PYTHAGORAS OF THE FIRST PRINCIPLES

From elementary musical harmony to the music of the spheres was already a giant leap, but Pythagoras is not stopping there. On the contrary, he makes an even larger leap from the spheres into the mystical realm of the first principles. Summarized in one short catchy phrase, he is ready to pronounce that all things are numbers. Having no records of anything from Pythagoras himself, we have to rely on Aristotle and others, but Aristotle being the flagship of Pythagorean criticism, let us concentrate on what he is saying about this in his Metaphysics (i. 5; 985 b 23-986 b 8):

Those called Pythagoreans applying themselves to sciences, first developed them, and brought up in them, thought that the first principles of these numbers were the first principles of all things. And since of these (sciences) numbers are by nature the first, in numbers, rather than in fire and earth and water, they thought they saw many likenesses to the things that are and that are coming to be, as, for instance, justice is such a property of numbers, and soul and mind are such a property, and another is opportunity, and of other things one may say the same of each one.

It is actually quite instructive to think about all these weird Pythagorean ideas. Anybody who is tempted to dismiss this stuff as so much nonsense ought to be repeatedly and forcefully reminded that Pythagoras was himself a science genius, whose geometrical discoveries belong to the gold reserve of human thought, also that all his disciples and future followers, too, must have been exceptionally bright men in their own right, probably, among the brightest minds of their time. One can appreciate them much better and learn much more from the treasures of their ingenuity, if he or she takes my approach to science: as fiction, which all science, modern science no exception, should be seen as. After all, the best of history is mythology, that is fiction, all mathematics is fiction, as I have observed in my Euclid-Lobachevsky entries, and, unless we are prepared to treat the Pythagorean ideas about numbers in the same manner, we’ll end up learning nothing much from them. Incidentally, when we talk about actual discoveries in technology, medicine, and in other practical fields, we are not looking at the sciences there, but at their applications, which do, indeed, possess practical value. This basic philosophical distinction between science and application has to be understood, otherwise, the mind will dwell in a state of perpetual confusion. For instance, the much-admired relativity formula of a young Einstein was a purely fictional construct, whose veracity has always been doubted, and recently debunked, rather unfairly, I might add, considering how many practical applications of his theory have all been very successfully implemented.

And further, discerning in numbers the conditions and reasons of harmonies, since other things appeared to be like numbers in their entire nature, and numbers were the first of every nature, they assumed that the elements of numbers were the elements of all things, and the whole heavens were harmony and number.

Once again I may point out that, talking about heavens, the Pythagoreans had in mind a peculiar mixture of the physical sky above their head and an imagined supernatural being of religious and mystical fancy, the Great Beyond, the Heaven of Religion. From the vantage point of our modern knowledge, which they did not possess in their time, every schoolchild may know more about certain things in physics than they ever did, but if we should dismiss what they say on those grounds, we end up ill-served, because our knowledge which contradicts them is mechanical information we have picked up from books, whereas these passages are inviting us beyond conventional wisdom, on a think-along journey of creative imagination, and this is where, and only where, we must by all means accept such intellectual challenge. Let us keep in mind that a great scientist, if we want to be one, debunks the science of his own day, not of the bygone days of the past millennia. Anybody draping himself in modern science is deficient in that invaluable imagination, which alone shatters the barriers to human endeavor and places the pathfinder on a par with the greatest minds of the past, even though none of the latter would pass a simple middle-school test that should be a cinch for any mediocre student of our day.

And whatever characteristics in numbers and harmonics they could show in agreement with the properties of the heavens and its parts and with its whole arrangement, these they collected and adapted; and if there chanced to be any gap anywhere, they eagerly sought that the whole system might be connected with these (stray phenomena). To give an example of my meaning: inasmuch as ten seemed to be the perfect number and to embrace the whole nature of numbers, they asserted that the number of bodies moving through the heavens were ten, and when only nine were visible, for the reason stated they postulated the counter-earth as the tenth.

Once again I would like to note that the utterly ridiculous concept of a counter-earth does not look all that ridiculous anymore, when we rise above the school textbooks and consider the bigger picture, such as the dialectical opposition of the thesis and the antithesis for instance. Without the intention to diminishing the importance of formal schooling, I insist that our need to think with our own head is by far greater than our obligation to remember whatever we were taught at school by others. Anybody whose creative imagination is alive and well ought to appreciate the creative inducement that sparks the flame of thinking as we come across something as delightfully wacky as this Pythagorean counter-earth treasure.

We have given a more definite account of these thinkers in other parts of our writings, but we refer to them here with this purpose in view that we might ascertain from them what they asserted as the first principles, and in what manner they came upon the causes that have been specified. They certainly seem to consider number as the first principle and as it were the matter in things and in their conditions and states; and the odd and the even are elements of number, and of these the one is infinite and the other finite, and unity is the product of them both, for it is both odd and even, and number arises from unity, and the whole heaven, as has been said, is numbers.

“The whole heaven is numbers…” If this sentence were given as a theme for an essay to a class of college students, I wonder how many of them would consider it a joke. But it is not a joke. Here is a declaration of a religious principle, and in this case the follow-up question is “What is wrong with such a religion?” My answer is that it lacks the ethical component, which ought to be essential to any legitimate religion. Thus it is obvious (at least to me) that the Pythagoreans have produced a clearly deficient religion, but this should in no way diminish their value as a terrific intellectual challenge, and a sumptuous feast for thought!

A different party in this same school say that the first principles are ten, named according to the following table: finite and infinite (how about comprehensible and incomprehensible?) even and odd (if this is about numbers, the pair of rational and irrational should make even more sense!) one and many (it is interesting to mention that although there exists a linguistic parallel in many languages of one and many to the singular-plural dichotomy, in some languages, particularly in old Russian, and rudimentarily in modern Russian, a third number is added, which is dual, referring to nouns, which form natural pairs; and it appears that the Pythagoreans ought to be sensitive to this “dual number,” which however destroys the opposition that they are so eager to build) right and left (yes, but why on earth not above and below, which to me seems a much more significant opposition than right and left, indicative of heaven and earth, but not covered by the first group of finite and infinite?!) male and female, rest and motion, straight and crooked, light and darkness, good and bad (this sudden infusion of ethics into a motley collection dominated by geometry and numbers seems out of place, especially when followed next by another geometrical opposition, which however has a mystical significance in Pythagoreanism, but still rather awkward), square and oblong (generally speaking, this grouping of ten principles is rather arbitrary and riddled with holes).

After this manner Alkmaeon of Kroton (there will be a separate entry on him later on in this series!) seems to have conceived them, and either he received this doctrine from them, or they from him; for Alkmaeon arrived at maturity when Pythagoras was an old man, and his teaching resembled theirs. For he says that most human affairs are twofold, not meaning the two opposites reached by definition, as did the former party, but opposites by chance. (There it is: anything that is chance by nature can be codified by definition. How can I disagree with my own principle that anything accepted by definition is above the need to be proven. However, I have added a caveat: as long as such thing makes sense, and this part, unlike the other one, needs to be proven, otherwise, this thing-by-definition becomes too superfluous, and does not merit any legitimacy.) As, for example, white-black, sweet-bitter, good-bad, small-great. (Alkmaeon) let fall his opinions indefinitely about the rest, but the Pythagoreans declared the number of the opposites, and what they are. From both, one may learn that opposites are the first principles of things; but from the latter he may learn the number of these, and what they are. (If this is indeed about the opposites, then there are many more similar “principles” than the ten mentioned earlier. On the other hand, if this motley collection of principles is about things in that case the good-bad opposition has no place here, because ‘things-as-such’ are not supposed to be ethically charged. A poison can be considered a bad thing, but when it is used as a cure, the very same thing becomes good, just by virtue of the manner in which it is being used. This coincides with my thinking on the tool and usage distinction in my piece on International Justice, where I call all science a tool of human endeavor, like a hammer, and propose that a tool is in itself an ethically neutral thing) But how it is possible to bring them into a relation with the causes of which we have spoken, they have not clearly worked out, but they range their elements under the category of matter, saying that being is compounded and formed from them, and that they inhere in it. (The last passage exemplifies what I have called a general theory, all theories of this nature being false, in my opinion. At the same time, as soon as we start looking at them as fiction, they become true. So, how can this apparent contradiction be resolved? Yet again, in terms of my thinking on this subject, the truth of fiction is only maintained as such within the world of its creator and loses its license as soon as it crosses the border, unless it is appropriated by the new host as its own fiction. This logic holds on here just as well. As long as we regard this thinking as Pythagorean, or Pythagorean-plus, fiction let it be, provided we do not look at it as a general truth, and do not start passionately arguing against it (which would be a totally senseless waste of time).