Saturday, March 06, 2010

On Explaining Existence

"The strategy I am advocating is that physics, in becoming more or less completely aligned to mathematics (in terms of content, at least), will be able to penetrate down the ladder of explanation to the very deepest rung of all: existence."

Philosopher of Physics Dean Rickles has an interesting paper which proposes an explanation for why there is something rather than nothing. Rickles submitted his article, On Explaining Existence, to a recent essay contest organised by the Foundational Questions Institute. The resolution he proposes is simply that the physical world is identical to the mathematical world, hence the existence of the physical world is necessary rather than contingent:

"Either existence is contingent or it is necessary. If it is contingent then there is no complete coherent account of existence. If it is necessary then we need a necessary structure to ground this fact. Mathematical structures are of this kind. If reality is mathematical then it must exist. Reality is mathematical (as evidenced by the effectiveness of mathematics in the sciences). Therefore, there is existence. This is not a case of logic 'causing’ existence, or bringing existence into being 'out of nothing’. Mathematical structures are timeless. We can add to this the fact that if this is the only reason that can be found for existence to be the case, then physical reality (or just reality) has to be mathematical. In other words, the universe is mathematical because there is existence, and the only reason for there to be existence is that there are mathematical truths."

I agree with this, not least because I proposed the same answer to the question of Why is there something rather than nothing?, back in 2007:

Martin Heidegger claimed that this is the most important question in philosophy. Here I wish to focus on a special case of this question, namely: 'Why is there something physical rather than nothing physical?' The implicit assumption which underlies this question is that the existence of the physical universe is contingent. If one rejects this assumption, then one possible answer to the question is that the physical universe exists necessarily. Mathematical structures exist necessarily because mathematical existence is merely absence from contradiction, and modern theoretical physics represents the physical universe as a mathematical structure, hence the physical universe exists necessarily as a special case of mathematical existence.

Rickles also makes the following excellent point about Godel's theorem:

"The theorem does not tell us that there is any problem with mathematical truths per se; only that there is no algorithmic way of generating all such truths. The mathematical universe is safe from Godel’s theorem. We must distinguish between truth and provability."

Elsewhere, however, Rickles comments that "Godel’s theorem would surely bite: for a theory will be a representation and any such mapping will be lossy," and on this point I don't totally agree. It is important to emphasise the distinction between theories and models which exists in mathematical logic, and to reiterate the point made in my 2009 post, Theories of Everything and Godel's theorem, that "whilst the theory of a model, Th(M), may be undecidable, it is guaranteed to be complete, and it is the models of a theory which purport to represent physical reality." The theory of our universe's mathematical structure is guaranteed to be complete and consistent, even if it might transpire to be undecidable, and this is far from 'lossy'.

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