History of Philosophy – Lesson 5: Pythagoras and the World of Numbers

“…the crucial point is the vital importance of mathematics in discovering the laws of the world, in making sense of the universe […] modern science is in part a development of this discovery of the Pythagoreans.”
— Leonard Peikoff, “History of Philosophy” course, ARI, Lesson 5.
(The Drake equation is a probabilistic argument used to estimate the number of civilizations in our galaxy with which communication might be possible. How crazy is that? I bet Drake would not have come up with that idea if it weren’t for the Pythagoreans. Original source: Kevin Gill; CC BY 2.0 / Desaturated from original)

So, Parmenides created a problem. The world was made of one single stuff but it appeared to change, while Logic asserted that was impossible. How to reconcile this in one single world? Well, you don’t. There are two worlds: the “world of appearances” here below, always changing and apprehended by the senses; the “real world” high above, immutable and hidden. And the real one, believe it or not, is made of numbers.

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History of Philosophy – Lesson 3: Heraclitus and the World of Contradiction

A great many children live in that kind of world thanks to the wanton irrationality of their parents, whose behavior is characterized by constant switching and swimming so that nothing ever holds true from one moment to the next, and by constant contradictions. That is the perfect recipe for the Heraclitean world.
— Leonard Peikoff, “History of Philosophy” course, ARI, Lesson 3.
(Since very early in the history of philosophy, Heraclitus disregarded the senses as invalid and accepted contradiction in reality. Two and a half thousands years later, we still see the effects of such errors.)

Thales gave rise to philosophy by relying on sensory experience and reason. The next philosopher in line [1]Heraclitus — not only trailed a different path, but ignited a chain-reaction that ran through history toppling like dominos all that man tried to erect with his reason. It all began with the problem of change and multiplicity; it all ended with my thirteen-year-old niece asking petulantly: “Why can’t I simply decide I am a boy?”

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