> On Apr 19, 2016, at 10:28 AM, Jerry LR Chandler > <jerry_lr_chand...@icloud.com> wrote: > > Pure mathematics avoids the concept of scaling, and its implication of > natural units. It makes no appeals to nature. For a pure mathematician to > appeal to nature would defy the Gods of the mathematical universe!
I suppose this depends upon what it means to appeal to nature. I recognize you are more concerned with discreteness in nature that’s not there in the same way in mathematics. (Perhaps) I do think though in other ways there is a relationship between nature and mathematics. (Perhaps unsurprisingly so given scholastic realism) Certainly there is a large class of mathematician who holds to a certain ideal of mathematical proof. I think that starting in the 70s with Putnam’s paper on semi-empirical methods in mathematics and continuing through the discovery of the four color problem via computer based “proof” that things are much more complex. There are also mathematical conjectures held to be true because of their fruitfulness in physics. Admittedly they are referred to as conjectures thus suggesting a somewhat diminished status. Related to the above there are the controversial proofs of Mochizuki who I believe mixes quite a bit of physics with his mathematics. (We’ll see if his latest proof of some important conjectures holds up) http://www.nature.com/news/the-biggest-mystery-in-mathematics-shinichi-mochizuki-and-the-impenetrable-proof-1.18509 I raise this not necessarily to disagree but to just suggest that things are more complex than they first appear - and perhaps in a fashion Peirce would have agreed with. (I think Putnam’s paper on semi-empirical methods is in its way very Peircean - it in particular makes me think of how metaphysics can be verified) Returning to the question of units and mathematics/nature if the unit of mathematics is the sign and we simultaneously embrace a semiotic realism as underlying nature then I wonder if they are different as they sometimes appear. That is, is the basic unit of nature really some finite spatial object?
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