Axiomatic method:
The way of trying to explain things
by making axiomatic assumptions
or by making definitions, from which
one deduces by logic what one wants to explain.
The axiomatic method originates
in mathematics, and Euclid's "Elements", that presented geometry in
this form, is the first, and dates back to the third Century B.C.
The great advantage of the method is
that it clearly identifies what is assumed
or defined, and that everything else
must be inferred by logic from this, with
the consequence that, supposing all inferences
are logical, whatever follows from the assumptions is true if the
assumptions are true, and whatever follows
from the assumptions that is false shows
that at least one of the assumptions must be false.
Thus all fundamental problems are
shifted back to whatever assumptions, definitions and rules of
inference one uses, since everything else follows deductively from these.
When the axiomatic method is combined
with careful and objective empirical testing of the consequences
deduced from the axioms, when these axioms
concern empirical subjects, we have the outlines of the scientific
method, that was first fully clear to Galileo.
