William Waterhouse has argued that Hegel seriously intended
to give a philosophical derivation of the distances of the
planets. He offers four main considerations:
>I think there is extremely
>clear evidence that Hegel took his theory seriously. Here
>are the major points:
>
>1) In the introduction to the dissertation, Hegel says that he
>will treat three aspects of his subject, and he describes them
>as follows:
>
> "I shall discuss those primary concepts on which the physical
> part of astronomical science commonly and customarily rests;
> then I shall explain what true philosophy establishes about the
> structure of the solar system, so far as the orbits of the planets
> in particular are concerned; AND FINALLY, BY AN OUTSTANDING EXAMPLE
> TAKEN FROM ANCIENT PHILOSOPHY, I SHALL SHOW WHAT PHILOSOPHY
> CAN DO ["quid ... philosophia valeat"] EVEN IN DETERMINING THE
> MATHEMATICAL RATIOS OF QUANTITIES." (emphasis added)
Exactly. After showing what true philosophy DOES establish
about the solar system, he will show just what we can hope from it,
by using the Timaeus. Plato's famous treatise repeatedly states
that philosophy can give no proofs or certainty in astronomy:
TIMAEUS: ...If we can come up with tales that are no less likely
than any, we ought to be content, keeping in mind that both I
the speaker, and you the judges, are only human. So we should
accept the likely tale on these matters. It behooves us not to
look for anything beyond this.
SOCRATES: Bravo Timaeus! By all means! We must accept it as you
say we should. This overture of yours was marvelous. Now go on and
let us have the work itself.
(29c-d, similar thoughts occur throughout the dialogue)
Timaeus specifically declines to describe the distances
of the planets (38d).
Hegel takes a certain number series from the Timaeus,
noting that in the Timaeus it was not applied to planetary distances.
He never in any way suggests it is MORE likely than Bode's law.
He merely states it immediately after describing Bode's law. He
means to suggest that the two are quite equally likely. Such
groundless number slinging can 'argue' just as well that there
is a planet between Mars and Jupiter or that there is not.
Contrast Kepler's arguments (which I call "numerological" but
I will not argue about it) which rest on real mathematical
patterns (i.e conic sections and simple ratios of interest
since ancient times) and give excellent fits to the data.
Actually, Hegel does not use the series from the Timaeus
as it was. Where Plato had 1,2,3,4,9,8,27 Hegel puts 1,2,3,4,
9,16,27 and merely says "we can legitimately put 16 where the
Timaeus had 8". Of course this is legitimate in exactly the same
way that Bode could legitimately ignore the one member of his
series that corresponded to no planet: each is an ad hoc step to
suit the data.
And then Hegel does not use that series either, but the
series of fourth powers of cube roots of those numbers. Again,
like Bode's several steps of manipulation, an ad hoc step to
match the data.
In fact the Timaeus gives many different number series.
It opens with a series missing one member:
SOCRATES: One, two, three, ... Where is number four, Timaeus?
The four of you were my guests yesterday and today I'm to be
yours.
(The fourth guest has "come down with something or other". 17a)
Timaeus claims that geometric series (series of
constant proportion) give the only "true bond" between things
(31c-32a). Hegel echoes this, saying that because Bode's law
is not a geometric progression "it has no meaning for philosophy"
(dissertation 400). And Hegel's alternative is also NOT a
geometric progression. He does not believe it is better than
Bode's law, he believes both are ad hoc and without philosophical
meaning.
Hegel gives many series also, as William notes:
>2) He is not content with suggesting an alternate pattern in place
>of Bode's law for the planets; he goes on to give patterns for
>the orbital distances of the satellites of Jupiter and Saturn.
Yes, he illustrates a fact mathematicians were coming to
appreciate, and know well today: If you only have a few data points
you can always come up with a formula for them--even a simple
formula if a rough approximation will suffice. Indeed, as he showed
for the planets, you can choose among different ones. Data fitting
is fun.
>3) In Hegel's papers after his death, the German first draft of
>the dissertation was found together with "a chaotic mass of
>computations on the topic" ("ein Wust von zu ihnen gehoerigen
>Rechnungen": K. Rosenkranz, _Georg Wilhelm Friedrich Hegels
>Leben_ (Berlin, 1844), p. 154).
Hegel enjoys data fitting, while he insists that the
particular formulas it gives have "no meaning for philosophy"
(Dissertation 400). They are merely empirical, we would say
ad hoc.
>4) When Hegel later returned to the subject in the _Philosophy
>of Nature_, he wrote
>
> "I can no longer view as satisfactory my attempt along this line
> in an earlier dissertation." ("Was ich in einer frueheren
> Dissertation hierueber versucht habe, kann ich nicht mehr
> fuer befriedigend ansehen.")
>
>(Unfortunately I can't find the precise reference now, and the book
>is not currently in our library.) Certainly this hardly sounds
>like what he would have said if he had meant the whole thing as a joke.
Hegel never understood "jokes" as the opposite of "truth".
Compare his raucous jokes about boxing physiognomists on the ears,
and battering in the skulls of phrenologists, in the PHENOMENOLOGY.
I have not got the reference here at home, but it is in the section
on "observing reason".
He makes a perfectly serious point by parodying
his opponent. If enthusiasts for Bode's law value their number
series so highly, Hegel will give them a very similar series
with the opposite conclusion. If a physiognomist claims that
the shape of your ears reveals you have a tendency to lie (even if
you do not actually lie) then he has placed reason on the level of
ear shape, and you may aptly respond by reshaping his ears.
Hegel liked jokes. The point of this joke is to separate
the merely empirical from the philosophical--today we would say,
to separate ad hoc data fitting from theoretically grounded laws.
colin