Michelangelo's Stone , contra Platonism

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Michelangelo's Stone , contra Platonism

Postby hyksos on April 9th, 2017, 10:00 pm 

Michelangelo's Stone :
an Argument against Platonism in Mathematics


by Carlo Rovelli (6 Sept 2015)

https://arxiv.org/abs/1508.00001

If there is a "platonic world" M of mathematical facts, what does M contain precisely? I observe that if M is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it is not independent from us. Both alternatives challenge mathematical platonism. I suggest that the universality of our mathematics may be a prejudice hiding its contingency, and illustrate contingent aspects of classical geometry, arithmetic and linear algebra.
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Re: Michelangelo's Stone , contra Platonism

Postby Braininvat on April 10th, 2017, 9:46 am 

Marshall, Neuro, and I have each posted this paper, maybe a half dozen times total. Probably should have had its own thread right from the start, heh.
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Re: Michelangelo's Stone , contra Platonism

Postby BadgerJelly on April 14th, 2017, 2:04 am 

Looks like something I should read
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Re: Michelangelo's Stone , contra Platonism

Postby Dave_Oblad on April 17th, 2017, 12:27 pm 

Hi All,

Carlo Rovelli's paper is a poor attempt to convince us that we Invented Mathematics rather than Discovered Mathematics.

In his Analogy to a Stone, he tries to convince us that the Stone represents Potential and is not very interesting as a simple Stone Block and that the act of carving such into a Statue makes it more interesting and is thus a Creative endeavor.

Firstly.. this is false speculation after the fact. As every Artist knows.. the Blank Stone or Blank Paper or Blank Canvas is the most exciting, as it represents the Potential to become anything the Artist wants. You may also note that for every artistic piece of work that makes it to public view, there exists dozens or even hundreds of versions that got scrapped as incomplete because the Artist didn't feel the project was progressing towards the ideal goal.

So, from the Artists point of view, the Potential is far more exciting, and thus more interesting, than the finished, or unfinished, products of their creative efforts. Very few Artists are truly satisfied with their finished products, it's more a matter of completing the effort.. so they can get started on their next project.. that is the driving force behind every true Artist.

Rovelli likens the Full Embodiment of Mathematics to the Potential of a Blank Stone. His intent is to argue that Man doesn't Discover Mathematics but rather Creates Mathematics, by the act of Carving away at the Full Embodiment of Math (the stone) to the finished product that is a minor subset of the Original Potential.

It is his intention to distract you from the observation that the Stone "Existed" in the first place, before the Artist can refine it into a selective set of choices to produces the final outcome that is arguably more interesting for Public Consumption.

Thus; Rovelli's whole argument rests on the assumption that Man has Created Mathematics by the act of reducing the Full Embodiment to a selective set of choices by said Artist or Mathematician.

The obvious Fallacy here is that by Reductionism, Man has Created Mathematics rather than Discover Mathematics. The Fallacy is, of course, that by Reductionism, the Artist has gotten more from the Stone than the Stone originally Possessed in it's original Potential Form.

Thus an attempt is made in this paper to convince us that: Selectivity equals Creativity.

While such an argument may seem rational, it attempts to ignore the simple fact that nothing can be selected that wasn't "Already" present in the Original Full Embodiment or.. the Original Stone.

Regards,
Dave :^)
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Re: Michelangelo's Stone , contra Platonism

Postby neuro on April 18th, 2017, 6:55 am 

The matter contained in the stone comprizes the matter contained in any of the statues you may sculpt out of it.
It does not contain the forms (idealized patterns and sets of relations) or the shapes of the statues.
Those are aspects that someone imposes onto it from the outside (whether they actually sculpt them or they only imagine them into the stone).
Exactly the same way as the interstellar vacuum does not contain as parts of itself all the possible paths a spaceship may travel in it.

As I proposed in another thread, you may claim that any dream you dream belongs to the realm of all possible dreams you may ever dream.
However, such set of all possible dreams is a pure abstraction. It does not exist per se.
Once you have dreamt a dream, you can state that that dream exists, if you wish. But before you dreamt it, it simply did not exist.
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