On 11/3/2012 8:12 AM, Bruno Marchal wrote:

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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 consideredas the (only) object. truth concerns only the propositions aboutthose objects and the derivative notions.OK, then how is it that you seem to imply that truth isindependent 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 43depends 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. 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`

`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.`

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