>If we cannot program it... it's not a Theory of EVERYTHING. It's just a >description. You really should be an intuitionist mathematicien. It is consistent with most intuitionist mathematical system that 1) all function from N to N is computable. 2) all function from R to R is continuous. In my approach the intuitionist philosophy correspond to the first person viewpoint. But I'm a Platonist, at least about numbers and functions from N to N. This includes a lot of uncomputable functions. For exemple the function which gives for each n the greatest number you can compute in fortran with program of length n. (This function grows quickly than any computable function; you can "approximate" it, in a very weak sense by using transfinite induction: this illustrates that higher infinities can help to manage finite combinatorial problems). >Let us take the realist approach and focus on the things we can actually >compute fully. Would you formalise that by the total (defined everywhere) functions from N to N, or do you accept the partial computable functions as well? And why would you not accept also the functions computable relatively to the halting problem? They correspond naturally to the function computable in the limit and are quite usefull if you accept infinite histories ... Bruno PS I will comment you other post (from the same thread), where you say you are a materialist, ASAP.