Pythagoras
• Pythagoras: 6th century philosopher, mathematician, and leader of
a religious community.
• Mathematical-Metaphysical Philosophy
 all things are numberable,
 relationship between two things can be expressed as a
numerical proportion indicating the degree of their relationship.
 observed that the musical intervals between the notes on a
lyre may be expressed mathematically.
• Just as musical harmony was dependent on number (ratio) so the
harmony of the universe depends on number: “the whole of heaven
[is] a musical scale and number.” [Music of the Spheres]
• Pythagoreans were not content with stressing the importance of
numbers in the universe, they went so far as to say that things are
numbers.
 Here they were probably thinking of numbers spatially
rather than numerically: one = point, two = line, three =
surface, four = solid.
• The tetraktys was a symbol they regarded as sacred
Philosophy: Pythagoras
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KD McMahon
• The Pythagoreans viewed all material bodies as an expression of
the number 4.
• Pythagoreans assigned definite numbers to definite things:
justice = 4
men
= 3
women = 2
marriage = 5
• Pythagoreans believed the earth was spherical. The earth, planets,
and the sun revolved around a central fire or “hearth of the Universe”
which they identified with the Number One.
Comment:
We see in the Pythagorean thinking a breaking away from de facto
materialism which will influence Plato.
Philosophy: Pythagoras
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KD McMahon