No, but you are choosing how to describe it. You cannot aviod that. Hence synthetic.
But I don't chose how it's
related, and you can't avoid
that. An accurate description of reality is one that correctly describes the relationships. The ultimate thing I'm after when I describe reality is making sure I have the proper relationships.
But even this is beside the point with respect to mathematics. No matter what reality is like, in Euclidean geometry, the square of the hypotenuse is exactly the sum of the squares of the other sides. Euclidean geometry defines a particular class of relationships in itself. Even if science and physical reality turns its back on Euclidean geometry, mathematics still cares. It leaves this abstract world untouched, unharmed, because the relationships
in themselves are what math is about.
I'm not entirely sure I see how this applies - consistency implies that the same system would behave in the same way every time.
That's translational symmetry in time. That's one of many symmetries in the universe.
They are consistent with the digits of pi.
Okay, but isn't that a tautology?
I'm even more confused about how pi's digits being consistent with pi's digits relates to this:
Either the behaviour of objects is consistent in which case their is an algorithm of finite length that can describe their behaviour or the behaviour of objects in inconsistent in which case there is no algorithm of finite length that can describe their behaviour.
(Furthermore, there has to be a consistency to begin with in order for us to speak of things such as "objects" in the universe in the first place--you don't
just get to have objects--there has to be some form of thing with a separable and meaningfully consistent identity first).
They don't allow for anything new - they exist on the edges of these descriptions which makes them quite intractable.
Even more confused. How would QM fit into the "law of excluded middle"? I'm trying to figure out if by "law of the excluded middle" you really mean something I would call "false dichotomy". It really severely looks like reality can be both describable and not, at the same time--that there are things that can be described, and things that cannot be.
I'm generally flexible with the way people describe things. But I'm pretty firmly against the notion of a priori reasoning about the nature of ontological entities.
You said reality was either one way or the other. I claim it not only can be both, but probably is. If you didn't mean to imply an exclusive or to this case, I'm perfectly fine with it. Otherwise, I object.
That reality is mathematical.
Be more specific. Is it your position that reality is not mathematical? That, say, there are no relationships in reality?
That mathematics contains an isomorphism to the behaviour of reality is hardly surprising since physics was constructed for that purpose.
But you do isomorphisms all of the time to get the answers anyway. When you multiply 15 by 15, you may do either of the following:
- 25+50+50+100=125
- 100+25+2*10*5 (a^2+b^2+2ab)
- Make a grid of 15x15 dots, and count them
Either way, the goal is to get 225. But 225 is shorthand, in itself, for 2*100+2*20+5. It's the thing we want because it is a standard form that allows many other kinds of standard games to be played (such as counting using the decimal system).
But what all of this is about is how many dots there are when you arrange them in a square, or how much a pack of 15 flubnars costs at 15 pence a piece, or the momentum of a 15kg ball traveling at 15 m/s. 225 is the thing we want, because that's our goal. 225 is related to the number of dots, or the cost of flubnars, or the momentum of the ball in kg m/s.
Whether you call the games you play to get 225, or the particular relationships between the entities 15, 15, and 225 using this multiplication type relatedness, mathematics, is
in itself nothing but semantics. But the real piece of interest is that 15 and 15 under this multiplicative relatedness is related
to 225. Or if your problem happens to be different--you may take interest in the fact that the relatedness of interest between 15, 15, and your answer
is the multiplicative kind of relationship.
This entire subject of concern is mathematics
dict--the games we play to get there, the fact that we can get there multiple ways, other ways to get there, what game we play to get there--it's all mathematics.
ETA: Left out "where we want to be".