The question isn't whether metaphysics is significant or meaningful, though how anyone could affirm the negative on that score without undermining their own conclusions, is an obvious thorn in the side of those that do - so don't. Instead, the question is whether maths is of any metaphysical significance/relevance. If you can't construct a sophisticated answer to the question, then just get yourselves a bag of popcorn. I'm not at all interested in hearing the usual spin.

In a few short paragraphs, I can undermine the metaphysical significance of empirical (observable) evidence. The question is, can the same thing be said about any/all mathematics?

Of course, maths deals with empirical evidence, so any maths on that score is going to carry the same null metaphysical (materialistic) weight as empirical evidence itself. But, not all maths correlates directly with the observable - which is why maths doesn't necessarily require empirical evidence to substantiate any claim thereof.

So, if maths does not have the same empirical requirements as science, does this then mean that [non-physical] maths is of metaphysical significance/meaning/relevance?

My answer would be a qualified 'yes', because in such instances mathematicians are talking about the truths of concepts which have no requirement to be verified in the non-metaphysical (observable) domain. One obvious example would be about the way mathematicians treat 'infinity' - but there are probably many more sophisticated examples which are beyond the scrutiny of all but a few of us. However, in such instances, what other means of assessment are available to us to determine whether mathematical conclusions are of metaphysical value?

Going back to our example of 'infinity'… there are 'proofs' which show that a certain definition of infinity can be proved to be correct. So, the proof is self-sustaining. But what does this show on the metaphysical front? Not much, for one major reason:

… There is no rational requirement that 'infinity' should have the specific definition that mathematicians impose upon it, least of all that there should be a mathematical proof of such a concept. Bear in mind that my own definition of 'infinity' correlates with absolute/definitive singularness. There is no absolute/definitive proof of singularness - note that maths proceeds conceptual understanding; it doesn't dictate it. Concepts fuel maths, not vice versa.

So, the point is that 'maths' proves fuck all, even when the maths we're talking about has no requirement to be empirically verified. The base concepts maths grounds itself upon - one, zero, infinity, etc. - are certainly of interest to metaphysicists, but what mathematicians have to say about them is of no relevance to the metaphysicist. The mathematician - supposing he/she has an interest in metaphysics - must first prove that their conceptualisation of any given notion is metaphysically rational, prior to blinding us with their seemingly complex symbols.

This is why the mathematical treatment of 'infinity' fails to undermines Zeno's fundamental argument against metaphysical (read 'real') motion. There are other examples we can discuss. However, for now, my response to the question I posed in the thread-title is 'yes' - maths is metaphysically significant because it deals with concepts which are significant to metaphysics. BUT, 'no', mathematicians are fucking everything up on the metaphysical front, for they are basing their [seemingly] good maths on duff conceptualisations… and then using their [seemingly] good maths to undermine metaphysical claims, such as the one Zeno made. And several others.

In other words, mathematics is almost as guilty as science of abusing our contemplations of metaphysical concerns. Twats.

Thank you.

math works. Metaphysics doesn't. Fuck metaphysics.

It's undeniable that math has metaphysical significance. The universe clearly has a mathematical structure. The list of mathematical properties seems unending: Atomic weight, the chart of the elements, the mathematical relations between properties and forces...

Maths & philosophy can be used to describe both existing [evidence rich] and non-existing [evidence poor] systems using logic. Just because a system can be described logically it is NOT a given that it exists just because the logic works. So we must remain technically agnostic about the "real" existence of ANY system. But a system that is evidence rich can be assumed to be 'working knowledge" and useful.
As evidence can change over time, it may be that previously non-evidenced systems can be confirmed with new data. All good. But so what? Nothing to see here folks, except the intelectual bankrupcy of metaphysical belief systems.

First of all it's called math. Don't make us come over there again!

SpeedOfSound wrote:First of all it's called math. Don't make us come over there again!

mathematics so math or maths is fine. And sound has velocity, not speed.

jamest wrote:So, the point is that 'maths' proves fuck all, even when the maths we're talking about has no requirement to be empirically verified. The base concepts maths grounds itself upon - one, zero, infinity, etc. - are certainly of interest to metaphysicists, but what mathematicians have to say about them is of no relevance to the metaphysicist. The mathematician - supposing he/she has an interest in metaphysics - must first prove that their conceptualisation of any given notion is metaphysically rational, prior to blinding us with their seemingly complex symbols.

jamest (on 28th June 2013) wrote:I'm not familiar with that term, 'asymptotic'.

Just how much do you know and understand about mathematics and especially pure mathematics (such as Analysis, Algebra) jamest?

DrWho wrote:It's undeniable that math has metaphysical significance. The universe clearly has a mathematical structure. The list of mathematical properties seems unending: Atomic weight, the chart of the elements, the mathematical relations between properties and forces...

Mathematics is a very precise and flexible language, and there aren't many structures that you couldn't, in principle, describe and model using maths - even extremely baroque and arbitrary structures straight out of your imagination. That we can use maths in science is hardly surprising, given the flexibility and precision of maths as a language. What you're you're implying, if I'm reading you correctly, strikes me as a bit silly. It would be like saying that, because you can describe a house to a given level of detail and informativeness, using only words in English, that the house has a metaphysically "English structure" at certain levels.

jamest wrote:Of course, maths deals with empirical evidence, so any maths on that score is going to carry the same null metaphysical (materialistic) weight as empirical evidence itself. But, not all maths correlates directly with the observable - which is why maths doesn't necessarily require empirical evidence to substantiate any claim thereof.

We don't know to what extent our math is determined by our human experience.

jamest wrote:Going back to our example of 'infinity'… there are 'proofs' which show that a certain definition of infinity can be proved to be correct. So, the proof is self-sustaining.

What "proofs" are you referring to here? The way you describe them makes me wonder what you are talking about.

jamest wrote: … There is no rational requirement that 'infinity' should have the specific definition that mathematicians impose upon it, least of all that there should be a mathematical proof of such a concept. Bear in mind that my own definition of 'infinity' correlates with absolute/definitive singularness. There is no absolute/definitive proof of singularness - note that maths proceeds conceptual understanding; it doesn't dictate it. Concepts fuel maths, not vice versa.

Which "specific definition of infinity" are you talking about?

jamest wrote:This is why the mathematical treatment of 'infinity' fails to undermines Zeno's fundamental argument against metaphysical (read 'real') motion.

Excuse me, but that statement is extremely weird. Motion isn't metaphysical. It is physical - it is clearly something that physics deals with - so why do you say it is metaphysical?

jamest wrote: and then using their [seemingly] good maths to undermine metaphysical claims, such as the one Zeno made. And several others.

What do you think Zenos metaphysical claim was?

DrWho wrote:It's undeniable that math has metaphysical significance. The universe clearly has a mathematical structure. The list of mathematical properties seems unending: Atomic weight, the chart of the elements, the mathematical relations between properties and forces...

Empirical significance is one thing, metaphysical significance another.

Given that there are those who think their confused brain farts are metaphysically significant, I doubt that mathematicians need overly concern themselves with metaphysical significance. The mathematics they do either works or it does not. And before you pick apart the term "works", it is indeed confined to the material, perceptible world here. The business of exploration of Deep Wibble and the Imperceptible Reality is not mathematics and is best left to those for whom metaphysical significance is important.

that's so meta-nigificant!

Blackadder wrote:Given that there are those who think their confused brain farts are metaphysically significant, I doubt that mathematicians need overly concern themselves with metaphysical significance. The mathematics they do either works or it does not. And before you pick apart the term "works", it is indeed confined to the material, perceptible world here. The business of exploration of Deep Wibble and the Imperceptible Reality is not mathematics and is best left to those for whom metaphysical significance is important.

Maths 'works' irrespective of its pragmatic value. Maths has its own means of self-assessment, just like reason/logic. The application of maths to physical order, is science.

jamest wrote:

Blackadder wrote:Given that there are those who think their confused brain farts are metaphysically significant, I doubt that mathematicians need overly concern themselves with metaphysical significance. The mathematics they do either works or it does not. And before you pick apart the term "works", it is indeed confined to the material, perceptible world here. The business of exploration of Deep Wibble and the Imperceptible Reality is not mathematics and is best left to those for whom metaphysical significance is important.

Maths 'works' irrespective of its pragmatic value. Maths has its own means of self-assessment, just like reason/logic. The application of maths to physical order, is science.

I wasn't referring simply to applied mathematics. Mathematics either works or does not according to its own formalism, if you prefer. Either way, metaphysical significance is irrelevant. Here's one for you. Let us assume that there were no humans, no human brains, no intelligent life, no observers, no atoms, fields, forces, no physical universe whatsoever. Where then would mathematics reside?

jamest wrote:

Blackadder wrote:Given that there are those who think their confused brain farts are metaphysically significant, I doubt that mathematicians need overly concern themselves with metaphysical significance. The mathematics they do either works or it does not. And before you pick apart the term "works", it is indeed confined to the material, perceptible world here. The business of exploration of Deep Wibble and the Imperceptible Reality is not mathematics and is best left to those for whom metaphysical significance is important.

Maths 'works' irrespective of its pragmatic value. Maths has its own means of self-assessment, just like reason/logic. The application of maths to physical order, is science.

There is the bit to wonder about.

If we claim that math applied to world is just science and has no meaning outside the application, then we can equally claim that logic applied to some human reasoning constructs is metaphysics and has no meaning outside the application.

Given that we are attempting to use reason and logic to figure all of this out we are left in a rather tight and squishy circle are we not?

when someone reasons "the only thing I can be certain of is X" what is left unspoken is how certain you are of reasoning.

From the OP:

jamest wrote:The base concepts maths grounds itself upon - one, zero, infinity, etc. - are certainly of interest to metaphysicists,

I'll bet they are. You must be very tempted to try usurping maths for your metaphysics, as you've tried in the past with various English words.

And, you might as well include -1 and -∞ in your concepts, if only for symmetry. Try adding all of your metaphysical concepts together.

but what mathematicians have to say about them is of no relevance to the metaphysicist.

That sounds close to an excuse for the mathematically illiterate to mangle maths to prop up metaphysical belief systems. When caught making basic errors in mathematical concepts, or even in basic arithmetic, you could cry, "Not fair! I'm using my own metaphysical understanding of 27! Maths has nothing to say about it!"

Humpty-Dumpty sat on the wall. Humpty-Dumpty didn't have a great fall. It was impossible for him to fall because, by his own definition of falling, falling was an impossible metaphysical contradiction of the concept that falling was metaphysically impossible. Just ignore the merely phenomenal bits of egg shell.

Darwinsbulldog wrote:Maths & philosophy can be used to describe both existing [evidence rich] and non-existing [evidence poor] systems using logic. Just because a system can be described logically it is NOT a given that it exists just because the logic works. So we must remain technically agnostic about the "real" existence of ANY system. But a system that is evidence rich can be assumed to be 'working knowledge" and useful.
As evidence can change over time, it may be that previously non-evidenced systems can be confirmed with new data. All good. But so what? Nothing to see here folks, except the intelectual bankrupcy of metaphysical belief systems.

Assuming the scientific evidence is correct and our brains are machinery, there are all kinds of questions around both truth and existence. Common sense takes for granted that there’s a clear and fundamental distinction between truth and falsehood, and between existing and non-existing, but as you say there are grey areas that don’t go away. I would say that maths does constitute an exception to pure empiricism, it’s as certain that the square root of 2 is irrational and not 1.5 as it is that horses exist and unicorns don’t, and the truth of Fermat’s last theorem and the existence of the Higgs boson depend for most of us on the agreement of experts; in both cases the agreement about maths doesn’t depend on empirical evidence.

We are biological robots with an unusual capacity for simultaneously cooperating and competing; I suspect strongly that both “truth” and “existence” are primarily matters of social agreement. Maths is one of the few areas where we agree extensively and in detail without being able to point to things outside our bodies, we agree because our brains are similar and when doing maths we are cooperating. At the same time, many of our thoughts, such as desires and beliefs, are often different because we are not cooperating and we can easily hide our brain activities from each other; our genetic interests differ and we are often keen to mislead other people (this is where we are different from most living things which cooperate as extensively as we do); the upshot is that we often think of thoughts as unreal because there isn’t social agreement.