn’t imply it either; otherwise we wouldn’t be able to derive “some” from “all”. Hence, “some of my hats are green” doesn’t imply that “at least one of my hats is green”. That’s a claim that contradicts both traditional formal logic interpretation and common sense English interpretation.
- Supermancho 2y agoI think the same of your interpretation of some vs all. Some can contain all, just as it contains none. Both some/all imply, but do not assert existence. Claiming it tautologically defies logic is not compelling.
- LudwigNagasena 2y agoWell, I think showing that it defies logical inference is quite relevant in the context of that thread being about translating typical English into first order logic to do logical inference.
- Supermancho 2y agoI worry about sets and consideration of edge cases. Legal, programmatic, medical. Adhering to a convention that presupposes meaning and claim that interpretation is the only interpretation, cannot be resolved with repetition. I remain unconvinced.
- LudwigNagasena 2y agoYou were the one to claim the only interpretation (in opposite of OP who merely claimed "typical English" interpretation). Moreover, your interpretation directly contradicts both conventional typical English interpretation, which would be relevant in legal context (where making such claims with empty set in mind would be deemed misleading), and conventional formal-logical interpretation, which would be relevant in programming (where the truth of `array.every()` doesn't imply the truth of `array.some()`).
- tantalor 2y agoNo. (assuming you have no unicorns) "all of my unicorns fly" is true; "some of my unicorns fly" is false; "true->false" is false.
- LudwigNagasena 2y agoSo you claim that in normal English “all” doesn’t imply “some”?
- tantalor 2y agoDoes "when pigs fly" imply that some day pigs will be able to fly? No; people can understand impossibility when it is used rhetorically in every day speech. For example I might say, "all the honest politicians are doing a great job", which conveys my actual meaning, "all politicians are dishonest".
- spencerflem 2y agoThat stops working when its not obviously rhetorical. Someone else in the thread mentioned: 'All my kids are in high school'. If you said this to a stranger with no other context, they will 100% think that you have kids. There is no possibility that you meant, 'I am asserting that in the set of my children, each element satisfies the property of being in high school'
- LudwigNagasena 2y agoI don't understand what point those examples are supposed to convey. "All of my unicorns can fly -> some of my unicorns can fly -> at least one of my unicorns can fly" still seems to be a valid inference that may get lost in conventional translation into first order logic. And a proposed "allsome" quantifier still seems like a valid remedy for that.
- unbalancedevh 2y agoThis reminds me of one of my favorite threads on the old Internet Infidels web site, in their Philosophy forum. The question was, "Do dogs bark?" There was an enormous amount of discussion on it!