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2.2 Post-Aristotelian Sources for Pythagoras

The problems regarding the sources for the life and philosophy ofPythagoras are quite complicated, but it is impossible to understandthe Pythagorean Question without an accurate appreciation of at leastthe general nature of these problems. It is best to start with theextensive but problematic later evidence and work back to the earlierreliable evidence. The most detailed, extended and hence mostinfluential accounts of Pythagoras’ life and thought date to the thirdcentury CE, some 800 years af...

2.3 Plato and Aristotle as Sources for Pythagoras

In reconstructing the thought of early Greek philosophers, scholarsoften turn to Aristotle’s and Plato’s accounts of their predecessors,although Plato’s accounts are embedded in the literary structure ofhis dialogues and thus do not pretend to historical accuracy, whileAristotle’s apparently more historical presentation masks aconsiderable amount of reinterpretation of his predecessors’ views interms of his own thought. In the case of Pythagoras, what is strikingis the essential agreement of...

References to Pythagoras by Xenophanes (ca. 570–475 BCE) andHeraclitus (fl. ca. 500 BCE) show that he was a famous figure in thelate sixth and early fifth centuries. For the details of his life wehave to rely on fourth-century sources such as Aristoxenus,Dicaearchus and Timaeus of Tauromenium. There is a great deal ofcontroversy about his origin and early life, but there is agreementthat he grew up on the island of Samos, near the birthplace of Greekphilosophy, Miletus, on the coast of Asia Minor. There are a number ofreports that he traveled widely in the Near East while living onSamos, e.g., to Babylonia, Phoenicia and Egypt. To some extent reportsof these trips are an attempt to claim the ancient wisdom of the eastfor Pythagoras and some scholars totally reject them (Zhmud 2012,83–91), but relatively early sources such as Herodotus (II. 81) andIsocrates (Busiris 28) associate Pythagoras with Egypt, sothat a trip there seems quite plausible. Aristoxenus says that he leftSamos at t...

One of the manifestations of the attempt to glorify Pythagoras in thelater tradition is the report that he, in fact, invented the wordphilosophy. This story goes back to the early Academy, since it isfirst found in Heraclides of Pontus (Cicero, Tusc. V 3.8;Diogenes Laertius, Proem). The historical accuracy of thestory is called into question by its appearance not in a historical orbiographical text but rather in a dialogue that recounted Empedocles’revival of a woman who had stopped breathing. Moreover, the storydepends on a conception of a philosopher as having no knowledge butbeing situated between ignorance and knowledge and striving forknowledge. Such a conception is thoroughly Platonic, however (see,e.g., Symposium204A), and Burkert demonstrated that it couldnot belong to the historical Pythagoras (1960). For a recent attemptto defend at least the partial accuracy of the story, see Riedweg2005: 90–97 and the response by Huffman 2008a:207–208; seealso Zhmud 2012a, 428–430. Even...

In the modern world Pythagoras is most of all famous as amathematician, because of the theorem named after him, and secondarilyas a cosmologist, because of the striking view of a universe ascribedto him in the later tradition, in which the heavenly bodies produce“the music of the spheres” by their movements. It shouldbe clear from the discussion above that, while the early evidenceshows that Pythagoras was indeed one of the most famous early Greekthinkers, there is no indication in that evidence that his fame wasprimarily based on mathematics or cosmology. Neither Plato norAristotle treats Pythagoras as having contributed to the developmentof Presocratic cosmology, although Aristotle in particular discussesthe topic in some detail in the first book of the Metaphysicsand elsewhere. Aristotle evidently knows of no cosmology of Pythagorasthat antedates the cosmological system of the “so-calledPythagoreans,” which he dates to the middle of the fifthcentury, and which is found in the fra...

As noted, none of Pythagoras’ writings – if he wrote anything – have survived and, owing to the secrecy he demanded of his students, the specifics of his teachings were carefully kept. The philosopher Porphyry (l. c. 234 - c. 305 CE), who wrote a later biography of Pythagoras, noted:The Greek historian Herodotus (l.c. 484 - c. 425/413 BCE) alludes to Pythagoras (though famously refuses to name him) in his Histories:Like the Pythagorean Theorem, Pythagoras’ concept of the transmigration of sou...

It is possible that Plato began as a student of Socrates, adhering to dialectic in establishing truth, and then only gradually moved toward embracing the idealism of Pythagoras – as some scholars have claimed – but it seems more probable that Socrates himself was aligned with Pythagorean thought. There is really no way of establishing any claim along these lines since most of what we know of Socrates comes from Plato’s Dialogues which were written after Socrates’ death when Plato was already...

The Phaedo also establishes the geography of the afterlife which would later be used by the Church in creating the concepts of Hell, Purgatory, and Heaven. The concept of purgatory first appears in Phaedo 108b-d, judgment of the dead in 113d-e, Hell in 113e-114a, and heaven in 109d-110b. Plato’s argument for an ultimate, undeniable, realm of truth, from which all other truths are established, is also evident in the gospel narratives of the Bible, most notably the Gospel of John, and in the ep...

Write it down as an equation: Then we use algebrato find any missing value, as in these examples: You can also read about Squares and Square Roots to find out why √169 = 13 It works the other way around, too: when the three sides of a triangle make a2 + b2 = c2, then the triangle is right angled.

Get paper pen and scissors, then using the following animation as a guide: 1. Draw a right angled triangle on the paper, leaving plenty of space. 2. Draw a square along the hypotenuse (the longest side) 3. Draw the same sized square on the other side of the hypotenuse 4. Draw lines as shown on the animation, like this: 5. Cut out the shapes 6. Arrange them so that you can prove that the big square has the same area as the two squares on the other sides

Here is one of the oldest proofs that the square on the long side has the same area as the other squares. Watch the animation, and pay attention when the triangles start sliding around. You may want to watch the animation a few times to understand what is happening. The purple triangle is the important one. We also have a proof by adding up the areas.