The longer I think about it, the less I am convinced that infinity and/or finiteness is a done deal. In fact, the longer I think about it, the more urgent it seems to me that science starts to fully acknowledge the problems surrounding infinity <–> finiteness.
As a model for the physical universe, both infinity and finiteness seem to me impossible to maintain.
But where does that leave us?
All too frequently we seem content to choose classical mathematics as the vehicle for physics. Infrequently constructive-math alternatives are advocated. But the real difference between all these alternatives can be traced back to the problem infinity <–> finiteness.
Would it be possible somehow to build a theory of everything (in physics), which is thoroughly finitary? Has anyone tried to do so?
I’m hopelessly ignorant in physics, please excuse me for this. But I would expect these questions to receive more explicit attention. Still, let me see if I can find some answers on the internet in the coming time.