On 10/30/2012 12:51 PM, Bruno Marchal wrote:
On 30 Oct 2012, at 17:04, meekerdb wrote:
On 10/30/2012 4:30 AM, Bruno Marchal wrote:
My argument is that concepts of truth and provability of theorems
apply only to the concepts of numbers and their constructions, not
to numbers themselves.
Truth applies to proposition, or sentences representing them for
some machine/numbers. If not, comp does not even makes sense.
So your are agreeing? "Two" has no truth value, but "Two equals one
plus one." does.
Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert
that the truth of, say "Two equals one plus one." depend on some
numbers or subject having to discover it, or prove it.
My point is that a number is not a capable of being an ontological
primitive *and* having some particular set of values and meanings. A
statement, such as 2 = 1+1 or two equals one plus one, are said
truthfully to have the same meaning because there are multiple and
separable entities that can have the agreement on the truth value. In
the absence of the ability to judge a statement independently of any
particular entity capable of "understanding" the statement, there is no
meaning to the concept that the statement is true or false. To insist
that a statement has a meaning and is true (or false) in an ontological
condition where no entities capable of judging the meaning, begs the
question of meaningfulness!
You are taking for granted some things that your arguments disallow.
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