Focus said:
the reason why maths and physics is similar is due to the fact that physics is maths with added axioms.
There was already objections on this, but I also reacted a bit on this description, although I must confess it is what one might express when a pure mathematician takes on physics, but then he might not be interested in the physics itself.
Focus said:
You need to draw these axiom from real life (such as continuous time, free fall acceleration, etc..). It is often that these axioms are wrong or incomplete or do not represent real life accurately.
If we for a second consider that you insist of this view, that knowledge of the natural physical world (physics), is best accomplished by "finding" the axioms/postulates, from which everything else should supposedly follow by deduction, then you are decomposed the problem into a two parts.
And clearly the difficult part here is finding the right axioms or "fundamental principles" from which all else follows from deduction.
This traditionally leads us into a version of the philosophical problem of induction - howto soundly infer the future from that past. Hume's critics is that such deductive inferences is impossible, and while it might not be possible to prove, I agree with his inductive skeptisism.
Karl Popper who one might see as one of the founders of the modern falsification/hypothesis generation style of the scientific method tried to solve by bypassing the induction, and instead come up with the idea of putting hypothesis to tests, where one risks falsfying a theory by deduction. However Popper doesn't solve the whole problem deductively.
One question is the logic of hypothesis generation, in case the previous hypothesis was falsified. Clearly this is hardly a deductive process.
So my own interesting in physics lies at the level of the scientific method.
If you insist on thinking of it like axioms + deductions, then the real problem is how to soundly induce the axioms from experience - this is the scientific problem.
One you have an axiom or hypothesis on the table, for testing, it's easy. The interesting part is what I would like to call "resolving an inconsistency". This is where I possibly
associate to godel. I personally think this becomes more of an issues in the quest for quantum gravity.
I think the basic problem of natural sciences, is howto "infer" from experience and observations the laws of nature, and indirectly infere the future from the past.
So howto do that?
Clearly many questions appear here. And whatever inductive scheme we come up with, how do we konw this can be trusted? IMO we don't. But here is IMO, where three concepts come in, the logic of guessing, the logic of correction, the logic of evolution.
This is my very personal view of things, somewhat in line with many others who think inductive reasoning rather than deduction is the right way to go in physics. And IMO, there is a possible different solution to the problem of induction, that I think might give rise to a "new logic", it would turn the sometimes claim circular argument of induction, into a evolutionary argument. (Ie. the circle is a spiral).
Logic improves, science improves.
/Fredrik
