On 10/30/2012 2:00 PM, 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.
Quentin
Unless multiple entities can agree that the sequence of symbols "17
is prime" is an indicator of some particular mathematical object and one
of its particular properties, then how does "17 is prime" come to mean
anything at all? Can you stop subconsciously assuming an invisible
observer whose sole job is to observe everything from infinity? It seems
that you cannot if what I am writing is mysterious to you!
How is it not absurd that meaningfulness exists in the absence of
anyone that can apprehend it? Please note that I am not considering the
absence of any one entity; I am considering the absence of all possible
entities in the degenerativeness or vanishing of meaningfulness. I am
asking "Why is it OK to think that meaningfulness exists in the absence
of any means to determine it?".
--
Onward!
Stephen
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