Kant supplied a priori arguments for Newtonian Physics in his Metaphysics of Natural Science
Has something similar been done for Modern Physics; which in its geometrical intepretation are concieved as G-Principal Bundles for some group G?
The following argument occurs to me; which derives from Aristotles oservation in his Physics that all philosophers agree that contraries are the principles of things.
(Its possible to argue that its this adherence to this principle that suggested to Aristotle that light things moved away from the Earth - they were 'repelled'; and that heavy things moved toward the earth - they were 'attracted'; and also hat the motion contrary to linear motion is circular).
He argues that contraries, being the principle of change, and which come in pairs of opposites; act not on themselves - this would be incoherent but on some other which is the receptacle of change - a substance.
And that any change can be negated or undone by its opposite; but sometimes substances change - and sometimes they do not; we could suggest sometimes then the principle of change acts and sometimes not; but by invoking a principle of continuity of action; and also that actions can be large or small, and thus smaller - there ought to be an action that acts but does nothing.
Then we can concieve a contrary as a group - which has a positive part, a negative part (the inverse); and rest - the identity; and this group should act ie group actions such as GM -> M.
Now, G-Principal Bundles when interpreted in the right category are exactly that: group actions.
What kind of group should G be? Pythagoras argued that spheres are the simplest of objects and fundamental in his conception of cosmology; they can also be concieved as groups; so we suppose that G is a Sphere, or related to it somehow.
Electromagnetism for example - is a Circle Bundle.
Does this work as an a priori argument?