Full Idea
Many axioms have been proposed, not on the grounds that they can be directly known, but rather because they produce a desired body of previously recognised results.
Gist of Idea
Axioms are often affirmed simply because they produce results which have been accepted
Source
Michael D. Resnik (Maths as a Science of Patterns [1997], One.5.1)
Book Reference
Resnik,Michael D.: 'Mathematics as a Science of Patterns' [OUP 1999], p.84
A Reaction
This is the perennial problem with axioms - whether we start from them, or whether we deduce them after the event. There is nothing wrong with that, just as we might infer the existence of quarks because of their results.