44 Lehoux
The infi nity of the cosmos likewise emerges elegantly from a thought ex-
periment: if the world were fi nite, what would happen to a spear thrown
directly against its inside edge? If the spear bounced back, then there
must be something outside of the cosmos resisting it. If the spear fl ew
on through, then there must also be something outside. Therefore the
cosmos cannot be fi nite, and if not fi nite, then not spherical or any other
defi nite shape.^16 The apparent rotation of the heavens around Earth on a
day- by- day basis created some problems for this idea (problems exploited
by competing schools), and the Epicureans attempted to get around this
by arguing that several explanations can be forwarded to account for these
phenomena, one of which must be right. Moreover, since the goal of life
is happiness (defi ned by Epicurus as the absence of fear), and since knowl-
edge of minutiae about stellar motions can contribute nothing to easing
fear, then we need not waste time on these problems.^17 Here we see how
a shift of emphasis in one area (in this case ethics: the particular defi ni-
tion of happiness espoused by Epicurus) can have a profound effect on
the framing of the problem set that a group of thinkers considers worth
engaging. Secondly, we see how privileging different questions and differ-
ent kinds of explanations can lead to radically different physics between
the different schools.CERTAINTY
A spherical cosmos was also accepted universally by ancient mathematical
astronomers, scientists whose aim was not to understand elemental causes
(physics) but to mathematically understand the very complex motions of
the heavenly bodies. Classical antiquity offers no greater practitioner of
the exact sciences (those with a mathematical substructure) than Clau-
dius Ptolemy (second century CE). Writing defi nitive works on astronomy,
astrology, optics, harmonics, geometry, geography, and more, Ptolemy
combined exceedingly careful observation and experimentation with so-
phisticated mathematical analyses to produce one of antiquity’s greatest
scientifi c legacies. If we had the now- old- fashioned aim of looking back to
antiquity to try and fi nd practitioners whose work most closely approaches
the methods and aims of the modern sciences, we could hardly do better.
This is not to modernize Ptolemy—my aim is quite the contrary—but to
clarify what sets his work slightly apart from the projects of the natural
philosophers and philosophical schools we have been discussing so far.
Ptolemy’s work in astronomy, for example, involved the careful design
of astronomical instruments, the taking of fi ne- grained observations, the