This is easy to see in a simplified situation of games, but harder to see in the situation of mathematics and the natural world. — Asphodelus
So here's a kind of anthropological explanation for the effectiveness of mathematics to the natural sciences. Of course our cosmos yields to the great book of mathematics, because a cosmos that didn't wouldn’t have us in it. In short, only a regular universe can harbor intelligence, and a regular universe is mathematically describable. — Asphodelus
How could it be that mathematics formulated in a priori necessity in the armchairs and heads of mathematicians, applies to the messy, far-off, contingent, natural world? — Asphodelus
How could it be that mathematics formulated in a priori necessity in the armchairs and heads of mathematicians, applies to the messy, far-off, contingent, natural world? — Asphodelus
For most practical purposes abstracts of academia math are used and only rarely truly new math is developed for practical situations. — Goldyluck
Mathematicians prosper as mathematicians by undermining previous mathematics, by thinking of new things to do — Banno
Most math is embedded in academia minds — Goldyluck
It isn't "formulated in a priori necessity in the armchairs and heads of mathematicians".
That's a relatively recent image of mathematics, a consequence of the advent of modern academia.
Mathematics is embedded in the world. — Banno
The game analog breaks down, because any move can be made to fit into the rules of a game in which part of the game is to re-write the rules. — Banno
The world is rich enough to exhibit multiple regularities, depending on how you look at it, and those regularities can be modeled in multiple ways. Still, when you get into the nitty-gritty of said modeling, you will quickly discover just how tightly nature constrains our efforts - ask any working scientist! For better or for worse, scientists aren't free to make any moves they wish. — SophistiCat
mathematics fits the world so well because the world just is "mathematical." — SophistiCat
Of course, that's one possible explanation. Another is that we expect to find structure, are constrained by our mental constitution to find structure, and that is why we find it. This isn't as neatly self-contained as the first explanation, since it doesn't explain why we are constituted this way and how it is that we exist at all, in contrast to this: — SophistiCat
But what if there is some truth to the second possibility? What if the world is not quite as regular as our science implies, but we are biased against noticing this fact, because we have evolved to seek out and take advantage of regular structures? — SophistiCat
On the fundamental level of matter, space, and time, the world has proved to be extremely regular. Our best theories about these fundamental entities (QM and GR) make astoundingly precise predictions, — Asphodelus
I agree that with the above, but that does t necessarily mean the below follows from it. — Joshs
Saying the world is mathematical is like saying that it consists of propositional statements. — Joshs
On the other hand, you can't just make up anything and apply it anything equally successfully. It's a very tight fit, especially at the most basic (aka fundamental) level. This is what makes the fit seem to remarkable. — SophistiCat
I can think of two arguments against this possibility.
1. Consider just how implausible it would be for the development of structure in the world--any structure, never mind galaxies, solar systems, complex molecules, life, or intelligent life--without regularity. — Asphodelus
2. On the fundamental level of matter, space, and time, the world has proved to be extremely regular. — Asphodelus
it has been asserted by a number of philosophers that the predicational logic underlying mathematics is not irreducible. There may be more ‘precise’ ways to render
the world than via a mathematical language. — Joshs
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