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/ 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>> 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. EricOn Dec 27, 2022, at 11:46 AM, Frank Wimberly <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>> 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>> 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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