The Reliance Of Science On Mathematics

Is mathematics a science or a self-contained and separate thing that bleeds over into science?  If one uses the word science to refer to a discipline, then mathematics, of course, is a science.  But if one uses the word in the modern sense to refer to a particular method of empirical observations and predictions about how the material world behaves, then mathematics is not a science at all, though it, by its very nature, is inescapably connected with the scientific method.

Mathematics, as a numeric function of logic, is something that science depends on that does not depend on science.  One can know the answer to a mathematical equation without ever performing an experiment in the external world, just like someone can deduce the conclusion of a syllogism without scientific experimentation.  This is because logic and math are grasped by the mind, not the senses, and are true irrespective of scientific inquiry or scientific laws, having nothing to do with the scientific method in themselves--one cannot perform science without logic and math, but one can obviously utilize logic and math without engaging in science.  They are separate disciplines that overlap.

Mathematics governs the entirety of the material world just as the broader laws of logic do.  Just as a rock is a rock and not a ghost or a tree (the logical law of identity), two atoms plus two atoms will always equal four atoms by necessity.  So math inescapably applies to the material world, including to all scientific experiments and all unobserved phenomena.  Yet, despite its cruciality to the scientific method, mathematics and the scientific are themselves two separate categories united together.  Math is not science; it is one of the foundations of science, alongside logic and philosophy.

Those who think that the scientific method is self-evident and at the foundations of reality and epistemology are entirely mistaken!  Science is in no way self-verifying (only logic and math are) or reliable by necessity (it uses induction, whereas logic and math use deduction).  There is no guarantee that scientific laws will hold in the future, but logical and mathematical laws cannot not hold.

Though some might take math for granted, it is universally binding, its laws omnipresent in our daily lives.  It, like logic, which it is inherently attached to, lies at the core of reality.  Its necessary truths impose themselves on everything.  I want to start delving deeper into mathematics in future posts!