Anaximander & Pythagoras

Anaximander & Pythagoras

By Dr. N. V. Kulkarni

“The conception of the Infinite in Anaximander which has been legitimately regarded, as by Windelband, as the first European philosophical conception of God.  It is unfortunate that though Pythagoras and Aristotle came after Anaximander, they could not understand the full significance of Anaximander’s Apeiron-Infinite.  Pythagoras did great injustice to it by saying that the conception of the unlimited was an even, and not an odd number, and therefore capable of multiplicity and evil”.

– Dr. R. D. Ranade, “Pathway to God in Hindi Literature”, P. 404 – 405

An effort has been made here to throw some light in order to grasp, if not full, at least some more significance of the above quoted statement of Shri Gurudev Ranade.


“Anaximander, the second philosopher of the Milesian school, is much more interesting than Thales.  His dates are uncertain, but he was said to have been sixty-four years old in 546 B.C. and there is reason to suppose that this is somewhere near the truth.  He held that all things come from a single Primal Substance, but that it is not water, as Thales held, or any other of the substances that we know.  It is infinite, eternal and ageless, and it encompasses all the worlds’ for he thought that our world is only one among many.  The Primal Substance is transformed into the various Substances which we are familiar with, and these are transformed into each other.  As to this, he makes an important and remarkable statement.

“Into that from which things take their rise, they pass away once more, as is ordained, for they make reparation and satisfaction to one another for their injustice according to the order of time.””

Anaximander had an argument to prove that the primal substance could not be water, or any other known element.  If one of these were primal, it would conquer the others.  Aristotle reports him as saying that these known elements are in opposition to one another.  Air is cold, the water is moist, and the fire is hot.  ‘And therefore, if any one of them were infinite, the rest would have ceased to be by this time.’  The primal substance, therefore, must be neutral in this cosmic strife.

Anaximander was full of scientific curiosity.  He is said to have been the first man who made a map.

The doctrine of evolution, that different forms of life had evolved gradually, was also maintained by him.  Further his metaphysics is dominated by a conception of cosmic justice, which prevents the strife of opposites from ever issuing in the complete victory of either.

  • Bertrand Russel, History of Western Philosophy

This aspect of cosmic justice will not be discussed here.


Sankara says “True Being” is ‘sat’,‘सत्’ alone, being itself, the Eternal Brahman, unchanging and unchanged undivided and without parts.  “Ekam eve Advitiyam! ‘Sat’ itself the one only, without parts, without any multiplicity, and therefore without the multiplicity of differences and delimitations.”…

“Eckhart says …”  It is absolutely ‘unum’ – one not only in comparison with others, but in itself.  This eternal one, undivided, non-multiple Being is God.”…

  • Rudolph Otto – Mysticism.

“Pythagoras, as we all learnt in youth, discussed the proposition, that the sum of the squares on the sides of a right angled triangle is equal to the square of the hypotenuse …”

But the theorem, though it has remained his chief claim to immortality, it was soon found to have a consequence, fatal to his whole philosophy!  Consider the case of a right – angled triangle whose two sides are equal, such a triangle as is formed by two sides of a square and a diagonal.  Here, in virtue of the theorem, the square on the diagonal is double of the square on either of the sides.  But Pythagoras or his early followers easily proved that the square of one whole number, cannot be double of the square of another.

The pythagorean proof is roughly as follows.  If possible, let the ratio of the diagonal to the side of a square be m/n, where m and n are whole numbers, having no common factor.  Then we must have m2 = 2n2.  Now the square of an odd number is odd, but m2, being equal to 2n2 is even.  Hence ‘m’ must be even.  But the square of an even number divides by 4, therefore n2, which is half of m2, must be even.  Therefore ‘n’ must be even!  But, since ‘m’ is even, and ‘m’ and ‘n’ have no common factor, ‘n’ must be odd.  Thus ‘n’ must be both odd and even, which is impossible.

  • Bertrand Russel. “Our knowledge of the External world.”

It is left to the readers to view this, vis-à-vis the injustice done by Pythagoras.

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