Those of us who are not totally deficient in humility, must all agree that God, an infinitely superior being to man, is, of necessity, totally incomprehensible to his creatures, to the point that even His very existence can in no way be ascertained through human reason, and can only be accepted irrationally, on faith, or formally, by postulate. This is why throughout history man has been making persistent efforts to find an indirect road leading to God through a variety of more or less comprehensible intermediaries. Christianity, in this sense, has advanced the farthest of all religions, in the tangible person of Jesus Christ: a humanly comprehensible flesh-and-blood individual, yet, at the same time, God Incarnate. Yet before we are carried away visualizing Jesus as “one of us,” let us not forget that there always has been a thick and virtually impenetrable cloud of mysticism surrounding Him, as testified to by the Evangelist John, in John 1:1-10. (“…And the light shineth in darkness; and the darkness comprehended it not…”) Thus, we have to admit that, although we think that we “know” Jesus from the Scriptures and from numerous artistic representations of Him, the truth of the matter is that paradoxically we know less about Him than we know about God from all other non-Christian religions.
Long before Christianity would come into existence, an amazing effort was made to represent God through the mystical medium of numbers, and the man to do it was the legendary (literally so!) Pythagoras. And now the reason why I started to tell this story with a reference to Christianity will become clear, as I am about to do the following, seemingly irreverent, but philosophically justifiable paraphrase of John 1:1:
“In the beginning was the Number, and the Number was with God, and the Number was God.” Let the good reader not get emotional about this shocking substitution of the traditional Logos, but, rather, enjoy the feast on the abundant food for thought, resulting from this challenging, but intellectually exciting substitution…
Continuing with this entry on Pythagoras proper (there will be also a very large subsection on Pythagoras in my PreSocratica Sempervirens section that will be posted later), I find it most fitting to quote this short, but monumental tribute, opening the Pythagoras Chapter in Bertrand Russell’s History of Western Philosophy:
“Pythagoras… was intellectually one of the most important men who ever lived, both when he was wise and when he was unwise. Mathematics, in the sense of demonstrative deductive argument, begins with him and in him is intimately connected with a peculiar mysticism. The influence of mathematics on philosophy has ever since his time been both profound and unfortunate.”
(Here again we are facing the same problem of mathematics terribly overrated as an “exact science”, which we have encountered so explicitly in Hobbes and less explicitly in most other philosophies. I am particularly happy that Russell pinpoints this particular problem, but, alas, he does not go far enough in generalizing it!)
And later, in the same chapter:
“Pythagoras is one of the most interesting and puzzling men in history. Not only are the traditions concerning him an almost inextricable mixture of truth and falsehood, but even in their barest and least disputable form they present us with a curious psychology. He may be described as a combination of Albert Einstein and Mrs. Eddy. He founded a religion, of which the main tenets were the transmigration of souls and the sinfulness of eating beans. His religion was embodied in a religious order, which, here and there, acquired control of the State and established the rule of the saints… I do not know of any man who has been as influential as he was in the sphere of thought. I say it because what appears as Platonism is, when analyzed, found to be in essence Pythagoreanism.”
(Plato as a derivative of Pythagoras? Perhaps, Nietzsche may have been more correct calling Plato a “hybrid type,” which must include a number of pre-Socratic influences, not limited to Pythagoreanism alone! Curiously, all this goes very neatly together with Alfred North Whitehead’s shocking pronouncement that all Western philosophy is nothing but a series of footnotes to… Plato! Then vivant Pythagoras and the pre-Socratics!!!)
“The whole conception of ‘eternal world’, revealed to the intellect, but not to the senses, is derived from him. But for him, Christians would not have thought of Christ as the Word; but for him, theologians would not have sought logical proofs of God and immortality.”
[The first part of the last sentence is not altogether accurate, as the concept of Logos had long existed in Ancient Greek thought, not exclusively courtesy of Pythagoras’ influence, but otherwise the connection between Pythagoreanism and Christianity does exist, except that the same can be said of all religions, always trying to make God comprehensible to their adherents through a variety of more accessible mediums.]
Ironically, all that we know about this “most important, most interesting and puzzling man in history” has a seal of myth imprinted on it. Nothing of his original writings is extant, and much of what is attributed to him has been done so spuriously.
Much of what we know about Pythagoras, or rather about the ancient Pythagoreans, comes to us courtesy of Aristotle, who is by no means an objective observer here, but displays an occasionally strong bias against them, for which reason his testimony (particularly, in its negative portion) must be taken with a giant chunk of rock salt.
The following are short excerpts from Aristotle’s Metaphysics and Physics, dealing with the Pythagoreans. Much more of this will be found in my PreSocratica section, but my intention here is to concentrate on the particular subject of numbers as the substance of both Divinity and Nature.
“Those called Pythagoreans… thought that the first principles of these numbers were the first principles of all things. And since in sciences numbers are by nature the first, in numbers rather than in fire and earth and water they thought they saw likenesses to 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.”
There is a clear-cut connection here to the Kantian Ding an-Sich, which is in essence what Aristotle calls “the first principles.” I wonder whether Kant himself ever considered the Pythagorean solution for his quest, choosing numbers as the “itself “of things? As far as I remember, he never alludes to such a possibility.
“Discerning in numbers the conditions and reasons of harmonies also; since moreover other things seemed 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.”
Well, it does make some sense that inasmuch as musical harmony is actually counted in numbers, and God and His Creation contain harmony, numbers can be somehow related to God and nature, and serve at least as certain attributes of Divinity.
“(The Pythagoreans) both hold that the infinite is being, and divide it… As they say, all things are defined by threes; for end, and middle, and beginning constitute the number of the All, and also the number of the Triad.”
Dividing the infinite, in my view, downgrades the infinite, and raises the power of numbers to a status above Divinity, thus, in numbers, the Pythagoreans have found a substitute for God. As for the power of the triad, an immediate association with the mystery of the Trinity leaps to mind, but turning such association into a tempting conclusion would be very superficial. My invariable conception of the Trinity has been the three Manifestations of God, the unknowable Father, the knowable Son, and the immanent Holy Spirit, which, apparently, has nothing to do with most of what the Pythagoreans must have had in mind. But what strikes me as very clever is their unity of space and time, in the concept of the Triad, yet this Triad fails to reach beyond the Kantian Undinge, and therefore the infinite has to be free of these limitations and non-divisible by definition. The triad would make sense only as God who thus controls the universe by arranging it into “before, now, and after,” on the one hand, and “the beginning, the middle, and the end,” on the other. But this whole arrangement is riddled with holes, as Aristotle rightly observes in other passages.
Curiously, by placing the number in excelsis, the Pythagoreans did not quite solve the mystery of the Deity, but only came up with a superior concept of the number, turning it into a substitute for God. This, however, is not a failing, in my book, as what they have given us in abundance, with their challenging theory, is fresh and nourishing food for thought, compensating, more than generously, for the holes in their philosophical construction.
Long before Christianity would come into existence, an amazing effort was made to represent God through the mystical medium of numbers, and the man to do it was the legendary (literally so!) Pythagoras. And now the reason why I started to tell this story with a reference to Christianity will become clear, as I am about to do the following, seemingly irreverent, but philosophically justifiable paraphrase of John 1:1:
“In the beginning was the Number, and the Number was with God, and the Number was God.” Let the good reader not get emotional about this shocking substitution of the traditional Logos, but, rather, enjoy the feast on the abundant food for thought, resulting from this challenging, but intellectually exciting substitution…
Continuing with this entry on Pythagoras proper (there will be also a very large subsection on Pythagoras in my PreSocratica Sempervirens section that will be posted later), I find it most fitting to quote this short, but monumental tribute, opening the Pythagoras Chapter in Bertrand Russell’s History of Western Philosophy:
“Pythagoras… was intellectually one of the most important men who ever lived, both when he was wise and when he was unwise. Mathematics, in the sense of demonstrative deductive argument, begins with him and in him is intimately connected with a peculiar mysticism. The influence of mathematics on philosophy has ever since his time been both profound and unfortunate.”
(Here again we are facing the same problem of mathematics terribly overrated as an “exact science”, which we have encountered so explicitly in Hobbes and less explicitly in most other philosophies. I am particularly happy that Russell pinpoints this particular problem, but, alas, he does not go far enough in generalizing it!)
And later, in the same chapter:
“Pythagoras is one of the most interesting and puzzling men in history. Not only are the traditions concerning him an almost inextricable mixture of truth and falsehood, but even in their barest and least disputable form they present us with a curious psychology. He may be described as a combination of Albert Einstein and Mrs. Eddy. He founded a religion, of which the main tenets were the transmigration of souls and the sinfulness of eating beans. His religion was embodied in a religious order, which, here and there, acquired control of the State and established the rule of the saints… I do not know of any man who has been as influential as he was in the sphere of thought. I say it because what appears as Platonism is, when analyzed, found to be in essence Pythagoreanism.”
(Plato as a derivative of Pythagoras? Perhaps, Nietzsche may have been more correct calling Plato a “hybrid type,” which must include a number of pre-Socratic influences, not limited to Pythagoreanism alone! Curiously, all this goes very neatly together with Alfred North Whitehead’s shocking pronouncement that all Western philosophy is nothing but a series of footnotes to… Plato! Then vivant Pythagoras and the pre-Socratics!!!)
“The whole conception of ‘eternal world’, revealed to the intellect, but not to the senses, is derived from him. But for him, Christians would not have thought of Christ as the Word; but for him, theologians would not have sought logical proofs of God and immortality.”
[The first part of the last sentence is not altogether accurate, as the concept of Logos had long existed in Ancient Greek thought, not exclusively courtesy of Pythagoras’ influence, but otherwise the connection between Pythagoreanism and Christianity does exist, except that the same can be said of all religions, always trying to make God comprehensible to their adherents through a variety of more accessible mediums.]
Ironically, all that we know about this “most important, most interesting and puzzling man in history” has a seal of myth imprinted on it. Nothing of his original writings is extant, and much of what is attributed to him has been done so spuriously.
Much of what we know about Pythagoras, or rather about the ancient Pythagoreans, comes to us courtesy of Aristotle, who is by no means an objective observer here, but displays an occasionally strong bias against them, for which reason his testimony (particularly, in its negative portion) must be taken with a giant chunk of rock salt.
The following are short excerpts from Aristotle’s Metaphysics and Physics, dealing with the Pythagoreans. Much more of this will be found in my PreSocratica section, but my intention here is to concentrate on the particular subject of numbers as the substance of both Divinity and Nature.
“Those called Pythagoreans… thought that the first principles of these numbers were the first principles of all things. And since in sciences numbers are by nature the first, in numbers rather than in fire and earth and water they thought they saw likenesses to 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.”
There is a clear-cut connection here to the Kantian Ding an-Sich, which is in essence what Aristotle calls “the first principles.” I wonder whether Kant himself ever considered the Pythagorean solution for his quest, choosing numbers as the “itself “of things? As far as I remember, he never alludes to such a possibility.
“Discerning in numbers the conditions and reasons of harmonies also; since moreover other things seemed 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.”
Well, it does make some sense that inasmuch as musical harmony is actually counted in numbers, and God and His Creation contain harmony, numbers can be somehow related to God and nature, and serve at least as certain attributes of Divinity.
“(The Pythagoreans) both hold that the infinite is being, and divide it… As they say, all things are defined by threes; for end, and middle, and beginning constitute the number of the All, and also the number of the Triad.”
Dividing the infinite, in my view, downgrades the infinite, and raises the power of numbers to a status above Divinity, thus, in numbers, the Pythagoreans have found a substitute for God. As for the power of the triad, an immediate association with the mystery of the Trinity leaps to mind, but turning such association into a tempting conclusion would be very superficial. My invariable conception of the Trinity has been the three Manifestations of God, the unknowable Father, the knowable Son, and the immanent Holy Spirit, which, apparently, has nothing to do with most of what the Pythagoreans must have had in mind. But what strikes me as very clever is their unity of space and time, in the concept of the Triad, yet this Triad fails to reach beyond the Kantian Undinge, and therefore the infinite has to be free of these limitations and non-divisible by definition. The triad would make sense only as God who thus controls the universe by arranging it into “before, now, and after,” on the one hand, and “the beginning, the middle, and the end,” on the other. But this whole arrangement is riddled with holes, as Aristotle rightly observes in other passages.
Curiously, by placing the number in excelsis, the Pythagoreans did not quite solve the mystery of the Deity, but only came up with a superior concept of the number, turning it into a substitute for God. This, however, is not a failing, in my book, as what they have given us in abundance, with their challenging theory, is fresh and nourishing food for thought, compensating, more than generously, for the holes in their philosophical construction.
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