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

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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

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.

> 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.
True logical entailment requires semantic relevance.

True logical entailment must be anchored in the set theory operations 
performed on conceptual classes.

3. Model-theoretic consequence
All monarchs are human beings. No human beings are infallible. Therefore 
no infallible beings are monarchs. Boole would interpret the symbols 
P,Q,R as names of classes:

P is the class of all monarchs.
Q is the class of all human beings.
R is the class of all infallible beings.
Then he would point out that the original argument paraphrases into a 
set-theoretic consequence:

(P ⊆ Q),(Q ∩ R = 0) ⊨ ( R ∩ P = 0)
(a) Monarchs are a subset of People.
(b) The intersection between People and Infallible_Beings is the empty set.
(c) ∴ The intersection between Monarchs and Infallible_Beings is the 
empty set.
https://plato.stanford.edu/entries/model-theory/#Cons


-- 
Copyright 2020 Pete Olcott

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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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