Well, that argument only goes through if the other theory is recursively enumerable, so PA isnt as awesome as you make it sound.
Agreed. For example, we can’t learn “all truths about the integers” by bootstrapping from PA in this way. But we can get all of formalist mathematics.
Well, that argument only goes through if the other theory is recursively enumerable, so PA isnt as awesome as you make it sound.
Agreed. For example, we can’t learn “all truths about the integers” by bootstrapping from PA in this way. But we can get all of formalist mathematics.