On Jun 16, 12:34 am, Virgil <Vir...@home.esc> wrote: > In article <874oh3ir6m....@dialatheia.truth.invalid>, > Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> > Let f : N --> N be a function such that > > > f(x) = 0 if Goldbach's conjecture is true, and 1 otherwise. > > > Is f computable? > > Not yet!
There exists an algorithm to compute f. We don't know what the algorithm is (we don't know whether it is to set f(x) = 0 for all x, or to set f(x) = 1 for all x), but still the algorithm exists - either the algorithm is to set f(x) = 0 for all x, or the algorithm is to set f(x) = 1 for all x..
In ordinary study of computability, that is what it means to say that a funciton is computable - that there exists an algorithm to compute it.
If you wish to include also that the algorithm is KNOWN (known to whom? and known when?) then you need to find some treatment that supports that notion or invent your own.
But then would you say that each function becomes computable only historically as certain people, through history, figured out algorithms for various functions? So whether a function is computable is relative to what certain people know at certain times (and even as some people know at a certain time but other people don't)?