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

Subject Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V34 (Logical implication ERROR)
Newsgroups comp.theory
References (1 earlier) <87sgdgr0nj.fsf@nosuchdomain.example.com> <2Y6dnX93V_vr-obCnZ2dnUU7-VnNnZ2d@giganews.com> <87imecjxm4.fsf@bsb.me.uk> <VNSdnY4F1-y0H4bCnZ2dnUU7-IvNnZ2d@giganews.com> <rfg1tr$val$1@dont-email.me>
From olcott <NoOne@NoWhere.com>
Date 2020-07-25 23:04 -0500
Message-ID <Jt-dnYx36fMnnYDCnZ2dnUU7-LfNnZ2d@giganews.com> (permalink)

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On 7/24/2020 8:29 PM, André G. Isaak wrote:
> On 2020-07-24 18:51, olcott wrote:
>> On 7/24/2020 6:34 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> Then "p ⇒ q" is a fricking God damned liar thus proving that symbolic
>>>> logic is broken.
>>>
>>> This again.
>>>
>>> p ⇒ q means ¬p ∨ q.  If you forget the arrow and the word "implies" and
>>> just write ¬p ∨ q instead, you won't get upset.  You can't get rid of it
>>> because ¬p ∨ q is just one of the 16 ways in which truth values can be
>>> combined.  If it does not express what you want, that's because you
>>> picked the wrong connective to express the relationship.
>>>
>>
>> p = "I will go to the store"
>> q = "I will buy eggs at the store"
>>
>>      p  q  ¬p ∨ q
>> (a) T  T     T
>> (b) T  F     F
>> (c) F  T     T
>> (d) F  F     T
>>
>> (a) I will either not go to the store or buy eggs while I am there T
>> (b) I will either not go to the store or buy eggs while I am there F
>> (c) I will either not go to the store or buy eggs while I am there T
>> (d) I will either not go to the store or buy eggs while I am there T
>>
>> This is a quite backasswards way to say If I go to the store I will 
>> buy some eggs while I am there.
> 
> Note that your p ⇒ q does not translate to "If I go to the store I will 
> buy some eggs while I am there'. To the extent that it translates to an 
> English sentence it would be "If I will go to the store, then I will buy 
> eggs at the store". There's no 'while I am there' anywhere in that 
> statement.
> 
> You need to *stop* trying to think of logical connectives in terms of 
> natural language. Logic is not a theory of natural language, and its 
> connectives don't correspond to natural language constructions. More 
> importantly, logic doesn't *claim* that logical connectives correspond 
> exactly to natural language connectives. Every introductory logic text 
> will emphasize this within the first chapter or two.
> 
> None of the connectives ∧, ∨, →, or ¬ correspond to natural language 
> and, or, if...then, or not. That is because in natural language, every 
> single one of these connectives is ambiguous. 

I am not going to the store translates to what: I might go to the store?

All of the logical connectives correspond to their English counter-parts 
perfectly. (Except for the one that lies: "⇒").

That some people do not say what they mean or mean what they say is 
neither the fault of natural language nor it limimitation.

> In logic, each of these is 
> precisely defined to have exactly one meaning.
> 
> I suggest you simply stop thinking of ∧, ∨, →, and ¬ as 'and', 'or', 
> 'if..then' and 'not' and instead just think of them as 'caret', 
> 'turned-caret', 'right arrow', and 'broken dash'.
> 
> André
> 

We really need a way to say if p then q
if not p then no one knows about q.

To formalize natural language we need a correct underlying infrastructure.

That logic does not have the English IF-THEN makes some key elementary 
ideas inexpressible in logic.

-- 
Copyright 2020 Pete Olcott

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Thread

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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