The Benefits of Mathematical and Logical Training for Studying Philosophy

7,356 characters2008.02.15

Although I entered the philosophy department as an undergraduate, I still unabashedly identify myself as “from a science background.” Of course, the current Chinese practice of splitting high school students into arts and sciences is very bad; the so-called “science students” in high school are not necessarily all that “scientific” in any meaningful sense—after all, most of them choose physics. And it is even harder to say how much “literature” arts students have actually come into contact with—how can middle-school history, politics, and the like be called “literature”?

But when I say I am “from a science background,” I do not mean that I was a high school science student; I mean that I spent more than ten years from elementary school onward doing science competitions, and after so many years of Olympiad training, I believe that compared with some university undergraduates from science and engineering backgrounds, I can also claim my “scientific background” with a perfectly clear conscience.

My “science” is the science of mathematics and physics, the science of theory, the science of understanding, the science of reason—not merely the “science” of “science and engineering.” For some people, a science background is manifested only in being good at calculation and experiment, or, worse still, only in revering calculation and experiment. But calculation and experiment are nothing more than technical proficiency; in fact, they are of no overriding significance. It is much like how some people’s so-called “arts background” is manifested only in being skillful with ornate language, or, worse still, only in deliberately pursuing ornate language.

To take “science” as the technique of calculation and experiment, and “literature” as the craft of wording and sentence-making, is equally to miss their true essence.

And speaking of “literature”: many philosophical scholars are more willing to emphasize their “arts background,” or to emphasize the influence literature has had on them. I have no standing to say exactly how a literary background promotes a philosophical path. But we can hear many different ways of stressing that “literature is the study of humanity,” or that literature reveals human nature, and so on—in short, that literature brings “humanity” to light.

This is, of course, not bad. Yet some “literary youths” easily get hotheaded, as if “humanity” were literature’s exclusive patent, as if one could not understand what a human being is without reading literature. And there lies the harm of “literature.” Moreover, if you try to press them: what exactly has literature done to “humanity”? What on earth do you mean by “human”? then they cannot say it clearly or explain it coherently, and in the end they may perhaps toss you the phrase “something that can be understood intuitively but not expressed in words” and leave it at that; if you then continue to pry, you are merely making a fool of yourself.

Indeed, poetic language is often resistant to “inquiry,” and novels and fables alike are closed to questioning. After reading a fable, you can take the occasion and spin out all kinds of associations; but if you insist on asking how exactly the animals in *Animal Farm* learned to speak, that would spoil the mood entirely.

That is the characteristic of literature: freedom, unrestrainedness. But if one carries this characteristic over into philosophy, then things become utterly disastrous.

So we can see many philosophers “from a literary background” carrying precisely this tendency. Thinking back, one of my earlier remarks could also be classified as “Keyword Fever Syndrome”—“not caring about the preface and the postscript of a sentence, its sense and reference, intension and extension, and so on; just as soon as one sees certain ‘keywords,’ one immediately becomes mentally agitated.”

Scholars deeply influenced by the “arts” are probably more prone to this condition. For example, the moment they hear the word “human,” they get excited right away; others are especially sensitive to words like rights, democracy, freedom, and so on, and as soon as these are mentioned, they begin waving their arms and legs; still others are “allergic” to words such as science, theory, system, elite, and so forth, and the moment these are mentioned, they become resistant and opposed. By contrast, people from a science background have long been accustomed to carefully examining every concept, and only after rigorous definition do they dare to use it cautiously. Thus they often have a much higher immunity to “keyword fever syndrome.”

Apart from keyword allergy, those lacking mathematical and scientific training are also prone to “aphorism allergy.” They often like to seize upon some pleasing-sounding yet seemingly profound saying and enshrine it, such as “literature is the study of humanity,” “one flower, one world,” “the unity of knowledge and action,” “the unity of Heaven and humanity,” “poetic dwelling,” “remain silent about that which cannot be spoken,” and so on, thinking them brilliantly expressed, wanting to carve them on their desk. But those with mathematical and scientific training tend not to care for this. Our math teachers taught us from childhood: merely arriving at the answer to a problem by chance means nothing at all; what matters is your entire problem-solving process. People lacking mathematical and scientific training tend to read books sentence by sentence, treating philosophical works as collections of aphorisms, whereas people from a science background want to understand the philosopher’s whole conceptual system. For us, a philosopher’s conclusions and assertions are not important; what matters is the entire system of thought and mode of thinking—at least for us: if the process is flawless but you only miscalculate the final step, you can still get 8 points; if the process is completely off the mark and only the final answer happens to come out right, you get at most 2 points, or even 0.

Many “science students” also belong to the category I call “lacking mathematical and scientific training.” They merely study mathematics as if it were a set of ready-made formulas and tricks, without knowing to trace things back to their roots and savor the meaning of “proof.” In that case, even if he gets perfect marks in mathematics every time, I would still say he lacks mathematical and scientific training, or that his training method is misguided. In fact, by my lights, the “mathematicians” of early analytic philosophy also had an insufficient grasp of “science”; when reading Kant they would simply snatch out a line like “being is not a predicate.” Of course, the problems of that group are more complicated and would need to be handled as a separate case.

Of course, I do not want to stir up an atmosphere of opposition between the “two cultures,” and I am even less advocating that mathematical and scientific training is a required course for philosophy, just as I do not think literature is the only path to the so-called “study of humanity.” Nonetheless, there is no doubt that mathematical and scientific training is a shortcut to acquiring a good style of thinking—seriousness, responsibility, gravity, systematicity, creativity, and so on.

February 15, 2008