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> All my hats....", you are simultaneously making an existence statement that you have at least one hat It does not. All my unicorns fly. There is no assumptio
by Supermancho 2y ago
> All my hats....", you are simultaneously making an existence statement that you have at least one hat
It does not. All my unicorns fly. There is no assumption that I have a unicorn. There is an assumption, based on the claim but it is not a fact.
The puzzle also assumes that "my" implies there is some ownership (we'll take for granted "my" means "has" for simplicity), which is another quibble that unravels the whole thing.
E is correct. I don't see how A comes to be the accepted answer.
- grraaaaahhh 2y agoE cannot be correct. "All my hats are green" is still false even when I own a red hat and a green hat.
- Supermancho 2y agoI would agree that's obvious, if not for the original error. The liar doesn't necessarily "have" any hats. Again, the assumption that the liar has hats is incorrect because it's relying on an conversational implication, rather than a specific assertion.
- grraaaaahhh 2y agoSure, but the question isn't about which statement is possible from the liar's statement, it's about which statement we can conclude from the liar's statement. The liar could be lying because they have no hats. They could be lying because they have a non-green hat. We cannot conclude E because it's possible that E is not correct.
- LudwigNagasena 2y agoWould 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()`).
- scoofy 2y agoI mean, it's important to remember that the axioms of first-order logic are arbitrary. We could easily argue that the truth value of an empty group is undecidable, and that would better correlate to natural language logic. The fact that we compact these edge cases into arbitrary truth values is just for ease of computing. This is also relevant to the arbitrary choice of the 'inclusive or' as a default over an 'exclusive or', which most people use in natural language.
- Supermancho 2y agoI have to interpret the question at face value, which may equate to natural language logic. I dont know the specific rules of any of these systems, which are obviously particular or wildly different from a layman interpretation. Most of the arguments seem to center around specialized conveniece rules (as you mention), which are eventually equated to the one true way to deconstruct meaning. At least, that is what I got out of this thread.