Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR)

From	Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups	comp.theory, comp.ai.philosophy, comp.ai.nat-lang, sci.lang.semantics
Subject	Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR)
Date	2020-07-24 15:47 -0700
Organization	None to speak of
Message-ID	<87sgdgr0nj.fsf@nosuchdomain.example.com> (permalink)
References	<lO-dnTkq-vOt_YbCnZ2dnUU7-aHNnZ2d@giganews.com>

Cross-posted to 4 groups.

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olcott <NoOne@NoWhere.com> writes:
> Logical implication
>     p  q  p ⇒ q
> (a) T  T    T
> (b) T  F    F
> (c) F  T    T
> (d) F  F    T
>
> p = "I will go to the store"
> q = "I will buy eggs at the store"
>
> (a) I will go to the store and buy eggs while I am there is true
> (b) I will go to the store and not buy eggs while I am there is false
> (c) I will not go to the store and buy eggs while I am there is true
> (d) I will not go to the store and not buy eggs while I am there is true
>
> (c) I will not go to the store and buy eggs while I am there is true
> Proves that Logical implication derives incorrect consequences

No, it doesn't.  (c) just means if it were the case that you don't go to
the the store *and* you buy eggs at the store, p ⇒ q is still true.  The
fact that that's not possible (unless you buy eggs remotely? or maybe
you were born at the store?) doesn't make the conclusion invalid,
because that's what "p ⇒ q" *means*.

The impossibility of buying eggs without going to the store is outside
the scope of the original statement, and "p ⇒ q" doesn't say either than
you can do that or that you can't.  Choosing an example that has
implications beyond the meaning of "p ⇒ q" doesn't make "p ⇒ q" invalid.

Let p be "it rains" and q be "I will carry an umbrella", so p ⇒ q is "If
it rains, then I will carry an umbrella".  (Note that "⇒" doesn't carry
the same implication of causation that the English if/then construct
sometimes does.)  If it *doesn't* rain tomorrow but I carry an umbrella
anyway (which is of course quite possible), that doesn't falsify the
statement that "If it rains, then I will carry an umbrella".

In other words, the statement
    If it rains, then I will carry an umbrella
is consistent with:
    It rains and I carry an umbrella.
    It doesn't rain and I carry an umbrella.
    It doesn't rain and I don't carry an umbrella.
but inconsistent with
    It rains and I don't carry an umbrella.
Only that last set of circumstances falsifies "p ⇒ q".

Yet again, you try to refute a statement in mathematical logic because
you dislike the way it's expressed in informal English words.

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips Healthcare
void Void(void) { Void(); } /* The recursive call of the void */

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Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 17:26 -0500
  Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) David Kleinecke <dkleinecke@gmail.com> - 2020-07-24 15:45 -0700
    Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 17:53 -0500
      Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Kaz Kylheku <793-849-0957@kylheku.com> - 2020-07-24 23:55 +0000
  Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 15:47 -0700
    Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 17:57 -0500
      Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 16:19 -0700
        Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 19:20 -0500
          Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 18:29 -0700
            Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-25 23:14 -0500
              Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) André G. Isaak <agisaak@gm.invalid> - 2020-07-25 23:13 -0600
      Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-25 00:34 +0100
        Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-24 19:51 -0500
          Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) André G. Isaak <agisaak@gm.invalid> - 2020-07-24 19:29 -0600
            Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) olcott <NoOne@NoWhere.com> - 2020-07-25 23:04 -0500
              Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) André G. Isaak <agisaak@gm.invalid> - 2020-07-25 23:05 -0600
          Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-25 02:39 +0100

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