Saturday, November 1, 2008

Understanding Science, Mathematics, and Philosophy

I propose the following definition of "science":

Science is the formalization of discovery.

All knowledge is ability, be it mathematical, empirical, kinesthetic, or what have you. Discovery is the attainment of new abilities. Discovering that something is the case is not essentially different from discovering how to do something.

Science, as the formalization of discovery, is the formalization of methods and principles which produce new abilities. Any method may be considered science, so long as it produces new abilities in a formally definable way. And any abilities may be considered scientific, in so far as they are defined with respect to some formal method of discovery. (We can have grey areas here. We don't have to decide ahead of time how formal is formal enough.)

Math, the empirical sciences (physics, chemistry, etc.), and philosophy (which includes logic) are focused on different sets of tools, all of which are required for the formalization of new knowledge. They are thus all a part of science. We don't need to worry about borderline cases between them ("Is applied math an empirical science?" "Can the philosophy of mind be an empirical science?") to accept this undertanding.

The different tools of science have different standards of measurement. The empirical sciences, for example, are ultimately concerned with discovering nature's laws and/or regularities. They therefore require that theories make testable predictions. Empirical sciences can be speculative, such as the case with string theory, if they promise more explanatory power than our established knowledge, but cannot yet be tested.

Mathematics is concerned with discovering the formal principles of abstract patterns and their relationships. It is our ability to systematically represent abstract patterns. Mathematical discoveries are thus discoveries about how to represent patterns consistently and coherently within a given mathematical language. As such, mathematical theorems cannot be falsified by appealing to some other standard of measurement. It is for this reason that we say mathematical theorems are not falsifiable, but absolutely true.

Logic, as a branch of philosophy, is similar to mathematics, in that it is a purely formal science. It formalizes our ability to analyze the relationships between propositions in terms of their truth values. It also formalizes our ability to represent valid principles of deduction and induction.

Philosophy, which may be called "thinking about thinking," is more generally concerned with our understanding of understanding itself. Philosophy is thus concerned with developing and applying metaconcepts which allow us to clarify and correct our conceptual frameworks. The value of such philosophical ideas is determined by their ability to eliminate confusion without postulating new entities.

Philosophy has most recently developed a strong focus on understanding the functional properties of systems which exhibit understanding. Thus, the philosophy of mind and artificial intelligence have emerged as two of the most forward-thinking subdisciplines in philosophy. Both are helping to shape various empirical sciences, including neuroscience and cognitive science.

One cannot develop the empirical sciences without mathematics or philosophy. We may thus regard philosophy, math, and the empirical sciences as more or less distinct enterprises which are all part of the same process of formalizing discovery. They work together to create science as we know it.

This view of science, math, and philosophy does not run contrary to dominant trends in any of these disciplines. It is, I think, a very simple, common-sensical way of understanding science. Most importantly, it clarifies why science itself is not an optional view, as if one could find some other path towards truth.

It is possible to learn in an informal way. We often learn by instincts alone, following our intuition, and not with formal procedures. This is learning by accident, and as often as it happens, it is not a distinct path to knowledge. It is rather the most basic form of learning, the abilities we harness and build upon to produce science.

Many people criticize science, or "scientism," claiming that science is just one path to truth. They regard this as a philosophical issue, as though philosophy were neutral on the question of science. As my understanding indicates, however, this is not the case. Far from being neutral on the issue of science, philosophy is part of science. If one's philosophy leads them away from science, then one's philosophy is not producing clarity or wisdom. There is no sense in the claim that one could use philosophy to undermine scientism and develop some alternative path to knowledge. Any legitimate path to knowledge is, by definition, science.

This isn't dogma. It's just what the words mean.