What is the most fundamental subject?

Maths, obviously. The only thing that precedes it is logic itself which is rarely studied as a subject much any more. Without maths there is no Physics, which means no Chemistry, which means no biology, which means no medicine and neuroscience and everything else that relies on the sciences. In that sense it's the most fundamental. It's possible to argue that philosophy is but it isn't very important nowadays and as a subject it isn't really necessary. It's the ideas and curiosity about the world that is part of philosophy that are an important prerequisite for the sciences and maths.

Fun Fact: Starting on any Wikipedia page at all, if you click the first link that isn't in brackets/quotation marks and keep following these links, you eventually get to the page 'Philosophy'. Works almost every time.

The Philosophy of Mathematics

Fair enough. Math talk coming up. As it happens mathematics doesn't really have a foundation. In place of an spotless foundation it has a collection of pretenders with one shared holistic theme. The theme is: "almost everything is nasty". In other words, taking a broad enough view, almost everything doesn't have any of the properties you want it to. Almost all statements can't be proved, almost all real numbers can't be computed, almost all real -> real functions are not continuous, etc.

Russell's paradox has to be avoided, which is probably even more of a pain in the butt.

So in light of the absence of a really coherent foundation for mathematics (sorry, but just saying "philosophy" is not good enough), and the almost total lack of problems engendered by this messy state of affairs, it is ironic that (a) mathematics is a foundation for other subjects, (b) that mathematics is seen as more solid and fundamental in general than other subjects, and (c) that being "fundamental" is even important at all.

The Language of Philosophy

Maths clearly does have a foundation: the axioms. There are statements that are taken to be true, whether they are self-evident or not. These axioms are valid so long as they do not cause paradoxes to occur within the system. It is from these statements that the rest of the edifice is constructed in mathematics. For instance, in euclidean geometry there is the axiom that parallel lines never cross. Of course space-time in reality is non-euclidean, and this is far from self-evident, however that is unimportant and irrelevant to euclidean geometry which is an axiomatic system that does not contradict itself.

Fun Fact: Starting on any Wikipedia page at all, if you click the first link that isn't in brackets/quotation marks and keep following these links, you eventually get to the page 'Philosophy'. Works almost every time.

Or, conversely, this.

Yeah, I did say it wasn't foolproof and there would be exceptions, but oh well.

no, no, no, a thousand times no. the axioms for euclidean space come from our physical intuition of the properties 'space' should have.

axioms don't just come out of thin air, you know.

Languages (English, or whatever your native language is)? Without the ability to read, understand and respond, there's not much you can do.

I agree that we have discovered the rules for this particular mathematical game come from physical intuition, however that does not mean to say the game can't exist without us having discovered it.

It's like a game of chess. We learn how to play it through seeing someone else play it in physical reality, but that doesn't mean the game and it's abstract rules didn't exist in a rule book, before we saw it being played, before we discovered it. Also we can abstract beyond the images, and do Euclidean geometry in just algebra. So Euclidean geometry seems to exist independently of our physical reality. Yes, I am a Platonist, and I believe Maths describes the objects of this Platonic realm- the rule book if you will.

Ok, so maybe mathematics exists independently of humans, but this doesn't explain how mathematics is the most fundamental subject (except maybe in relation to itself).

Or, in other words, mathematics is its own foundation and nothing else.

(also, the whole 'mathematics-as-a-game' language was mainly pushed by supporters of Hilbert-style formalism, which is very much the antithesis of Platonism)

Well, it seems like the axioms governing physical reality are just one subset of consistent axioms that can exist within the realm of pure forms, so to me maths seems more fundamental than physical reality. Again Plato said we were just shadows of a more fundamental reality, flickering on the wall of a cave. And I subscribe to this view, especially when I abstract myself from this world to consider what a universe would be like in4 or more dimensions, or if the cosmological constants differed. Perhaps even these universes could sustain life which could contemplate mathematical reality.

And anyway, applied maths is used in all scientific subjects- so I must say maths again seems more fundamental.

With regards to your last point, u've discovered an inconsistency in my axiomatic world view perhaps u could patch things up for me? Formalists=Logicists, right? I realise by godel that there will always be true statements unprovable by our mathematical systems, but as a Platonist I have no problem consigning these true statements to a Platonic world, which is unseeable even by the most powerful telescopes of modern mathematics.

Fun Fact: Starting on any Wikipedia page at all, if you click the first link that isn't in brackets/quotation marks and keep following these links, you eventually get to the page 'Philosophy'. Works almost every time.

Edit: I am really interested to know how this is worthy of neg rep, whoever did it please let me know, my curiosity is getting the better of me

Isn't it telling, however, that we don't consider all possible rules, and that the vast majority of axiom sets, we consider, even in 'pure maths', are those motivated by 'physical' example?

Once you start applying maths to the physical world, all kinds of new philosophical problems crop up. There is no such thing as a pure number three, so how can we use number to describe actual concrete physical reality? Answer: because our concept of number was motivated by physical reality . Arguably, the physical world came before maths ontologically.

Formalism is the concept that mathematical symbols don't have any inherent meaning and mathematics is just a game we play according to certain rules (the axioms we 'create'). Platonism/realism is the view that there is a mathematical world out there and our axioms are just our best attempts to capture objective mathematical reality.

Fun Fact: Starting on any Wikipedia page at all, if you click the first link that isn't in brackets/quotation marks and keep following these links, you eventually get to the page 'Philosophy'. Works almost every time.

Fun Fact: Starting on any Wikipedia page at all, if you click the first link that isn't in brackets/quotation marks and keep following these links, you eventually get to the page 'Philosophy'. Works almost every time.

Maths probably, but since I'm not fantastic at it I'm going to say philosophy!