Philoponus and Aristotelian demonstrations 217
term and the conclusion of a demonstration are related according to the
fourth sense of ‘in itself ’ – that is, they are related as cause and eff ect. 25 S o ,
according to Philoponus, the derivation of the demonstrative conclusion
is not solely based on the transitivity of the predicative relation stated in
the premises. In addition to the transitivity of the predicative relation, the
demonstrative derivation is based on causal relations between the middle
term and the conclusion. Such a distinction between logical relations and
extra-logical or causal relations is explicitly drawn at the beginning of
Philoponus’ introduction to his commentary on the second book of the
Posterior Analytics :
In the fi rst book of the Apodeiktike (i.e. the Posterior Analytics ), he showed how
there is a demonstration and what is a demonstration and through what premises it
has come about, and he showed further how a demonstrative syllogism diff ers from
other syllogisms and that in other syllogisms the middle term is the cause of the
conclusion and not of the thing and in demonstrative syllogism the middle term is
the cause both of the conclusion and of the thing. 26
It follows from this discussion that Philoponus’ ontological distinction
between physical and mathematical entities yields diff erent accounts for
physical and mathematical demonstrations. Th e distinction between the
three facets of physical entities – i.e. the form, the matter and the cause for
the realization of form in matter – is refl ected in Philoponus’ interpreta-
tion of the theory of demonstration. In this interpretation, demonstrations,
like physical entities, have three components: indemonstrable premises,
regarded as formal defi nitions, demonstrative conclusions, which are
material defi nitions, and the middle term, which serves as the cause that
relates the formal defi nition to the material defi nition. Philoponus’ distinc-
tion between the form of a physical entity and the cause of the realization
of form in matter fi nds expression in the distinction he draws between
the formal defi nition considered in itself and that formal defi nition in its
role as the middle term in demonstration. Th is distinction implies that
25 Th e analysis of demonstrative derivation in causal terms is widespread in Philoponus’
commentary on the Posterior Analytics (e.g., 24.22–4; 26.9–13; 119.19–21; 173.14–20;
371. 4– 19). Th e causal analysis of demonstrative derivation underlies Philoponus’ introduction
of a second type of demonstration, called ‘tekmeriodic demonstration’, in which causes are
deduced from eff ects ( In An. Post. 33.11; 49.12; 169.8; 424.13, Wallies; In Phys. 9.9–10.21,
Vitelli). On Philoponus’ notion of tekmeriodic proofs and its reception in the Renaissance, see
Morrison 1997 : 1–22.
26 334.1–8, Wallies. Th e distinction between the middle term as the cause of the thing and the
middle term as the cause of the conclusion is also found in the Latin medieval tradition of
interpreting the Posterior Analytics. See De Rijk 1990.