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

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olcott <NoOne@NoWhere.com> writes:
> On 7/24/2020 6:19 PM, Keith Thompson wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>> On 7/24/2020 5:47 PM, Keith Thompson wrote:
>>>> 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
>>>
>>> You can't buy egqs AT THE STORE remotely
>>
>> If you were born at the store, then you don't have to go to the store to
>> buy eggs there.
>>
>>> (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*.
>>>
>>> Then "p ⇒ q" is a fricking God damned liar thus proving that symbolic
>>> logic is broken.
>>
>> Dude, calm down.
>>
>> "p ⇒ q" does not say or imply that it's possible for p to be false while
>> q is true, nor does it say or imply that it's not possible.
>
> Yes it does row three.
> https://en.wikipedia.org/wiki/Truth_table#Logical_implication

No it doesn't.  (Would it help if I "stipulate" that it doesn't?  Things
that are "stipulated" are true by definition, right?  Or are you the
only one who gets to do that?)

> The logically correct way that IF-THEN actually works is that it only
> specifies rows 1 and 2. The logically correct evaluation for rows 3
> and 4 is to leave those rows out.

Let's think of this in programming terms.  Think of "⇒" as a function
that takes two Boolean arguments and returns a Boolean result.  It can be
defined as (using C-like or C++-like syntax, think of it as pseudocode):

    bool "⇒"(bool p, bool q) {
        if (p and not q) return false;
        else             return true;
    }

That's all it means.  Its value is determined entirely by the values of
its arguments, not by any causal relationship between them.  If you
think it means something else, you're wrong.  It doesn't stop meaning
what it means because you don't like it.

I'm sure that makes you unhappy.  Would that be resolved by calling it
"foo" rather than "⇒"?

If you want to define a new operator that specifies rows 1 and 2
and leaves rows 3 and 4 out, of course you can do that.  But that's
a different operator than "⇒" the way it's universally defined.
And the fact that it doesn't specify a result for all arguments is
going to have consequences.

Your new operator is not likely to be useful.

Again, "⇒" isn't about causation.

>> All "p ⇒ q" says is that *either*:
>>      p is true and q is true
>>      *or*
>>      p is false and q is true
>>      *or*
>>      p is false and q is false
>> *but*
>>      it is not the case that p is true and q is false
>>
>> There may well be other reasons why one or more of those three
>> cases might not be possible.
>>
>> "p ⇒ q" means "not (p and not q)".  That's *all* it means.  It doesn't
>> carry the implication of causation that the English if/then construct
>> sometimes does.  Is "not (p and not q)" a "fricking God damned liar"?
>
> It causes incorrect inference to be made.

Not if you understand it correctly.

To be clear, are you saying that "not (p and not q)" causes incorrect
inference to be made?  Am I not allowed to say that "either p is false,
or q is true, or both" without being called a liar?  (I presume you'll
acknowledge "not (p and not q)" is equivalent to "either p is false, or
q is true, or both".  Perhaps I shouldn't make that presumption.)

> True logical entailment requires semantic relevance.

If that's true, then "⇒" isn't about "true logical entailment".
What makes you think it is, or that it should be?

You're simply talking about something other than "⇒".

[digression snipped]

-- 
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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