On 10/30/2012 11:00 AM, Quentin Anciaux wrote:
2012/10/30 Stephen P. King <stephe...@charter.net
<mailto:stephe...@charter.net>>
On 10/30/2012 1:43 PM, Quentin Anciaux wrote:
2012/10/30 Stephen P. King <stephe...@charter.net
<mailto: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.
Bruno
http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
Dear Bruno,
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.
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).
Quentin
Hi Quentin,
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?
So in your view, no humans (no consciouness) implies... 17 is prime or not is not
meaningful ? Only consciousness gives meaning to thing... yet it seems absurd that truth
value would disappear without consciousness.
If there were no humans, no human level consciousness, would it still be true that Holmes
assistant is Watson?
Brent
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