[FRIAM] talking to bots is fun for everyone

Tue Dec 27 14:04:52 EST 2022

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 <gepropella at 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 <desmith at santafe.edu
> <mailto:desmith at 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 <wimberly3 at gmail.com
> <mailto:wimberly3 at 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 <desmith at santafe.edu
> <mailto:desmith at 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 <gepropella at gmail.com
> <mailto: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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> ꙮ Mɥǝu ǝlǝdɥɐuʇs ɟᴉƃɥʇ' ʇɥǝ ƃɹɐss snɟɟǝɹs˙ ꙮ
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