Doubting everything and believing everything are two equally convenient solutions that guard us from having to think. - Henri Poincaré

The axioms of geometry therefore are neither synthetic a priori judgments nor experimental facts.

All laws are... deduced from experiment; but to enunciate them, a special language is needful... ordinary language is too poor...
This... is one reason why the physicist can not do without mathematics; it furnishes him the only language he can speak. And a well-made language is no indifferent thing;
...the analyst, who pursues a purely esthetic aim, helps create, just by that, a language more fit to satisfy the physicist.
...law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise...
In a word, to get the law from experiment, it is necessary to generalize... But how generalize? ...in this choice what shall guide us?
It can only be analogy. ...What has taught us to know the true profound analogies, those the eyes do not see but reason divines?
It is the mathematical spirit, which disdains matter to cling only to pure form.

A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.