Recently, Scott Alexander of Astral Codex Ten (unofficially the favorite blog/column of most of a certain kind of philosopher) wrote a short piece on the interaction between arguments for theism and Max Tegmark’s “mathematical universe.” The headline?
At least in my lifetime, it always has seemed that if one can just get a big enough number - years, planets, multiverses, etc. - one can argue around God. Almost like big numbers of something becomes an object of one’s faith.
I also wonder if mathematics would exist if there were no God or being around to envision or work with it. It seems to me the answer is either “no” or “moot point.” So my thought is that if mathematics IS, then perhaps someone has tapped into a vision of God that is only part of what I imagine God to be. But if mathematics IS and God isn’t, then where did mathematics come from? If one can believe that mathematics always has been, it seems to me that one can also believe that God (as I generally imagine) always has been.
All this from the non-philosopher peanut gallery, so be merciful. ;)
>Whether Tegmark allows a ZFC+NotConZFC region of his mathematical universe then raises a dilemma. If he does not, he is not in fact allowing all consistent structures to be realized. If he does, then whether one structure in his universe ‘ought to be included’ will itself be at issue: in the NotConZFC region, ZFC is out the way a geometry of square circles would be.
I don’t see the issue here. NotConZFC isn’t really saying that ZFC is inconsistent; this is just a convenient way of talking that reflects the fact that that hypothetical axiom is false in the standard model of ZFC iff ZFC is consistent. But in any Tegmarkian structure that validates ZFC+NotConZFC, the interpretation of the theory’s symbols is going to be something very different, such that NotConZFC is really saying something else if it’s saying anything at all.
Nice bit of ‘splaining, Daniel!
At least in my lifetime, it always has seemed that if one can just get a big enough number - years, planets, multiverses, etc. - one can argue around God. Almost like big numbers of something becomes an object of one’s faith.
I also wonder if mathematics would exist if there were no God or being around to envision or work with it. It seems to me the answer is either “no” or “moot point.” So my thought is that if mathematics IS, then perhaps someone has tapped into a vision of God that is only part of what I imagine God to be. But if mathematics IS and God isn’t, then where did mathematics come from? If one can believe that mathematics always has been, it seems to me that one can also believe that God (as I generally imagine) always has been.
All this from the non-philosopher peanut gallery, so be merciful. ;)
>Whether Tegmark allows a ZFC+NotConZFC region of his mathematical universe then raises a dilemma. If he does not, he is not in fact allowing all consistent structures to be realized. If he does, then whether one structure in his universe ‘ought to be included’ will itself be at issue: in the NotConZFC region, ZFC is out the way a geometry of square circles would be.
I don’t see the issue here. NotConZFC isn’t really saying that ZFC is inconsistent; this is just a convenient way of talking that reflects the fact that that hypothetical axiom is false in the standard model of ZFC iff ZFC is consistent. But in any Tegmarkian structure that validates ZFC+NotConZFC, the interpretation of the theory’s symbols is going to be something very different, such that NotConZFC is really saying something else if it’s saying anything at all.