At the end of the 19th Century, epistemology has officially adapted the principle of factual falsifiability as the cornerstone of axiomatic models.
It appears incredible, but the common "wisdom" did not notice it and stays 2300 years behind concurrent rationality, as can be seen in English dictionaries defining axiom as:
-generally accepted truth.
-a statement or proposition that needs no proof
because its truth is obvious, or one that is
accepted as true without proof.
-an obvious or generally accepted principle.
-self-evident or universally recognized truth.
-self-evident and necessary truth, or a
proposition whose truth is so evident as first
sight that no reasoning or demonstration can
make it plainer; a proposition which it is
necessary to take for granted.
-self evident truth, or a proposition whose
truth is so evident at first sight, that no
process of reasoning or demonstration can make
it plainer.
-necessary and accepted truth; basic and
universal principle.
[..]
Now, mathematical axioms seem to lack factual falsifiability. Would therefore mathematics be
dogmatic?
We shall examine it in the chapter "FOUNDATIONS OF MATHEMATICS".
