I think that's arguable. (Which doesn't mean I'd want to advocate the opposite position myself, but I think it's interesting.) There might be absolute truths in aesthetics too - the fact that people argue about them doesn't change this, any more than the fact that some people think 3 x 17 = 53 alters what you said about mathematical truths.

No it doesn't of course, but let me put it another way: you could define mathematics, as some do, as being "the study of absolutely necessary truths", which implies that any other field of thought contains absolute truths only in so far as it's mathematical. I don't think aesthetics comes into that category. Nor do I think anyone thinks 3 x 17 =53, except possibly Ben Watson.

I suppose Maths has many areas of beauty.  I haven't ever really got into the maths of Bach, but gut-feel tells me his beauty is in proportion.  Perhaps subconsciously he was some sort of Mathematical Savant of Fibonnacci numbers, Primes, or some other series, who expressed himself in music rather than numbers....

Maths also has a dynamic beauty - Chaos theory and non-linear differential equations can give rise to some wonderful curves, which have movement in them.  I'm thinking of things like the Lorenz attractor.

And logic can be very attractive in the way that things fit together and don't contradict themselves - but isn't that something about the way logic works?

I think Douglas R Hoffstadter wrote about this relationship a lot in "Godel, Escher, Bach: An Eternal Golden Braid".  A long time since I read it, so I can't give more details.

But nowardays, I just view this as another aspect of how marvellous the brain is about linking concepts like Maths and Music.

Tommo

We've agreed on this point before. I think that however deep aesthetic objectivity may go, it's ultimately dependent on minds, while mathematical objectivity, appearing as it does to be fundamental not (just) to minds but to physical reality*, isn't. I think there's a clear distinction here, but I don't think I've quite put my finger yet on what. So I'll just throw it out in this form for now and see where it lands.

* ... as we experience it!

Mathematical truth is itself contingent upon certain things axiomatically assumed from the beginning (though the farther reaches of logic and set theory attempt to circumvent this). It can be said to be objectively true relative to these axioms, and also relative to an axiomatic assumption of the objective validity of the methods of deductive reasoning employed. A similar model might be able to be applied to the process of arriving at aesthetic truths.

Even the question of whether '3 x 17 = 53' is true or false depends on the construction of the numbers 3, 17 and 53 (that may seem an ultra-pedantic point, but it isn't from the point of view of set theory and the construction of numbers) and the definitions of the process of multiplication and the meaning of equivalence as represented by the equals sign.

I want to add some support to the Platonic/Kantian view here in terms of mathematical laws being abstracted. One can say that music obeys mathematical laws, but music has some sort of concrete existence (just in the sense of collections of sounds), some objective reality, which maths doesn't. I'd say it makes more sense to say that we can abstract some principles from music we find important which seem to concur with other abstractions from other phenomena. Maths is a philosophical construct (as is harmony, say, to allude to CD's post), a means for attempting rationalised understanding. The 'mathematical laws' only exist as an abstraction, 'why' music obeys these laws isn't to my mind the real question, rather why does it exhibit properties that can be mapped onto those of other objective phenomena?

I'm not just referring to the symbols, but the actual concepts themselves - that's what I mean by the 'construction of numbers', recalling long lectures when I was an undergraduate on how we can construct such a system so that additive principles work. 0 was the empty set, 1 was the set with 0 as a member, {0} (I would use the empty set symbol itself if I knew how to get it on here), 2 was  {0, 1} = {0, {0}} (I think!), 3 was {1, 2} = {{0}, {0, {0}}}, and so on (hope I've remember it correctly, it was a long time ago). So addition could then be defined by this process. Relative to that definition (and how you can build definitions of subtraction, multiplication, division, etc., from it), then it can be proved that, say, 3 x 17 = 53. Whether we replace 3 with £ and/or 17 with $ doesn't really affect this. By this type of view, I think the whole concept of 3 doesn't exist until we have defined it (this is the purest of pure maths, of course).

However, one could also argue that 3 (or 17 or whatever) are a priori categories of knowledge, and as such exist prior to any constructions of them such as that above. I'm not sure if the same could necessarily be said of multiplication or equivalence, though? We need those concepts as well as the concepts of the numbers in order to be able to prove that the proposition is true.

I've never had any epiphanies but I had a sort of hunch once that Group Theory might be an area of mathematics which would be fruitful for composers to draw on. Never followed it up though. Maybe it's old hat and people have done it for years?