On 03 Nov 2012, at 16:39, Stephen P. King wrote:
On 11/3/2012 8:12 AM, Bruno Marchal wrote:
On 03 Nov 2012, at 12:24, Stephen P. King wrote:
On 11/3/2012 5:39 AM, Bruno Marchal wrote:
I don't consider truth as an object. The numbers can be
considered as the (only) object. truth concerns only the
propositions about those objects and the derivative notions.
OK, then how is it that you seem to imply that truth is
independent of 1p, i.e. that it is a valuation internal to
experience?
Explain me why how you think that the content of the primeness of
43 depends on experience, and of whom.
Dear Bruno,
The primacy of 17 or 43 or any other number is such that it can
be apprehended, at least in principle, by at least one entity
(please note that this is a lower bound concept!). This implies that
in the absence of that possibility of apprehension (by at least one
entity) that there is no such thing as primeness.
This is totally ridiculous, Stephen. With comp, it is obvious that the
primacy of 43 is conceptually far simpler than the (true) fact that
the primacy of 43 can be apprehended by a type of machine/numbers.
You are like a biologist telling Morgan that it is stupid to hope to
understand the genetic of the fly before understanding the genetic of
the zoologist.
Bruno
The "dependency" that I am claiming for the properties of numbers is
no different from the dependency of properties (in the sense of
being definite) for physical objects; there must exist some means to
determine or otherwise measure or prove what those particular
properties might be.
Finitists fail because they assume that only a finite number of
entities can in principle exist that can determine the properties of
some arbitrary number. (See Normal J. Wildberger's ideas for an
example of finitism in mathematics) I propose that there are an
infinity of possible worlds, each with a potential infinity of
entities that can, at least in principle, determine the properties
of any arbitrary number. This is the same idea, I think, as Godel's
infinite tower of theories, each of which can determine the truth
value for any theory which is a subset of it or implied to exist
by it.
I am just inverting the idea of the Forcing axiom of Cohen. I
start with an ambiguous notion of the One and reduce it down to
where it is a fragment, a monad, a subset of the totality of all
possible, and yet it reflects all of its ancestors as it is
never not a proper part of the One. This is just an elaboration of
Leibniz' idea of monads...
The idea that a property has content is nonsensical, IMHO.
Primeness (of numbers) is a property of numbers, and like any other
object, they are nothing more than bounded bundles (clopen sets?) of
properties defined in relation to other bounded bundles of
properties. Only the One is isolated and independent of all things,
as it *is* all things! It cannot be "aware" of anything other than
itself, by definition.
--
Onward!
Stephen
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