I agree that this is too dreamy and programmatic, and it would have been better if I had presented a concrete plan.


The idea that logic can be an ultimate foundation seems difficult to justify.

Well, the foundation are the axioms, not the logic. The philosophical position of logicism (i.e. "mathematics can be reduced to logic") is accepted as untenable, let alone for science.

Since we're talking about formalizing empirical science, then these axioms don't even need to be "self-evident", general or anything like that.

Is it possible to have a non-logical "foundation" for something? (and what would that mean?)