On 1/17/2013 10:44 AM, WM wrote: > On 17 Jan., 17:38, fom <fomJ...@nyms.net> wrote: >> On 1/17/2013 4:52 AM, WM wrote: >> >>> On 17 Jan., 08:42, Ralf Bader <ba...@nefkom.net> wrote: >> >>>> In a similar way it seems to be >>>> impossible for M ckenheim to grasp something actually (not in the >>>> always-growing sense) countably infinite without a boundary at the far end. >> >>> Not at all! I consider and vivdly imagine the actually infinite set of >>> all terminating decimal representations of the reals containg all >>> natural numbers as indices. Alas I cannot imagine that there is >>> another decimal representations of the reals which deviates from all >>> of them. Can you? >> >> Then, do irrational numbers exist >> transiently on a problem by problem >> basis? (Vacuum energy numbers) > > They exist in many forms but certainly not as never ending decimal > representations that somehow manage to end or at least to be complete > nevertheless.
This is where I generally have a problem with what you are doing.
No question about the fact that the history of realism regarding the foundation of mathematics makes most of it comparable to Descartes' proof of the existence of God. But, in failing to provide reasonable alternatives (that is the hard part), you do nothing constructive. Thus Virgil is correct in referring to WMytheology.
You do bring up certain legitimate issues. For example, it it clear that the quantifiers are ambiguated. This probably comes from the structure of finite projective geometries,
Where the reversed order of non-zero entries on the first line is evident. It is not so difficult to imagine a "march to infinity" in terms of such geometries since one exists for every prime.
Moreover, if one treats the basic boolean functions as a "system," then truth-functional negation is nothing more than a certain projectivities of the 21-point plane with the boolean functions comprising the points of the associated affine geometry.
The ambiguation of the quantifiers is related to duality with respect to DeMorgan conjugation (negate the arguments..., then negate the connective. It works with the quantifiers viewed as unary truth functions.) and this too, can be modeled using finite projective geometry.