NJ might be thinking of the inferences we make about physical laws, namely that they are consistent and comprehensible. An example of such an inference is that the speed of light is the same everywhere, even though we only have data from a tiny proportion of the actual universe.
Sure, but even those things, we believe them because there's evidence for them. We discover physical laws (to the extent that laws exist, etc.) because of the evidence of their existence.
On the other hand, in mathematics,
axioms are things that you
assume are true. You just invent axioms, they're not derived from anything - you pick the axioms you want to support the derivations you want to derive.
Rrhain had a post on this on another thread, relating to Euclid's fifth postulate. If you accept it as axiomatic the way Euclid formed it, then you're operating in Euclidian geometry. If you accept instead an axiom that says "given a line L and a point p outside L, there exists no line parallel to L passing through p," you're operating in elliptic geometry.
You can pick and choose whatever axioms you want, because you don't have to prove them. They're
quote:
a sentence or proposition that is not proved or demonstrated and is considered as self-evident or as an initial necessary consensus for a theory building or acceptation. Therefore, it is taken for granted as true, and serves as a starting point for deducing and inferencing other (theory dependent) truths.
Axiom - Wikipedia
That's what I mean when I say there's no axioms in science. We don't simply accept things without proof or demonstration in science. There aren't "sacred cows" that we never stop to inspect or that are immune from a requirement of justification.
We don't take things for granted in the sciences. Things are demonstrated with evidence - not simply accepted as true because it's convenient to believe them. Or am I wrong?
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