The Vocabulary of Myth, Part XX

Pythagoras the Teacher of a Way of Life…

His Doctrine of Transmigration of Souls…

 “Philosophy” as a Methods for the Salvation of the Soul…

  Pythagoras and Mathematics…

Deductive Geometry and the Ascent of the Soul to the Divine…

     As Plato reports, Pythagoras taught “a way of life”, and it becomes apparent what that was:  a life “in accordance with what is highest in us”, in accordance, that is, with the soul whose divine origin and nature must be remembered and fully realized, and in detachment from the body and world in which it is a prisoner and exile.

One of the methods by which the Pythagoreans nurtured the soul at the expense of the body was a kind of purgatorial regime, including an abstention from meat. This was clearly enough connected with Pythagoras’ doctrine of the transmigration of souls.  As his contemporary Xenophanes records,

They say that once when a puppy was being whipped, Pythagoras, who was passing by, took pity on it, saying, “Stop!  Do not beat it!  It is the soul of a friend; I recognize his voice!”

The doctrine of transmigration of souls may have been borrowed by Pythagoras from the Orphic cult, which also flourished in southern Italy in the sixth century; or it may have been imported by Pythagoras directly from the East, if the tradition according to which he traveled eastward as far as Babylonia, before returning to Croton, is true.  Whatever its origins, Pythagoras’ belief that the soul undergoes a series of incarnations throughout the various ranks of the animal kingdom meant, amongst other things, that the killing of animals for food was a sin akin to murder.

But the Pythagorean taboo against eating meat seems to be part of a broader ascetical regime.  As Diogenes Laertius reports, Pythagoras restricted himself to the most meager diet of honey, bread, and vegetables, rarely drank wine, and never enjoyed carnal relations with a woman.  These abstinences were clearly meant to detoxify the soul, the highest and divine element of the human person, of the body’s contaminating influence.

Such ideas, as we’ll see, became salients of Platonism, as did Pythagoras’ conception of philosophical inquiry itself as a method for the purification and salvation of the soul.  Thus Diogenes Laertius says that Pythagoras was the first to use the word “philosophy”, and to call himself a philosopher, that is, a lover of wisdom:  “For no one, he said, is wise except god.”  For Pythagoras, then, as for Plato after him, the life of philosophy was essentially a religious vocation, whose purpose was the salvation and deification of the soul, or rather, the restoration or repristination of its original nature, which was divine.

Above all, philosophical inquiry for Pythagoras meant the investigation of the first principles of mathematics.  Pythagoras’ many and seminal geometrical, algebraic, and arithmetical discoveries include far more than merely the famous triangle theorem named for him, but we don’t have the space (nor do I have the expertise) to consider them here.

The major point to be noted about Pythagorean mathematics is the way it accorded with Pythagoreanism as a soteriological method, by emancipating the rational intellect from its reliance on the world of matter and the senses.  As the fifth-century A.D. Neoplatonist Proclus explains in his commentary on Euclid, geometry was first discovered by the Egyptians, who used it to measure the areas of farmers’ fields whose boundaries were annually obliterated by the flooding of the Nile.  Geometry was, as such, an entirely practical “art”, and as applied by the Egyptians to the land, it remained purely inductive and empirical.  But “Pythagoras transformed this study into a form of liberal education, examining its principles from the beginning and tracking down the theorems immaterially and conceptually”.  In this way, continues Proclus, geometry “elevates the soul and does not allow it to descend to objects of sense in order to satisfy the common needs of mortals, and so neglect the turning of the soul to things above”.

By liberating geometry from the practical necessity of measuring the land through a kind of inductive trial and error, and discovering the universal conceptual principles upon which any area could be ascertained in theory, Pythagorean mathematics becomes a deductive method (where “deductive” retains its primary sense of “leading out of”) by means of which the soul abstracts itself from its dependence upon the entire material order.  The fact, that is, that the square of the hypotenuse equals the sum of the squares of the other two sides is not determined by what happens when any three sticks are laid in a closed figure on the ground by surveyors, but by a rational inference from first principles.  Mathematics proceeds, then, not from the uncertain testimony of the senses, but, as Proclus writes, “immaterially and conceptually”.  In this way, as Socrates would later put it in the Phaedo, the soul withdraws from the body and the world into itself, and lives as if by itself and alone.  Unencumbered by the material order and the sensory organs by which it is perceived, it rises, through the contemplation of mathematical concepts, to the invisible spiritual world in which such concepts, in communion with the Divine, eternally reside.

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