A Historical Introduction to the
Philosophy of Science
Ch. 6: The Debate over Saving the Appearances
The following is a summary of the sixth 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: Nicolaus Copernicus (1473–1543); Johannes Kepler (1571–1630)
[LA: Note Copernicus and Kepler were deeply religious, but at opposite poles, with Copernicus being Catholic while Kepler was Protestant.]
Osiander on Mathematical Models and Physical Truth
[p. 40] Andreas Osiander supported Copernicus' suncentred model of the solar system as a superior mathematical model for saving the appearances.
Copernicus's Pythagorean Commitment
Copernicus, as a Pythagorean, thought his model really true of the solar system. Even though his model had a similar degree of accuracy to Ptolemy's for predicting motions of the planets, he argued superiority based on 'conceptual integration':
 Ptolemy had a separate model for each planet
 The Copernican model explained the magnitudes and frequencies of the retrograde motions of the planets
Bellarmine v. Galileo
[p. 41] Cardinal Bellarmine (1615) set Galileo's Pythagorean realism against saving the appearances (where accurate mathematical models do not reveal physical truths).
The Jesuit Christopher Clavius (1581) claimed that true theorems can be deduced from false axioms and that that is all Copernicus achieved.
Galileo's Dialogue Concerning the Two Great World Systems advanced arguments for the physical truth of the Pythagorean Copernican system and claimed future experiments will vindicate it.
Kepler's Pythagorean Commitment
[pp. 41–2] Kepler's Mysterium Cosmographicum (1596) tried to prove a correlation between the distance of a planet from the sun with the radii of a spherical shell circumscribed by one of the five regular solids (revealing God's mathematical blueprint).
[p. 42] Later, using Tycho Brahe's [pronounced Teeco Bray] more accurate planetary data, Kepler accepted his theory was false, and yet remained committed to the Pythagorean mathematical harmony of the spheres.
[p. 43] Kepler went on to develop his three laws of planetary motion, the Third Law being a striking vindication of his Pythagorean approach. Kepler described other mathematical relations that were suspect (e.g., Kepler's Distance–Density Relation).
[LA: Note how Kepler broke radically with the Aristotelian/Ptolemaic idea that celestial bodies moved naturally in perfect circles.]
[p. 43] NonPythagoreans regard Kepler's distance–density correlation a coincidence.
Bode's Law
[p. 44] The Pythagorean Johann Titius (1772) roughly proved a simple mathematical formula for calculating planetary distances.
[p. 45] Johann Bode's championing of this Pythagorean relation led to its naming as 'Bode's Law'.
William Herschel's discovery (1781) of Uranus and the asteroids Ceres and Pallas (1801/1802) seemed further vindication of Bode's Law. The later discovery of Neptune finally disproved Bode's Law.
However, a contemporary Pythagorean could continue to accept Bode's Law using its fit with Pluto's orbit in conjunction with the hypothesis that Neptune is a captured planet.
Questions to Consider:

How important is conceptual integration in evaluating competing theories?

Do scientific theories really tell us about the nature of reality, or are they merely calculating devices?

How can we tell the difference between coincidental mathematical relations in nature and necessary correlations?