Routledge History of Philosophy Volume IV

RENAISSANCE AND SEVENTEENTH-CENTURY RATIONALISM 107
of both geometrical and physical causes. An important example is the question
of why there are six and only six (primary) planets, Mercury, Venus, Earth, Mars,
Jupiter, Saturn. (This question is quite rational, if it is assumed that the world
was created much as it is now some finite time ago.) Georg Joachim Rheticus,
Copernicus’s first champion, had answered it arithmetologically by saying that
six was a perfect number. This had a precise meaning, for 6’s factors 1, 2, 3,
when added together, produce 6 itself, a property shared by relatively few
numbers, the next example being 28. Kepler would have none of this mystica
numerorum, and firmly believed in geometry’s priority to arithmetic, so that it,
rather than arithmetic as Boethius had held, provided God with the archetype for
the creation of the world.
Kepler found the required linkage with geometry in the remarkable fact that
there are five and only five regular solids. He then discovered even more
remarkably, and we would say coincidentally, that these solids and the spherical
shells enclosing the planetary orbits could be fitted together in a sort of Chinese
box arrangement, so that, if an octahedron was circumscribed about the sphere of
Mercury, it was almost exactly inscribed in the sphere of Venus, and so on,
giving the order, Mercury, octahedron, Venus, icosahedron, Earth, dodecahedron,
Mars, tetrahedron, Jupiter, cube, Saturn. This idea understandably so
excited Kepler that he planned a model for presentation to the Duke of
Württemberg. Another preoccupation was with what moved the planets, for
Kepler remained in the tradition in which each motion demanded an efficient
cause. His answer was that there was a single ‘moving soul’ (later to be
depersonalized to ‘force’) located in the Sun. This had the natural consequence
that the planetary orbits lay in planes passing through the Sun, which in turn
virtually removed the messy problem of latitudes (the deviations of the planetary
paths from the plane of the ecliptic) from mathematical astronomy.
Kepler circulated copies of his book to other astronomers, includ ing Tycho
Brahe, who, perhaps surprisingly, was favourably impressed, although
complaining that Kepler had too great a tendency to argue a priori rather than in
the a posteriori fashion more appropriate to astronomy. He invited Kepler to
visit him, but this did not come to fruition until, after a series of disputes, Tycho
moved from Denmark and came under the patronage of the Emperor Rudolf II,
who granted him a castle near Prague for his observatory. Kepler went to see him
there and soon became a member of his team. The relationship between the
rumbustious and domineering Tycho and the quieter but determinedly
independent Kepler was not an easy one, but it did not last too long, for Tycho
died in 1601 and was succeeded by Kepler in his post as Imperial Mathematician.
On joining Tycho, Kepler was set to work on Mars, whose movements had
been proving particularly recalcitrant to mathematical treatment. We may count
this a fortunate choice, for, to speak with hindsight, its orbit is the most elliptical
of the then known planets. But it was one of Kepler’s important innovations to
seek for the actual orbit of the planet rather than for the combination of uniform
circular motions that would give rise to the observed appearances. However, he