A question about physicalism/materialism

[Matt R.]

Physicalism (a more general form of materialism) holds that everything which exists possesses a physical property. Things that do not have this characteristic do not exist.

This implies that physics is the most basic form of knowledge, correct? In other words, fields such as logic and mathematics must have a physical basis as well (rather than the opposite, physics having a basis in math/logic). This follows from the definition of physicalism... math and logic exist, all things are based on physics, therefore math and logic are based on physics.

Intuitively, it seems like the opposite is true -- that physics is based on math and logic, and physical statements are derived based on math and logic. It seems like most other people feel this way as well (although this is just the general idea I get), and even the posts I read on this forum from materialists give me this idea. Am I incorrect in assuming this?

I know there are some people who take to physicalism and materialism on this forum. What are your thoughts on this?

[Phil153]

I've always enjoyed this discussion:

http://www.cs.auckland.ac.nz/~chaitin/md.html

[ChrisV]

This is a semantic question about the definition of "exists". For instance, you could argue like this: the martial art of karate has no substance and therefore doesn't exist, so karate competitions are a figment of your imagination. The problem is that karate isn't a thing, it's a description of a complex set of processes. Math and logic are processes, not things. If you define "exists" as "is a thing", then you come up with the answer that math and logic don't exist.

I think it's true to say that math and logic are derived from reality rather than being fundamental, though. As with science, the reason we use them is that they model reality accurately. Sometimes different mathematics is required to model different aspects of reality - e.g. Euclidean geometry for "real world" tasks and Riemannian geometry for the curvature of space-time, although the difference there is in the axioms rather than the process. Quantum computing is an example of a field where a new type of logic is having to be invented to describe reality.

[bigpooch]

"As far as the laws of mathematics refer to reality, they
are not certain; as far as they are certain, they do not
refer to reality." - Einstein.

Mathematical objects exist, but they do not necessarily have
much to do with physical existence.

Math and logic are not based on physics. Almost every
mathematician believes that in some sense, e, pi and i
exist, and the idea of i originated in the 16th century,
attributed to Gerolamo Cardano, who was famous for his
general solution to the cubic and quartic equations. Now,
physicists make much use of i and the metric in the space
we inhabit implicitly shows its "existence". It is almost
certain that i was originally used as an extension of the
number system to accomodate solutions to some equations
(just as negative numbers, rational numbers, etc. were of
use to denote solutions), not because of a need in physics.

Mathematical objects can be viewed as either creations of
the mind, or discoveries of objects that do not necessarily
have any relationship with the physical world. The theorems
of mathematics that are discovered are true, but they are
only true relative to the axioms that we start with; the
axioms are often very reasonable, but sometimes lead to
"strange" results.

Almost every professional mathematician accepts the axiom of
choice, since it is very intuitive, but leads to very
counterintuitive results, e.g., Banach-Tarski paradox:

http://en.wikipedia.org/wiki/Banach-Tarski


The problem with focussing on physical objects is that
empiricism and science gives us only understanding and not
certainty. Mathematics conveys truth only in relation to
the set of axioms, but at least it is certain.

Also, in philosophy, what exists may not necessarily have
any existence in physical reality.

[wazz]

Logical rules would still be true in the absence of reality (whatever that means), and so mathematical rules derived from logical truths would still hold. The mathematical rules wouldn't really be of any use, though, as they wouldn't have anything to describe, so e and pi would be meaningless.

To answer the OP, physics is not based on maths or logic, it's based on (for want of a better description) the rules of reality. It just so happens that they coincide quite nicely with certain man-made mathematical constructs.

[wazz]

[ QUOTE ]
I've always enjoyed this discussion:

http://www.cs.auckland.ac.nz/~chaitin/md.html

[/ QUOTE ]

Could you by any chance break this down for the relative layman? I studied maths at university for 2 years but never really studied geometry, or at least don't remember enough of it to even vaguely understand this.

[Matt R.]

My intuition tell me, and it seems bigpooch and wazz agree, that logical rules (and mathematical statements) would still hold regardless of physics.

For instance, it seems the statements 1 = 1, 1 + 1 = 2, and logical statements such as if p, then q; p therefore q are true irrespective of physics. (It just doesn't make sense to me to say that the statement "If p then q. p therefore not q." is contradictory because of physics).

If it is true that math and logic are correct irrespective of physics, then this implies physicalism and materialism cannot be correct. Unless there is a formulation of physicalism I am not aware of.

Phil's link I think is the best reponse to this... that was an interesting discussion. I think it is the best position to take for a physicalist. However, I still haven't accepted the idea that ALL mathematical theorems are dependent upon physics. For example, imaginary numbers have absolutely no real meaning in any physical system (yet they are used, abstractly, to describe oscillatory systems). I find it hard to grasp that these abstract concepts depend on physics... and not the other way around. There are countless other mathematical statements that have absolutely no application to the real world; in fact, there is an entire field dedicated to this (pure mathematics) and only on occasion do they find that their work can apply to physics.

Also, Chris, I think this is deeper than a semantic issue. It is quite a stretch to say that "math and philosophy don't exist" when all or nearly all of our knowledge is built from a logical framework. And, due to uncertainty in measurements I do not think it is a stretch to say that ALL of our knowledge is based on logic.

I guess I am just mildly surprised that physicalism and materialism are so popular in Western philosophy (and this forum). I think the statements that "physicalism and/or materialism are true" and "math and logic are more fundamental than physics" are contradictory, and it seems like most physicalists think both statements are true.