Justification of the scientific method, anyone?

[fromderinside]

Is that clear enough?
EB

No.

Let's start with mathematics as the language of science rather than mathematics as a deductive system. Science isn't about truth, it is about reducing uncertainty of meaning in a deterministic world. Moving targets. Mathematics keeps changing to capture the new targets. Mathematical or scientific logic start with it being other than reducible to truths by principles. Rather scientific logic is about reducing uncertainty in a presumed determined system.

Compare what I just wrote with your OP:

Justification of the scientific method, anyone?

Physics relies a lot on maths and maths on logic. What is the justification of the method of logic used by mathematicians, do you know? Or is it that the only method of logic really used in maths is the mathematicians' own intuitive sense of logic?
EB​

Notice what I wrote doesn't correspond to what you presumed.

The answer to your question, bolded, is: the logic used is determined by the nature of the reality it is meant to represent. It's a convergent, error reducing with respect to the nature of reality, logic.