Re: Fitch's paradox and OWA

On Dec 31, 4:57 pm, Nam Nguyen <namducngu..._at_shaw.ca> wrote:
> Marshall wrote:
>
> >> I asked you before:
>
> >>    "(1) There are infinite counter examples of GC.
>
> >>     Tell me what you'd even suspect as a road-map to assign true or
> >>     false to (1)?"
>
> > You keep assuming that the mere fact that a sentence is
> > undecidable means that it has some definite truth value
> > that is not one of {true, false}. Apparently you just take
> > this as a given. I, however, regard it as a false statement.
>
> I'm not assuming anything in asking you the question, Marshall.
> If a simple question that you, I, or anyone could either know
> or don't know the answer.
>
> If I'm to answer the question I'd say I don't know of any possible
> road-map. If you you think (1) is false, as you seem to have so,
> present your road-map, reasons based on the _accepted definitions_
> of FOL models etc...to back it up
>
> Don't just evade the question and hope that people would understand
> your argument!

I have no opinion on whether (1) is true or false. I don't believe that question to be relevant to the question of whether statements in arithmetic are either definitely true or definitely false.

Suppose I tell you I have a natural number in mind, but it's impossible for you to know which natural number it is. However we all know that this natural number can be encoded as a binary string. Let me ask you a question about this number: does its representation as a binary string contain any characters in it besides "0" and "1"?

You don't need to know which number it is to answer this question. Likewise, you don't need to know the truth or falsity of (1) to know that its truth-value is limited to being one of those two.

Marshall Received on Fri Jan 01 2010 - 03:08:21 CET