2. Philosophy - Stefano Franchi

P HILOSOPHY’ S ENDS
goes, has chiefly only the pleasing business of relating amplifications. Elementary
geometry, for example, in its scope as expounded by Euclid, can
from them on be regarded as having no further history. (13/12. My emphasis.)
The relationship between the empirical as well as the formal sciences and their own end is
then quite simple, according to Hegel, because of the very limited role played by history in
their development. Sciences grow by accumulating results, by juxtaposing them, until they
exhaust the field of experience they deal with. At which point, they reach their end, in the
two senses of terminus and telos: they have fulfilled their goal by coming to an end. This,
Hegel says, is what happened to elementary geometry with Euclid: it came to its end by be-
ing completed. Before Euclid, it is reasonable to suppose, there must have been a history
of errors and corrections that led up to the final systematization in the Elements. What is
characteristic of science, stresses Hegel, is the linearity of the process, or, to be more pre-
cise, the monotonic character of the curve describing its process in time. 20
This view of science may strike us as extremely unfashionable and outdated. Who still
believes in the linear progress of the scientific acquisitions of mankind? Hegel seems irrep-
arably off-track in his scientific examples. However, we might begin by pointing out that
Hegel’s view, however unfashionable, is far from dead. As recently as 1980, Stephen
Hawking discussed a very similar position in the inaugural lecture as Lucasian Professor of
Mathematics at Cambridge, which he significantly titled, “Is the end in sight for theoretical
physics?” 21 Hawking discusses the possibility that physics, as a science, can be “achieved”
in the near future (before the end of the century, he says, or 20 years down the line.
20. A monotonic curve is a curve whose slope does not change sign, or direction: it is either always growing
or always decreasing, e.g. it has either one of the two following shapes:
A non-monotonic curve presents peaks or depressions, and the kind of curve that may represent philosophy’s
historical development with respect to truth that falls prey of the paradox is probably, in Hegel’s
view, of the form:
21. Stephen Hawking, Is the end in sight for theoretical physics? (Cambridge: Cambridge University
Press, 1980).
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