[Alamo-Girl]

How would it work in practice? I could make any calculation come out however I wanted by simply declaring whatever arbitrary axioms were required to produce the result I wanted.

That is the beauty of it. If the postulates or axioms are arbitrary, irrational, false or whatever - the theory built on them will be rejected out of hand.

For instance, Einstein's special relativity is built on several postulates one of which is a four dimensional space/time continuum. Falsify that and the entire theory is falsifed.

Mathematics is formal and thus the presuppositions are known up front. In my view, scientific investigations should be formalized the same way.

Thus, if the scientist starts with a presupposition that the earth sits on the shell of a giant, invisible turtle, there's no need to read further except perhaps for amusement.

[tacticalogic]

That is the beauty of it. If the postulates or axioms are arbitrary, irrational, false or whatever - the theory built on them will be rejected out of hand.

That presupposes that there is some way of testing the axioms. That gets to be problematic once you get outside the realm of physical causes and sensory perception.