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.
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. 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
<http://web.maths.unsw.edu.au/%7Enorman/>'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
<http://en.wikipedia.org/wiki/Forcing_%28mathematics%29>. 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 itsancestors
<http://en.wikipedia.org/wiki/Lowest_common_ancestor> as it is never not
a proper part of the One. This is just an elaboration of Leibniz' idea
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.
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