[FRIAM] talking to bots is fun for everyone
David Eric Smith
desmith at santafe.edu
Tue Dec 27 05:18:37 EST 2022
Interesting. Lack of global awareness duly noted.
But also, can you check me on this?:
> On Dec 26, 2022, at 7:21 PM, glen <gepropella at 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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