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

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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. 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

-- 
To email remove 'invalid' & replace 'gm' with well known Google mail 
service.

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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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