https://www.facebook.com/groups/529327040550143/posts/2363924313757064
INTERLOCUTOR:
What is Math?
The real question is this: what is an abstract mathematical object? Obviously, it is not just some physical thing. But also, it is not just an arbitrarily made-up idea. So, what is it? Hilbert thought it was a perfect game and a rational science, but math is not a science, or just a game. Brouwer's skepticism emphasized that we construct all of those math notions in our mind. Just like science, math cannot prove itself consistent, or understand itself through logic alone. Mathematics is more than just any given set theory, since it is also sets of ideas that quantify reality.
TP:
Math is just man-made patterns that can be used to express the laws of physics which are just cherrypicked mathematical patterns that supervene on reality
INTERLOCUTOR:
But they are not arbitrary conventions alone, otherwise math would have no power at all. They do correspond to actual patterns in reality, in some way, and that is what we should be looking at.
TP:
Right - because they supervene on reality they are useful. But not all equations supervene on reality. Thats why discovery is necessary.
INTERLOCUTOR:
Well, I am talking about why abstract objects have any power; viz. why they are part of reality. Supervene is a kind of fluff word, an additional consequence without really being important. Obviously abstract objects, and those of math, are important. Their power is not just some by-product, or additional product, but it is fundamental to what reality is.
TP:
The power is in reality. Math is merely a human language for describing that power. There is no power inherent in math. That's wizard talk - magical words and numbers.
Renowned physicist Sean Carroll's perspective on this issue - https://youtube.com/.../Ugkx4NYeE3QKjdNPMtoH7k11eVRlmG_Xa7lP
INTERLOCUTOR:
My question was: what is an abstract mathematical object? Math is not a language. That is a bad metaphor. Natural languages help us to create a social and ethical world, but math plays no part in that, or not as natural languages do. Math is not just arbitrarily made-up stuff. It has power because it corresponds to what quantifiable reality is. It has power through science. That is not the same as magic either.
Carroll is a physicist, not a philosopher. The world just cannot be only physical. That doesn't even make sense (since theories are ideas) and it certainly doesn't say anything about math. In particular, logical positivism has been discredited (in the 1950s) and totally debunked (in the 1970s), so physicalism-alone is not the answer.
TP:
Why does 1+1 = 2? This is ONLY true because our laws of physics allow for the accumulation of materials. If we lived in an antimatter-based world, 1+1 would equal 0, as each time things combine, they disappear rather than accumulate. We merely set up our mathematical axioms in such a way that they become useful to us by virtue of their coincidental supervenience on reality.
INTERLOCUTOR:
No, that is not how mathematics works, or how it is done. Mathematicians don't invent new math only to be of use to physics. Most of them know nothing about physics. Math is not based on usefulness. It is based largely on aesthetics, the aesthetics of internal coherence. You are just ignoring the real question: what are abstract objects? What are ideas? What are theories? None of those questions can ever be reduced to anything physical, because ideas are not physical.
TP:
I already answered this question - math is just a pattern in our minds. Abstract objects are only patterns in our minds. Ideas are only patterns in our minds. Theories are only sophisticated patterns in our minds.
INTERLOCUTOR:
Math is not just a pattern in our mind, or it would have no objective power. That doesn't make sense. Ideas are not just in our mind alone. You are not listening or responding to what I am saying.
TP:
Where is the evidence of the power of math?
INTERLOCUTOR:
People went to the Moon (and back) safely in 1969. Engineers build bridges and those bridges don't usually fall down (if they have been designed well).
TP:
That is not evidence that abstract objects have power. That is evidence that humans have power.
INTERLOCUTOR:
Why do humans have power?
TP:
Because we are concrete objects.
INTERLOCUTOR:
I don't see concrete objects doing very much, by themselves. That is a very silly comment. We have power because we can use reason, ethical goodness and imagination.
TP:
Concrete objects within the sun power our entire earth and make life possible. All power comes from energy. Concrete objects are made of energy.
INTERLOCUTOR:
That is a metaphysical claim, but it is wrong. Energy does not give us power. Directed energy in some intrinsic purpose gives us power, but the direction and purpose themselves are not reducible to anything physical. The ancient Greeks called reality nous, or mind. It is reason, ethical goodness and imagination that gives us power over inanimate material objects which do not have those attributes at all.
TP:
Mind is not possible without energy.
INTERLOCUTOR:
That does not mean that mind is energy. Mind is also not possible without direction and purpose, but they are both intrinsically non-physical.