How long would the following program run? while (true) {} I assume an ultrafinitist would argue that the question is ill-posed. It will always depend on the

How long would the following program run? while (true) {} I assume an ultrafinitist would argue that the question is ill-posed. It will always depend on the exact hardware that the program runs on (as every hardware will eventually fail). Or on us knowing when the heat death of the universe will be (which gives an upper bound). But that means that suddenly a theory of computability must deal with physical concerns and can't even talk about an abstraction such as "program" anymore. This seems completely contrary to how even just practically minded programmers who aren't deep into infinitary maths would think about their activity. Yes, you can make a philosophical argument for ultrafinitism - I would probably also say that arbitrarily large numbers don't "actually" exist in reality - but you just throw away so much useful abstraction that I honestly don't understand what the point is.