Science v. Math

As a math teacher and philosophy minor, I have for many years accepted the idea that propositional, deductive logic, like the kind found in mathematics proofs, is superior in defining reality than inductive logic, like the reasoning used in science, which moves from specific observations to general patterns or "laws" of nature.

I was wrong.

Both induction and deduction suffer from the same flaw: they are easily manipulated by a priori assumptions.

David Hilbert once wrote, "One must be able to say at all times-instead of points, lines, and planes---tables, chairs, and beer mugs." At the heart of this issue is a deeper problem in metamathematics, reviewed thoroughly in the following link: The Frege-Hilbert Controversy.

In short, Hilbert proposes that mathematics is subject to relativism. A mathematician can being with any set of propositions and arrive at any logical conclusion, whether or not it is consistent with reality.

This is a common criticism of science, that the "Theory of Evolution" is just a theory, for instance.

But even a commonly-accepted truth statement in math, like 1+1=2, depends upon context. When a child is conceived, 1+1=3. You may say, from a chromosomal perspective, 0.5+0.5=1, but the number of humans is nevertheless not constant, so this mathematical parsing is irrelevant.

1+1=3. Math is no more certain than science. Deduction is no more certain than induction.