Yeah, I know. But your answers were inadequate for answering Eric's question, without exhibiting that you were answering the question. I.e. you weren't answering the question, except by implied omission ... aka *lying* by omission. >8^D
It's (badly) analogous to if your S.O. asks you whether you're having an affair with a particular person. And you answer: "No, I'm not having an affair with *that* particular person." Sure, we all know ¬(A⇒B)⇒A⋀¬B. But that's not what gpt said, which was "the formula on the right is true *only* if the formula on the left is true". I'm guessing that would mean ¬B⇒¬A. And I'm further guessing the only way we can get to that is if we swap out the ⇒ with a ⇔ in the discussed premise. Brevity is your enemy. Previously, I asked gpt to contrast Richard Rorty and CS Peirce. It gave me this super simplified answer that woefully misrepresented both. They've weighted ChatGPT (at least) so heavily to brevity and summarization that the summaries are either flat out wrong, or (like Frank did here) fail to target the subject being discussed entirely. I think they could compensate by weighting rare tokens more heavily than common tokens. I'm sure they already do that to some extent. But whatever methods they're using aren't working very well. I want to say something about how LLMs might be able to get at *a* logic (or a finite number of logics) exhibited in our text(s), but won't be able to get at *theories* of logics, the kind of distinction Beall (via Weber) seems to be making in that book review. Whether one is tolerant of inconsistency (like me) or insists on metalanguages for resolving paradox is irrelevant. What matters is that a bot that can use either method will outperform one that can't. But, of course, I shouldn't say anthing of that sort, because I'll demonstrate my incompetence even more than I already have. What's the old saying? It's better to keep your mouth shut and appear stupid than to open it and show everyone you are stupid? Oh well. I guess that ship's sailed. 8^D On 12/27/22 11:04, Frank Wimberly wrote:
My definition is consistent with that. The only state of affairs excluded by A implies B is A is true and B is not. The truth table for A implies B is: A B A implies B T T T T F F F T T F F T --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Tue, Dec 27, 2022, 10:57 AM glen <geprope...@gmail.com <mailto:geprope...@gmail.com>> wrote: Well, I'm probably confused because I'm trying (and failing) to read this at the moment: Paradoxes and Inconsistent Mathematics https://ndpr.nd.edu/reviews/paradoxes-and-inconsistent-mathematics/ <https://ndpr.nd.edu/reviews/paradoxes-and-inconsistent-mathematics/> But I'm on Eric's side, here. "A⇒B" does not mean B can only be true when/if A is true. A can be false while B is true. But when A is true, B must also be true. So the set of conditions where B obtains can be larger than the set of conditions where A obtains. On 12/27/22 09:22, Frank Wimberly wrote: > A implies B is false iff A is true and B is false. > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz, > Santa Fe, NM 87505 > > 505 670-9918 > Santa Fe, NM > > On Tue, Dec 27, 2022, 10:15 AM David Eric Smith <desm...@santafe.edu <mailto:desm...@santafe.edu> <mailto:desm...@santafe.edu <mailto:desm...@santafe.edu>>> wrote: > > Are you sure Frank? > > The sentence from gtp that I highlight said: > >> "⊃" is the logical symbol for "implies." It is used to form conditional statements in which the formula on the right is true only if the formula on the left is true. > > As I understand “implies” (or just the conditional if A then B), it means that the formula on the right is true _if_ the formula on the left is true. Not “only if” as gtp is quoted to say above. Correct would be “the formula on the right is _false_ _only if_ the formula on the left is _false_. Conditional doesn’t say anything about whether B is true or false if A is not true. > > Eric > > > >> On Dec 27, 2022, at 11:46 AM, Frank Wimberly <wimber...@gmail.com <mailto:wimber...@gmail.com> <mailto:wimber...@gmail.com <mailto:wimber...@gmail.com>>> wrote: >> >> I've taken courses in formal logic at multiple levels. All that notation is familiar and the explanation seems correct if vacuous. >> >> --- >> Frank C. Wimberly >> 140 Calle Ojo Feliz, >> Santa Fe, NM 87505 >> >> 505 670-9918 >> Santa Fe, NM >> >> On Tue, Dec 27, 2022, 3:19 AM David Eric Smith <desm...@santafe.edu <mailto:desm...@santafe.edu> <mailto:desm...@santafe.edu <mailto:desm...@santafe.edu>>> wrote: >> >> Interesting. Lack of global awareness duly noted. >> >> But also, can you check me on this?: >> >> > On Dec 26, 2022, at 7:21 PM, glen <geprope...@gmail.com <mailto:geprope...@gmail.com> <mailto:geprope...@gmail.com <mailto:geprope...@gmail.com>>> wrote: >> > >> > This exchange was interesting. I've never seen ⊃° used. >> > >> > ⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄ >> > me: What is the difference between ⊃ and ⊢. >> > >> > gpt: The symbol "⊃" is the logical symbol for "implies." It is used to form conditional statements in which the formula on the right is true only if the formula on the left is true. For example, the formula "A ⊃ B" can be read as "A implies B," and it means that if A is true, then B must also be true. >> >> Am I somehow blanking on ordinary sign-flips, or mistaking left and right? >> >> Seems B Is true _if_ A is true. B is false _only if_ A is false == If A is true, then B must also be true. >> >> Given that English is not ensured to have any global internal logical consistency, one can see making sentences that don’t close internally. But in areas where English is capable of being used with internal consistency, I am surprised to see an “only if” transposed with an “if” everywhere. Did I completely misunderstand what “implies” means? >> >> >> On all this I feel completely exposed: I thought I remembered from Quine’s little book on propositional calculus that “implies” isn’t even an elementary operator; only enters in a context like modus ponens for proofs. In first-order logic one was supposed to write expressions such as “B or not(A)” to mean “if A then B”. And there was some other symbol (even simpler than the entails) for that conditional. >> >> Eric
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