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A Historical Introduction to the
Philosophy of Science

Ch. 2: The Pythagorean Orientation

Book cover: A Historical Introduction to the Philosophy of Science by John Losee

The following is a summary of the second chapter of John Losee's book, A Historical Introduction to the Philosophy of Science (fourth edition), with some ancillary notes.

Philosophers discussed in this chapter: Plato (428/7–348/7 BCE); Ptolemy (c.100–c.178 CE)

[pp. 14–15] The "Pythagorean Orientation" is the view that the fundamental structure of the universe consists in mathematical harmony. Galileo was a Pythagorean.

[p. 15] Pythagoras (or followers) (6th Century BCE) noticed mathematical ratios in musical harmonies are independent of the physical instrument. Likewise, motions of the stars and planets show "harmony of the spheres".

[pp. 15–16] Losee thinks Plato is unfairly criticized for being anti-science in recommending exclusively pursuit of abstract ideas. Plato thought that rational order lies behind observed empirical phenomena.

[p. 16] Platonism in the Middle Ages and Renaissance corrected religious objections to science and the excessive attention to academic texts. The Christian West melded Plato's creator god (Demiurge) with the Christian creator god to articulate a god who applied a mathematical form to matter.

[pp. 16–17] Plato suggested the five elements are each aligned with a geometrical shape:

  1. fire – tetrahedron
  2. earth – cube
  3. air – octahedron
  4. water – icosahedron
  5. celestial matter – dodecahedron

[p. 17] Plato suggested transformations between water, air and fire are the result of dissolutions of the triangular faces.

Geminus (1st Century BCE) complained that Pythagoreans, in drawing mathematical relations between observed phenomena, were not really providing an explanation. They are only "saving the appearances". For Geminus, it is the physicist who truly explains by appeal to essential natures.

[p. 18] Ptolemy devised two mathematical models that derived equally well the retrograde motion of the planets (1. Epicycle-Deferent Model; 2. Moving-Eccentric Model). Astronomers can choose either model for predicting celestial motions.

[p. 19] Ptolemy oscillated between saying his mathematical models (a) were computational devices only and (b) truly described the motion of celestial bodies.
[LA: We'll see this disagreement occur throughout the history and philosophy of science as the debate between an 'instrumentalist' view of scientific theories and a 'realist' view.]

Proclus (5th Century CE) insisted that astronomers not be content with 'saving the phenomena' and get scientific by deducing motions from the (Aristotelian) self-evident axioms that simple motion is either (a) perfectly circular or (b) toward/away from the centre of the universe.

Questions to Consider:

  1. To what extent does Plato's mathematical explanation for the transformation of water, air and fire prefigure modern chemistry and physics with its postulation of lattice-style atomic bonds?
  2. Do mathematical relations really reveal the nature of things, or do mathematical models merely 'save the phenomena'?

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