'When Are Relations Neither True Nor False? [Logic]

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From: Nam Nguyen on 27 Mar 2010 12:15

Jim Burns wrote:
> Nam Nguyen wrote:
>> Marshall wrote:
>>> On Mar 26, 8:57 pm, Nam Nguyen
>>> <namducngu...(a)shaw.ca> wrote:
>
>>>> Or you're just full of babbling words with
>>>> no technical substance, as usual? [It seems
>>>> like a habit of yours that when you couldn't
>>>> technically counter your opponent's argument
>>>> then you just call him a mad dog!]
>>>
>>> I have never called you a mad dog that I can
>>> recall. My term for you is "talentless bufoon."
>>> So much more apropos.
>>
>> "A mad dog" is just an idiom expression. There's
>> a saying like "To kill a dog just call it a mad
>> dog". So your "talentless bufoon", here, is the
>> same as "mad dog".
>>
>> But you missed my point: in argument here, Marshall
>> has been "full of babbling words with no technical
>> substance", like an *intellectual clown*.
>
> So, are you calling Marshall a mad dog here?
> Apparently, you only object to that /sometimes/.

There are real mad dogs and there are real non-mad dogs.
There difference is in the real symptoms they really do
or do not exhibit. Naturally.

From: Daryl McCullough on 27 Mar 2010 12:46

Nam Nguyen says...
>
>Daryl McCullough wrote:

>> [G(PA)] is a *relative* truth. It's true in the standard interpretation
>> of the language of PA.
>
>So you've agreed "G(PA) can be arithmetically false"?

It is false in nonstandard models of PA.

--
Daryl McCullough
Ithaca, NY

From: Jim Burns on 27 Mar 2010 13:08

Nam Nguyen wrote:
> Jim Burns wrote:
>> Nam Nguyen wrote:
>>> Marshall wrote:
>>>> On Mar 26, 8:57 pm, Nam Nguyen
>>>> <namducngu...(a)shaw.ca> wrote:
>>
>>>>> Or you're just full of babbling words with
>>>>> no technical substance, as usual? [It seems
>>>>> like a habit of yours that when you couldn't
>>>>> technically counter your opponent's argument
>>>>> then you just call him a mad dog!]
>>>>
>>>> I have never called you a mad dog that I can
>>>> recall. My term for you is "talentless bufoon."
>>>> So much more apropos.
>>>
>>> "A mad dog" is just an idiom expression. There's
>>> a saying like "To kill a dog just call it a mad
>>> dog". So your "talentless bufoon", here, is the
>>> same as "mad dog".
>>>
>>> But you missed my point: in argument here, Marshall
>>> has been "full of babbling words with no technical
>>> substance", like an *intellectual clown*.
>>
>> So, are you calling Marshall a mad dog here?
>> Apparently, you only object to that /sometimes/.
>
> There are real mad dogs and there are real non-mad dogs.
> There difference is in the real symptoms they really do
> or do not exhibit. Naturally.

Please correct me if I misinterpret what you are saying:

Marshall called you a talentless buffoon, and that
was wrong, because you are not a talentless buffoon.
You called Marshall an intellectual clown, and that
was okay, because he is an intellectual clown.

I'm a little disappointed, because I thought your
argument went a little deeper, that it was an
objection to shouting down unpopular views by
burying them under a pile of nasty accusations.
That would have made you a hypocrite, of course,
for trying to do the very same thing to Marshall.

So all this is just a difference of opinion as to
whether you are a talentless buffoon, on the one
hand, and Marshall is an intellectual clown,
on the other? Then I guess it doesn't matter.

Jim Burns

From: Nam Nguyen on 27 Mar 2010 13:25

Daryl McCullough wrote:
> Nam Nguyen says...
>> Daryl McCullough wrote:
>
>>> [G(PA)] is a *relative* truth. It's true in the standard interpretation
>>> of the language of PA.
>> So you've agreed "G(PA) can be arithmetically false"?
>
> It is false in nonstandard models of PA.

Why don't we make it more precise. When we say F, a formula written
in the language of arithmetic, is true or false _by default_ we
mean it's being arithmetically true or false: i.e. true or false
in the natural numbers. So we're *not* talking about F is being
true/false in any general kind of models here.

The point is Alan said he wouldn't know what an absolute truth
of G(PA) would mean and I've implicitly defined it for him, and
here is the explicit version:

There's _no other_ context in which the meta statement
"G(PA) is arithmetically true in the natural number" would
be false.

The question I was hoping you'd answer one way or another is
whether or not there's a context in which the meta statement:

"G(PA) is arithmetically true in the natural number"

would be _false_ ?

If your answer is "yes", then the [arithmetically-in-the-natural-
number] truth of G(PA) is a relative notion. Otherwise it's an
absolute notion.

Which answer would you have? And perhaps why?

From: Daryl McCullough on 27 Mar 2010 13:48

Nam Nguyen says...
>
>Daryl McCullough wrote:
>> Nam Nguyen says...
>>> Daryl McCullough wrote:
>>
>>>> [G(PA)] is a *relative* truth. It's true in the standard interpretation
>>>> of the language of PA.
>>> So you've agreed "G(PA) can be arithmetically false"?
>>
>> It is false in nonstandard models of PA.
>
>Why don't we make it more precise.

What I said was already perfectly precise.

--
Daryl McCullough
Ithaca, NY