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> 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/ > > 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. > > > > Eric > > > > > > > >> On 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 > >> > >> > >> > >> -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- > -.. . > >> FRIAM Applied Complexity Group listserv > >> Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p > Zoom https://bit.ly/virtualfriam < > https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,FACgozR-UqqCXQNuQwGDcUKOr9F8z9par_ZMWYigt5pt0zR5SRseqvtZvhgeXNhXZtJbOBMArZ894NdK7CRcE5elLELfxS5zueuLVPCUFvPwUnQ_&typo=1 > > > >> to (un)subscribe > http://redfish.com/mailman/listinfo/friam_redfish.com < > https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,Yhc5E5ab9UmYYG9HMLYkBuVWFStwPqiriJeHKTJEVbJx3gSi011Mhs_3KW7idMNg-N0XMR9DgpMC7rPIdS9XeZlcJ2U4se1WrqkjRwr_&typo=1 > > > >> FRIAM-COMIC http://friam-comic.blogspot.com/ < > https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,KjGjIbhNXx_Jkk8XVQeh0lyM3M6RydNqm286xij8qR8oHoHQcqigRNdtrPlFd2b8B98pogaXmWG6I4JoFfoHshueOTb-xfV86hrPhgpGlYoxVjU,&typo=1 > > > >> archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ < > https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,tKP0RmBbn5aXqMMP90FfZRUgR4SeRNAbCIPIHTmOOMKvYU9wbJQX8c6NaqJZF-ALbi5h5pfwbbR6XC7VfiNBZH8WQJvHUbf391P9nkUqxn-_LgrnFkGB5kRXKEY,&typo=1 > > > >> 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ < > http://friam.383.s1.nabble.com/> > >> > >> -. --- - 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