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In my opinion the answer to this question is, briefly, this: As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. It seems to me that complete clearness as to this state of things first became common property through that new departure in mathematics which is known by the name of mathematical logic or "

**Axiomatics**."
The progress achieved by

**axiomatics**consists in its having neatly separated the logical-formal from its objective or intuitive content; according to**axiomatics**the logical-formal alone forms the subject-matter of mathematics, which is not concerned with the intuitive or other content associated with the logical-formal.
Schlick in his book on epistemology has therefore characterised axioms very aptly as "implicit definitions." This view of axioms, advocated by modern

**axiomatics**, purges mathematics of all extraneous elements, and thus dispels the mystic obscurity which formerly surrounded the principles of mathematics.