"Ross A. Finlayson" <firstname.lastname@example.org> wrote in message news:email@example.com... > 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:firstname.lastname@example.org... >> >> >> 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. > > Popular articles in physics these days often ask: where is our > mathematics for our physics or data? > > https://www.simonsfoundation.org/features/science-news/is-nature-unnatural/ > > 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.)
Indeed no, it's the reductionist program that makes of the qualitative a weak version of the quantitative, that reduces all science to calculus, that reduces cosmos, life and intelligence to a machine (that is, nota bene, much less than mathematics itself): the title is not so misleading, after all.
> 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.
As already argumented, those are rather pre-logical / pre-mathematical.
> 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? <snip>
Numbers cannot affect physics, numbers are objects of thought, the whole thing has the cart before the horses, and the facts you talk about are the facts of numbers and of numbers only. This is not to deny the amazing effectiveness of mathematics to support the understanding of the world, of all worlds, but the reductionist program just gets rid of the world, and of all demarcations.
I won't object to your post line by line: overall, you express the very position that I am questioning.