The History of Mathematical Proof in Ancient Traditions

(Elle) #1

Philoponus and Aristotelian demonstrations 215


In his comments on the Posterior Analytics ii .2, Philoponus presents the
following explanation for Aristotle’s remark that the questions ‘what it is’
( ti esti ) and ‘why it is’ ( dia ti ) are the same:


For if the ‘what it is’ and the ‘why it is’ are diff erent, it is insofar as the former is
sought with regard to simple [entities] and the latter with regard to composite [enti-
ties]. Yet these [questions] are the same in substrate, but diff erent in their mode of
employment. Both the ‘what it is’ and the ‘why it is’ are studied in the case of the
eclipse being an aff ection of the moon. And we use these, the ‘what it is’ and the
‘why it is’, diff erently. But if we take an eclipse itself by itself, we seek what is the
cause of an eclipse, and we say that it is a privation of the moon’s light due to screen-
ing by the earth. But if we seek whether an eclipse exists ( hyparkhei ) in the moon,
namely why it exists, we take the ‘what it is’ as a middle term, namely privation of
the moon’s light coming about as a result of screening by the earth. 20


Although this passage is presented to account for the identity between the
questions ‘what it is’ and ‘why it is’, Philoponus dissociates these two ques-
tions. Th e distinction he draws here is based on the ontological distinction
between simple and composite entities. Th e question ‘what it is’ is asked
with regard to simple entities, whereas the question ‘why it is’ is asked with
regard to composite entities. In the case of composite entities, Philoponus
argues, ‘what it is’ and ‘why it is’ are diff erent questions. Th e defi nition
of an eclipse and the cause of its occurrence are not identical. Th e exact
signifi cance of Philoponus’ distinction between these questions is not clear
from this passage. Th e examples presented by Philoponus seem to blur his
distinction between an eclipse considered in the moon and an eclipse con-
sidered in separation from the moon, as the accounts given for both cases
are identical – ‘privation of the moon’s light due to screening by the earth’.
Th is diffi culty in understanding Philoponus’ distinction between ‘what
it is’ and ‘why it is’ may stem from his attempt to accommodate his view,
which dissociates these questions, with Aristotle’s claim that these ques-
tions are identical. As a result, Philoponus follows Aristotle in exemplify-
ing the answers to these questions by one and the same account. However,
according to Philoponus’ other discussions of the defi nitions of entities,
which are considered in separation from matter, the account for the eclipse
taken in separation from the moon should be the formal defi nition ‘screen-
ing by the earth’, whereas ‘privation of the moon’s light due to screening by
the earth’ is the full defi nition, resulting from a demonstration that relates
the formal defi nition to the material defi nition. 21 Despite the diffi culty in


20 339.20–9, Wallies.
21 371.19–25, Wallies.

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