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From: Daryl McCullough on 13 Aug 2010 06:49
In article <bf5be029-eddb-4306-8c37-63a4941e487f(a)g6g2000pro.googlegroups.com>,
Newberry says...
>
>On Aug 12, 8:48=A0am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
>wrote:
>> Newberry says...
>>
>> >Goedel's sentence is not true because it is vacuous, and we do not
>> >regard vacuous sentences as true.
>>
>> On the contrary! We certainly do.
>>
>> Look, *EVERY* theorem of pure first order logic is, in a sense,
>> vacuously true. For any other first-order theory, a sentence S
>> is a theorem if there is a finite conjunction A1 & A2 & ... & An
>> of axioms such that
>>
>> A1 & A2 & ... & An -> S
>>
>> is vacuously true. In a sense, then, logical deduction amounts to
>> showing that certain sentences are vacuously true, given certain
>> assumptions.
>>
>> Your goal of banishing the vacuously true sentences amounts to
>> banishing the use of logic.
>
>I do not think this is correct. For example
>
>P v ~P
>
>is a theorem of truth-relevant logic.
>
>P v ~P v Q
>
>is not. I suggest reading sectio 2.2.
>
>>
>> --
>> Daryl McCullough
>> Ithaca, NY
>

From: Daryl McCullough on 13 Aug 2010 07:35
Newberry says...

>I do not think this is correct. For example
>
>P v ~P
>
>is a theorem of truth-relevant logic.

If P is necessarily true, then P v ~P is vacuous, right?
So P v ~P is not always true.

--
Daryl McCullough
Ithaca, NY

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