MATHEMATICS AS PHILOSOPHY

It is quite customary for us to think of philosophy as a discipline that contemplates good and bad, right and wrong, the beginning and the end of days, etc., and the reasons for all of these. Yet, we must admit that this is not what philosophy is to be reduced to. We have talked about it earlier already, that philosophy is much more than a contemplation of certain things, no matter how great these things are. Philosophy is, first and foremost, the art of thinking as such: not out of some practical necessity, or having nothing else to do, but thinking for the love of it, that is in order to gain a better knowledge and keener understanding of the nature of things.

Thinking is both rational and irrational, just as God Himself is both rational and irrational. It is based on an elaborate set of hypotheses, all involving absolute standards and values, which alone rationally justify Kant in his quixotic quest after his famous synthetic aprioris.

How does mathematics fit into this suddenly esoteric discussion? The good reader has undoubtedly noticed that in the previous short paragraph I consciously, but by no means disingenuously, built a few bridges that closely connect philosophy to mathematics, or rather, the other way round.

Indeed, previously, I made an assertion that mathematics is, in fact, a subdivision of philosophy, rather than an exact science, and I stand by it. In this entry, on proper development, I intend to prove that mathematics fits the criteria of philosophy with a far greater precision than it can fit the criteria of any science.

One can argue of course that any science contains in its theoretical portion elements of philosophy, and that in this sense we can find philosophy anywhere we look around us, mathematics included. Theoretical physics, for instance is “full of gods,” playfully paraphrasing Thales. In other words, we can find plenty of both irrationality and philosophical analysis in physics alone, not to mention chemistry, biology, etc.

Yet I am not claiming that physics, chemistry and biology are branches of philosophy, although stipulating that elements of philosophy can be discerned in all branches of science. Unlike all these, mathematics in its essence is philosophical, and applied mathematics infuses philosophy into the areas of its application.

How does a mathematical mind work? Unlike a scientific mind, it abstracts from reality, rather than dwells on it. It is by far more intuitive, and whenever a great scientist displays a similar level of intuition, we can call that scientist a philosopher with a better justification than if we ascribe his intuition to science proper. Such differences may appear arcane at first sight, but they are real, and they go to the root of human mindwork.

Not accidentally, most of the early great philosophers were mathematicians par excellence as well. Which did not prevent them of course from being scientists as well, but it does not work the other way: not every great scientist can be a great philosopher or mathematician merely by implication.

In my later elaboration of this entry, I will discuss the parameters that are present in mathematics, which are indicative of its inclusion under the umbrella of general philosophy, but at this point what I have written so far will have to suffice.