Question on the universal correctness of mathematics

[Number Nine]

Maybe there is a break down in communication, but to say that our universe is a mathematical structure, is equivalent to saying it is a subset of mathematics. Tegmark claims that all our mathematical models (or at least the computable ones) are "physical" entities somewhere in the multiverse. The rules of a mathematical structure are mathematical, and thus i fail to see your point.

Mathematics is a discipline, not a "thing". A neuron is not "neurobiology", a government is not "political science", a collection of things with rules governing their behaviour is not "mathematics".

 

[Deveno]

Is there any purpose in this debate? Can there ever be an answer? This seems about as productive as Christians arguing with Muslims.

I, and others like myself, believe that the universe has always followed the same rules, that we discover those rules and learn more and more about their implications. I don't necessarily believe that, in some corner of a higher dimension, there are 5 euclidian solids floating around with the axioms and lemmas of all discovered and yet to be discovered mathematics. I just feel that reality exhibits certain properties, and that math is a way of taking the purest, most raw properties and using them.

Others feel that math is a human creation, and that(apparently) when we create math, the universe behaves accordingly.

Neither can be proven with science, though naturally I feel my own beliefs make the most sense.

one possible purpose of a discussion such as this, is to clarfy to yourself and others what it is you believe. the meanings of words are not precisely fixed, and when we understand more clearly the ways in which we each see things, it helps to communicate our ideas, we have a basis for deciding which analogies to make, for example.

the belief that the world acts in accordance with some fixed principles, which behave consistently, is not a new one, and i daresay held by a great many people. many of those people believe that mathematics is the purest and most unambiguous way to communicate this perceived behavior.

but even deterministic systems can exhibit behavior which is indistinguishable from non-determistic behavior. and some people see a conflict between a universe that "runs like clockwork", and the notion of personal choice and freedom, or even randomness.

furthermore, our best efforts to show that mathematics is itself free from contradiction (and for those people who believe the universe itself is free from contradiction, this is a necessary thing, since using an inconsistent mathematics to describe a consistent world is self-defeating) have met with some serious set-backs in terms of some justifiably famous incompleteness theorems (consider the analogy with the Heisenberg uncertainty principle, which posits a similar incompleteness in our abilty to measure, and thus know the world's behavior).

the tl,dr; version: some people believe Mathematics is Truth, but they can't prove it.

 

[disregardthat]

Well my point is that you express the former view but reject the latter, of which the latter seems to be a subset of the first.

If we accept that there is an external reality, then it is very hard to ignore platonism. If there certainly was an external reality, which we model to a certain degree of success then our mathematics must do the same!

Don't you see the difference between believing in platonic perfect forms in a non-physical realm, and physical objects in the physical world existing even though you haven't observed them?

The first one is almost a religious thing, and the second, in many regards just common sense.

 

[cmb]

This seems about as productive as Christians arguing with Muslims.

That's an outrageous analogy!

This is a bona fide point of 'natural philosophy', which intrinsically means there is 'no answer', so providing each party listens to each other's arguments, the learning and the 'philosophical act' is in the process of the debate itself. This is the fundamental inverse of a debate of religious zealots, who seek to destroy the argument for the sake of arriving at forcing an unprovable proposition and disallowing discussion.

So don't turn the thread into looking like a religious argument, please! Your're trying to close down the act of discussing [the nature of mathematics], exactly like a religious zealot would try to do.

 

[Hootenanny]

We are veering wildly from philosophy to utter nonsense here. I'm going to lock the thread, pending moderation.