From: Jesse F. Hughes on
Newberry <newberryxy(a)gmail.com> writes:

> On Aug 12, 6:41 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
>> "Jesse F. Hughes" <je...(a)phiwumbda.org> writes:
>>
>> > Newberry <newberr...(a)gmail.com> writes:
>>
>> >> Goedel's sentence is not true because it is vacuous, and we do not
>> >> regard vacuous sentences as true.
>>
>> > It is funny, then, that the overwhelming majority of respondents here
>> > *do* regard vacuous sentences like Goedel's theorem as true.
>>
>> What's vacuous about Gödel's theorem or the Gödel sentence of a theory?
>
> Nothing vacuous about Gödel's theorem. At least I would not put it
> that way.

Yes, I meant Goedel's sentence, not theorem.

Sorry.

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From: Jesse F. Hughes on
Newberry <newberryxy(a)gmail.com> writes:

>> > Wow! We are making a lot of progress. (Actually it is ~(T v F)
>> > regardless if Qm is true.)  
>>
>> No, we're not.
>
> It is disappointing. You need to read chapter 2.2.

Oh, I recall (now) your odd beliefs about vacuity. I just think
they're unmotivated.

Take a simple deductive rule: v-elimination, that is:

|- P v Q |- ~Q
---------------
|- P.

It seems to me that this rule is very hard to understand, given your
ideas. As soon as I prove that P is true, P v Q is neither true nor
false ... despite the fact that I have (by assumption) proved P v Q
prior to deducing P. I suppose I have to retroactively judge that my
purported proof of P v Q was not a proof after all, since P v Q is not
true.

--
Jesse F. Hughes
"[I]f gravel cannot make itself into an animal in a year, how could it
do it in a million years? The animal would be dead before it got
alive." --The Creation Evolution Encyclopedia
From: Jesse F. Hughes on
Newberry <newberryxy(a)gmail.com> writes:

> On Aug 12, 9:54 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote:
>> Newberry <newberr...(a)gmail.com> writes:
>> >> > Wow! We are making a lot of progress. (Actually it is ~(T v F)
>> >> > regardless if Qm is true.)  
>>
>> >> No, we're not.
>>
>> > It is disappointing. You need to read chapter 2.2.
>>
>> Oh, I recall (now) your odd beliefs about vacuity.  I just think
>> they're unmotivated.
>>
>> Take a simple deductive rule: v-elimination, that is:
>>
>>   |- P v Q  |- ~Q
>>   ---------------
>>   |- P.
>>
>> It seems to me that this rule is very hard to understand, given your
>> ideas.  As soon as I prove that P is true, P v Q is neither true nor
>> false ... despite the fact that I have (by assumption) proved P v Q
>> prior to deducing P.  I suppose I have to retroactively judge that my
>> purported proof of P v Q was not a proof after all, since P v Q is not
>> true.
>
> Truth-relevant logic is not classicl logic, and this rule is probably
> not compatible with it.

I think you need to reconsider this judgment. The same reasoning
applies to, for instance, Modus Ponens.

If P -> Q is provable and P is provable, then Q is provable and hence
Q is necessarily true. But if Q is necessarily true, then P -> Q is
vacuously true (right?) and hence neither true nor false.

Similarly for Modus Tollens.

So, it seems as if MP and MT are not rules of your truth-relevant
logic. Does that seem right to you?

--
Jesse F. Hughes
"[M]oving towards development meetings for new release class viewer 5.0
and since [I]'m the only developer, easy to schedule."
--James S. Harris tweets on code development
From: Jesse F. Hughes on
Newberry <newberryxy(a)gmail.com> writes:

> On Aug 13, 6:00 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote:
>> Newberry <newberr...(a)gmail.com> writes:
>> > On Aug 12, 9:54 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote:
>> >> Newberry <newberr...(a)gmail.com> writes:
>> >> >> > Wow! We are making a lot of progress. (Actually it is ~(T v F)
>> >> >> > regardless if Qm is true.)  
>>
>> >> >> No, we're not.
>>
>> >> > It is disappointing. You need to read chapter 2.2.
>>
>> >> Oh, I recall (now) your odd beliefs about vacuity.  I just think
>> >> they're unmotivated.
>>
>> >> Take a simple deductive rule: v-elimination, that is:
>>
>> >>   |- P v Q  |- ~Q
>> >>   ---------------
>> >>   |- P.
>>
>> >> It seems to me that this rule is very hard to understand, given your
>> >> ideas.  As soon as I prove that P is true, P v Q is neither true nor
>> >> false ... despite the fact that I have (by assumption) proved P v Q
>> >> prior to deducing P.  I suppose I have to retroactively judge that my
>> >> purported proof of P v Q was not a proof after all, since P v Q is not
>> >> true.
>>
>> > Truth-relevant logic is not classicl logic, and this rule is probably
>> > not compatible with it.
>>
>> I think you need to reconsider this judgment.  The same reasoning
>> applies to, for instance, Modus Ponens.
>>
>> If P -> Q is provable and P is provable, then Q is provable and hence
>> Q is necessarily true.  But if Q is necessarily true, then P -> Q is
>> vacuously true (right?) and hence neither true nor false.
>>
>> Similarly for Modus Tollens.  
>>
>> So, it seems as if MP and MT are not rules of your truth-relevant
>> logic.  Does that seem right to you?
>
> Theorem: The rule of modus ponens is compatible with TR:
> |- A, |- A -> B
> -----------------
> |- B
> Proof:
> A -> B is equivalent to. ~A v B. A and ~A v B are t-relevant by
> hypothesis. ~A is false.
> Assume B is not t-r. Then there exist a variable q such that q = U and
> B = T (for all
> possible valuations of B.) Then ~A v B = T contrary to the assumption.
> This is the case even if q is relevant in A. Then for q = U, A can
> take either U or T. But in either case ~A v B = T. Hence q is not
> relevant in ~A v B. QED.

Seems to me that your above argument uses v-elimination, which you
just suggested is not compatible with T-relevant logics.

In any case, I thought that if Q is necessarily true, then P -> Q is
vacuous. Is this incorrect?

--
"Every major result I have has been preceded by lots of stupid
mistakes. And I mean REALLY stupid mistakes. So making stupid
mistakes tells me that I'm in pursuit of something."
-- James S. Harris