On 10/30/2012 1:43 PM, Quentin Anciaux wrote:
2012/10/30 Stephen P. King <stephe...@charter.net
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
Hmm... but that's what arithmetical realism is all about... If you
deny meaning to '17 is prime' absent an entity which gives to it its
meaning... then you're simply negating arithmetical realism and with
it computationalism (ie: consciousness is emulable qua computatio).
Well, therefore I must reject arithmetical realism as "unreal" by
definition! Individual entities are incapable of "giving meaning" to
things, be they puppies or prime numbers. It requires an *agreement
between many entities* to have meaningfulness. I claim that it takes at
least three entities...
If objects that are proposed to be "real" are not observable by
anyone then they don't exist! Where am I going off the rails? I think
that the problem here is that the distinction between "not observable by
any particular entity" and "not observable by any entity" are being
confused. I am reminded of Einstein's silly quip about the Moon still
existing even if he was not looking at it. The poor old fellow neglected
to notice that he was not the only entity that was capable of being
affected by the presence or non-presence of the Moon!
You might have seen my definition of Reality. Do you recall it?
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