I’ve been listening to the Philosophy Bites podcast recently. One from a few years ago consisted of answers from philosopher’s to the question posed on the spot and without time for deep reflection: What is Philosophy? Some managed to give precise answers, but many struggled. I think one source of conflict they faced as they answered was that they didn’t know how to separate the question of what philosophers actually do from they should be doing. However, I think that a clear distinction between science, math and philosophy as methodologies can be specified precisely. I also think that this is important because practitioner’s in each subject should be aware of what methodology they are actually using and what is appropriate for whatever problem they are working on.
Here are my definitions: Math explores the consequences of rules or assumptions, science is the empirical study of measurable things, and philosophy examines things that cannot be resolved by mathematics or empiricism. With these definitions, practitioner’s of any discipline may use either math, science, or philosophy to help answer whatever question they may be addressing. Scientists need mathematics to work out the consequences of their assumptions and philosophy to help delineate phenomena. Mathematicians need science and philosophy to provide assumptions or rules to analyze. Philosophers need mathematics to sort out arguments and science to test hypotheses experimentally.
Those skeptical of philosophy may suggest that anything that cannot be addressed by math or science has no practical value. However, with these definitions, even the most hardened mathematician or scientist may be practicing philosophy without even knowing it. Atheists like Richard Dawkins should realize that part of their position is based on philosophy and not science. The only truly logical position to take with respect to God is agnosticism. It may be probable that there is not a God that intervenes directly in our lives and that probability may be high but it is not a provable fact. To be an atheist is to put some cutoff on the posterior probability for the existence of God and that cutoff is based on philosophy not science.
While most scientists and mathematicians are cognizant that moral issues may be pertinent to their work (e.g. animal experimentation), they may be less cognizant of what I believe is an equally important philosophical issue , which is the ontological question. Ontology is a philosophical term for the study of what exists. To many pragmatically minded people, this may sound like an ethereal topic (or worse adjective) that has no place in the hard sciences. However, as I pointed out in an earlier post, we can put labels on at most a countably infinite number of things out of an uncountable number of possibilities and for most purposes, our ontological list of things is finite. We thus have to choose and although some of these choices are guided by how we as human agents interact with the world, others will be arbitrary. Determining ontology will involve aspects of philosophy, science and math.
Mathematicians face the ontological problem daily when they decide on what areas to work in and what theorems to prove. The possibilities in mathematics are infinite so it is almost certain that if we were to rerun history some if not many fields would not be reinvented. While scientists may have fewer degrees of freedom to choose from they are also making choices and these choices tend to be confined by history. The ontological problem shows up anytime we try to define a phenomenon. The classification of cognitive disorders is a pure exercise in ontology. Authors of the DSM IV have attempted to be as empirical and objective as possible but there is still plenty of philosophy in their designations of psychiatric conditions. While most string theorists accept that their discipline is mostly mathematical, they should also realize that it is very philosophical. A theory of everything includes the ontology by definition.
Subjects traditionally within the realm of philosophy also have mathematical and scientific aspects. Our morals and values have certainly been shaped by evolution and biological constraints. We should completely rethink our legal philosophy based on what we now know about neuroscience (e.g. see here). The same goes for any discussion of consciousness, the mind-body problem, and free will. To me the real problem with free will isn’t whether or not it exists but rather who or what exactly is exercising that free will and this can be looked at empirically.
So next time when you sit down to solve a problem, think about whether it is one of mathematics, science or philosophy.