On Jun 1, 7:13 am, Nam Nguyen <namducngu...@shaw.ca> wrote: > On 01/06/2013 8:04 AM, Julio Di Egidio wrote: > > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote in message > >news:email@example.com... > > >> There's much to be said of the logicist's tools, plainly inference and > >> deduction, and the notion of most expressive theories with minimal > >> content in that they're foundations for higher-level theorems and > >> increasing abstration from the concrete, as to the concrete. > > > The tools are not the endeavour. Physics uses mathematics to a great > > extent, yet the initial and final words are to the facts of the physical > > world, not to those of the calculus. > > Agree. Mathematics is just a language, a description, of physics, not > the physical reality itself. > > By the same token, some of today mathematicians should realize that the > natural numbers (and truths of FOL language expressions about them) > don't exist as a concrete truths that logic has to reference, as they > tend to _wrongly believe so_ after Goedel's Incompleteness. > > -- > ---------------------------------------------------- > There is no remainder in the mathematics of infinity. > > NYOGEN SENZAKI > ----------------------------------------------------
Popular articles in physics these days often ask: where is our mathematics for our physics or data?
A misleading article title, for whatever is natural is natural, the notion is so that for physics: where there's reason for anything, that logic and mathematics and geometry are the only ways to have a science, for physics. (Plainly the qualitative is as simply logical as the quantitative, and there is found the quantitative in physics.)
Here in the context of the plainly and the purely logical, then there's a notion that the same rules of paucity and conservation and of balance and symmetry apply to each theory as natural.
Then, what are the _features_ of the numbers and spaces and of logic itself that would see in their natural carriage _features_ and _effects_ of the physical? Here to explain our rapidly expanding data of states and _effects_ in physics, then there's a notion that from the purely logical as to mathematics: there are _features_ and _effects_ of the _numbers themselves_, yet to be properly discovered.
In the numbers it's as to the infinite and infinitesimal. Then, where are derived from foundations: facts of the numbers themselves as they already are? Goedel's incompleteness isn't just that regular/well- founded theories have via diagonalization theorems not in the language: it's that there are facts about those objects not directly theorems of regular/well-founded theories. Where are derived new facts about the numbers, that aren't simply constructs outside not of the numbers of the continuum (trans-finite cardinals, hyper-reals) but _of_ them: of infinities and infinitesimals (ordinals and complete infinities, fluxions and the nilpotent): in the real, correspondingly: in the real.
I suggest that a theory of geometry of points and space, and of numbers as to the natural integers and to the natural integers redux: each as to the polydimensional, derived from zeroeth principles, is of its very being, the most truly fundamental (from the logical and monist). And, it is of relatively concise developments in the polydimensional: where _features_ and _effects_ of the numbers would extend _knowledge_, then fact and the empirical and scientific.
So: find applications, for physics, by discovering features and effects, of the numbers (of logic) as they already are.