Dear Sylvia,
I appreciate that your read and commented my essay, especially since this phase is closed. The exchange of ideas should not be limited to getting into the finals, so if we couldn't read and comment enough, nothing stops us to continue. So I read and commented your excellent essay too - I planned to do this earlier but the time was too short. You said "My general impression was that your essay mainly deals with fundamentalness within mathematics - which is fine -, although at crucial points it becomes clear that you do intend to address physics instead." Yes, I think that about the foundations of physics there's not much to be said beyond the mathematics, except of course the empirical and epistemological bridges, which connect the theory with the reality and with our understanding. More about this in a previous essay. Roughly, I had two major points, the first being that of "relativity of fundamentalness", which I think it is universal but can be better exemplified with mathematics, and also with physics, going beyond what you identified in your essay "concrete 'elements'" and "abstract principles" as usually seen, as you also went beyond these. In the second I proposed an 'extreme' possibility of the same, holomorphicity, which unlike relativity of fundamentalness is not universal, but I think it may be realized in physics. I had the idea that the world is holomorphic in the way described here (but with much less specific details) 25 years ago, and shortly after that I realized that it may have implications to the free will. Thanks for pointing me to Hoefer's chapter, Scott also told me about it in relation to my approach to QM [1, 2] and my adjacent comments of free will for those who may think that indeterminism allows it and determinism doesn't. Hoefer's proposal doesn't need holomorphicity, it is based on determinism, and at first sight it is, wrt physical consequences, a mere reinterpretation of deterministic causality to accomodate free will, based on the block world picture from relativity. But I think it is more than this, because when I tried to see what happens if in quantum mechanics we keep unitary evolution and remove the collapse (without appealing to MWI), I got that the initial conditions have to be "delayed", or that the solutions should satisfy some "global consistency conditions" which are spread at different places and times in the block world. I see this global consistency condition mathematically as being realized in sheaf theory, which arose partially from the study of complex holomorphic functions. Holomorphicity seems to me the best way to realize this as more than reinterpreting determinism, since they are the most constrained by global, topological conditions.
Best wishes,
Cristi Stoica
