
Re: LOGIC & MATHEMATICS
Posted:
Jun 2, 2013 4:11 PM


On Jun 2, 7:47 am, "Julio Di Egidio" <ju...@diegidio.name> wrote: > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote in messagenews:418e3c14341f41db9b668b7eca02f602@ve4g2000pbb.googlegroups.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:25a5a645596c42e8a0722df31dfc6b25@z10g2000pbn.googlegroups.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 higherlevel 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/sciencenews/isnatureunna... > > > 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 prelogical / premathematical. > > > 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. > > Julio
Mathematical logic and the technical philosophy of objects is basically the language of abstraction of which theory is.
I agree that a reductionist program isn't necessarily good if the foundation is not sound, here consistent and complete. Here it may be that a consistent theory need not be complete to be sound, but, as of a theory of its objects, the incomplete theory is not the theory of those objects, but a fragment.
Then where for example modern mathematics approaches questions of the universal with what would be the same questions left unanswered (and expressly ignored) for from the finite, it could be that particular reductionism was incorrectly followed as the course (here for example that additivity of the continuum of reals is left in the countable for results, that could only be in the continuum of reals, and that a cumulative hierarchy is then of the universe, but not itself).
So I'd agree that there's a danger to reason of improper reductionism, toward "as simple as possible, but no simpler", in terms of the soundness (here consistency and completion) of the resulting theory.
Some have that the numbers do affect physics, "meta" physics aside. For example the interview with Gross has him declare Platonism, as a physicist. As objects of reason, objects of here a mathematical physics have that indeed, mathematics had led our theories of mathematical physics, where these days, the data of experimental physics with the massive body of primary research in experimental physics, sees now in many cases a demand for the theory for the data, after the data. Of course, there are many discoveries of the experimental as of accidents in the laboratory, still there was the mathematics to then detail these effects. It's clear that whatever effects there are of the utterly micro and macro, that mathematics of the infinitesimal and infinite would detail them: lacking the mathematics of the infinite and infinitesimal as to there are _features_ and _effects_ of the numbers, _in the numbers_, has that then building theory from the misplaced reductionist foundations, is futility.
It's not even unreasonable to be anthropocentric for physics, though that may well be seen as simply mesocentric, and a false reductionism is too simple for all the rich interactions of all objects, still abstraction for theorization is as to reductionism. Here then in the most extreme of the macro and micro, then it is as to what may be called the "paradoxical" of the simplest and most complex, that the very state of affairs is "natural", and there are only paradoxes in inconsistent, or incomplete theories, as sound.
Then, there's very much the use of logic for mathematics for mathematical physics for sciences of physics, and a Platonist may have that all pure mathematics is applicable, for what it is, then as responsible to science: logic's mathematics in as to the universe and the point serves its purpose in the applied.
It's not unreasonable to question a reductionism, as the very act of theorymaking, as reductionism. Or, "it should be as simple as possible, but no simpler, and not wrong".
Regards,
Ross Finlayson

