an autodidact meets a dilettante…

Now we come to the argument that God is the best explanation of the applicability of mathematics to the physical world. My intuitive response to this – and of course I’m not a mathematician – is that mathematics appears to me to be be a kind of abstraction from, that’s to say a manipulation of, a play on and further development of, the regularities that exist in the world, and that if no such regularities existed, the world wouldn’t exist. Or at least would not be in any sense describable. For example, the most basic form of regularity required would be a binary contrast, describable in mathematical or logical terms as x and not x.  The real world, though , offers far more opportunities for playing on and manipulating regularities than this. So many opportunities have been found in fact, and so many beautiful theorems have been developed from them over the centuries that mathematics has often been given a mystical, miraculous status. One thinks of the Pythagoreans in ancient times, and the mathematically-obsessed philosophers of the seventeenth century, such as Descartes, Spinoza and Leibniz. However, I think it’s fair to say that, historically, when mathematics has been raised to mystical heights, great problems have ensued. So I don’t see anything particularly miraculous in the fact that a tool for understanding the regularities of the world can be developed and manipulated to underpin theories which further deepen or extend that understanding.

Eugene Wigner’s 1960 essay, ‘The unreasonable effectiveness of mathematics in the natural sciences’ is available online, and everyone should be encouraged to read it – though it doesn’t make for easy reading. I think it’s a little unfortunate that Wigner uses the word ‘miracle’ a number of times in the essay, but he certainly doesn’t refer at any time to a god. And while I would hesitate to interpret Wigner from my lay background, I’m not sure I agree with his view in the essay that, while elementary mathematical concepts derive directly from the perceived regularities of the actual world, more complex and abstract mathematical concepts don’t so derive, and yet can be applied with uncanny reliability, or if you like profitability, from our perspective, to that world, as is the case with much modern physics. If that were so, if the mathematical abstractions our minds create were completely removed from the world’s actual regularities, and yet just happened to apply to them to provide us with a richer and more developed view of our universe, then that would indeed be a ‘happy coincidence’. But abstraction doesn’t occur in a vacuum. Just as non-Euclidian geometry derives from the regularities of nature that Euclid strove to axiomise in a set of rules, and just as multi-dimensionality derives from the standard three-dimensional world of our experience, mathematical abstraction is always tied to some underlying actual regularity, however obscured by its overlay. The applicability of maths is not a happy coincidence (which isn’t to say all mathematical abstractions are applicable of course), but that is just because the world has regularity. Thus when we look at Dr Craig’s formal argument:

1. If God did not exist, the applicability of mathematics would be a happy coincidence.

2. The applicability of mathematics is not a happy coincidence.

3. Therefore God exists.

we see once again that the problem lies in the conditional statement – this time statement one. Our world has regularities, without which not. Mathematics is all about the play of regularities, so it isn’t coincidental that some mathematics has applicability. This is not mysterious, and it doesn’t imply anything about supernatural agency. Thus it isn’t reasonable to infer the existence of any god, let alone the human-obsessed, son-begetting god adhered to by Dr Craig.