I'm struggling with the idea of definability. For instance, in category theory, it's possible to define a product. So product is "definable." Is "definability" itself well defined? Can you define a set of definable things? Is such a set definable? And is there a well-defined set of things that are not definable in a given theory?
@BartoszMilewski Do you distinguish this 'definability' from 'constructability'?
https://en.wikipedia.org/wiki/Constructible_number
@bengo You can define the diagonal of a unit square even if you can't construct it with compass and straightedge .
@BartoszMilewski Are you speaking of definabilty in the sense of a "definable number" (i.e. one that can be uniquely specified by a sentence in the formal language)? Or are you talking about "definable" in a different sense? @bengo
@internic @bengo I am well aware that if you start diluting definability, you get into the paradox valley. But definability within a theory should make sense, even though it's a meta-statement.