How far is anyone going to get with a notion of God that's constrained by mathematics? If Gregory Chaitin is right, then mathematics is true, but for no reason. Mathematics is partly empirical, it discovers facts about this universe, but these facts do not, in general have any connection with each other. So why would your God be constrained by them? -- Keith Braithwaite

Now hold it. Does Chaitin argue that logic and deduction are arbitrary, or just that the axioms we happen to use for mathematics are arbitrary? -- Josh Grosse

What Chaitin seems to have shown is that nearly all known mathematical facts have no relation to any other known mathematical facts. So the structures and relations seen in the mathematics we study, most of which are ultimately derived from observation, are unrepresentative of mathematics (about almost all of which we know nothing as yet). This may be what you mean by 'arbitrary'. Compare with Lakoff and Núñez who attack what they call the Romance Of Mathematics from a cognitive scientist's perspective. -- Keith Braithwaite

This discovery of Chaitin should put the final nail in the idea that mathematics is limited by human reason. If instead, mathematics is the basis of any reality, conceivable or inconceivable, as it is the basis for physical reality, then the notion of a god unconstrained by mathematics is gibberish. -- Richard Kulisz

Actually, it seems like that line of reasoning is gibberish. The fact that I can fill a cup with water does not prove that water need have a form. Water flows. -- Peter Merel

And in any case doesn't seem to follow from what Chaitin has found. Chaitin claims that we get to have more mathematics in part by finding more bits of it, by inspection. It doesn't seem as if what's observed would need to be especially "basic" for this to be true. If Lakoff and Núñez are right, then what Chaitin's empirical mathematics observes is something to do with humans and how we fit into and understand the world around us, and not that world itself. I'm only a bear of very little brain, but I don't see any conflict. -- Keith Braithwaite