On 10/30/2012 10:39 AM, Stephen P. King wrote:
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,
I think you are confusing the tokens "2 = 1+1" with the proposition 2 = 1+1. The former
requires someone who understands the notation to interpret it, but the latter is the
interpretation, i.e. the concept. A concept has meaning by definition, otherwise we say
we cannot conceptualize it, e.g. klognee flarbles myrable, and so there is nothing to
assign a truth value to.
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!
That sounds like idealism, but whatever it is sll theories that will explain the world to
us are going to have to apply to times and places where there are no humans. So I guess
the question is whether 2=1+1 means to you what it means to the rest of us. If it does it
can be part of our explanation.
Brent
You are taking for granted some things that your arguments disallow.
--
Onward!
Stephen
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