@Tuna,
Empiricism needs not be limited to science. It's just the belief that the only trustable basis for knowledge is sensory experience. Add reason as another source of knowledge, and you do get the scientific approach (science = a mix or rationalism and empiricism), but one can certainly apply the idea to blind women commenting on traffic lights, as I did upthread...
In my experience, modern academia are a bit too quick to invent new words to describe their (supposedly) brand new ideas. But there's often nothing new in there beyond the label... Most of the time they are just repackaging something that goes back to Matusalem.
In this particular case, Socrates said it best: "All I know is that I know nothing" (for absdolutely certain). IOW, there can be no objective, air-tight basis for knowledge. Even our senses can be doubted, and sometimes they clearly mislead us, like in optical illusions.
Knowledge has an intuitive dimension, a degree of
fuziness which makes of it a very human thing.
The big difference bretween mathematical set theory or logic on the one hand, and natural intuitive logic and human sets on the other hand, is that the latter have fuzzy boundaries while mathematical ones cannot accomodate fuzziness. There ARE
borderline cases in real life, but not in mathematics. A door really CAN be open AND closed in real life (it's called being
ajar), but not in mathematics... Knowledge is like that: it is fuzzy, and therefore it is not mathematical - you can't prove it or even define it in mathematical terms, reason for which I believe your quest is futile.
A
real, practical and useful theory of knowledge would not lose time wondering how do we know that "apples are sweet". It would rather point out that sweetness is not an inherent characteristic of apples but rather a perception by humans of the sugars contained in apples; that such perception gives us pleasure because sugars are high-energy items and the pleasure is an incentive to eat more of them; that apples trees produce the sweet flesh of apples as an incentive for animals to eat apples and thus spread the apple
seeds wherever they dump a ****, helping the species propagate; that all apples are not equally sweet; that in fact some apples are not sweet at all (e.g. unripe ones, not yet ready for propagation)... and that in spite of all this murkiness, we can still say something
by-and-large true by stating: "apples are sweet"...