Copyright © 2008, S. Marc Cohen 1 Revised 1/1/08
Philosophy 433 S. M. Cohen
Aristotle
Definitions and the Tree of Porphyry
The Form of a Definition by genus and differentia
Each definition takes the form:
Definiendum =
df
differentia + genus
where the definiendum is a species (or genus), and the definiens is the formula that consists of the
differentia + the genus (or super-genus). Thus, just as a species is defined in terms of its genus
and a differentia that marks it off from other species of that genus, each genus is defined in terms
of its super-genus and a differentia that marks it off from other coordinate genera falling under
that super-genus.
Some of the definitions embodied in the tree above
Body =
df
material substance
Living thing =
df
animate body
Animal =
df
sensitive living thing
Human =
df
rational animal
Copyright © 2008, S. Marc Cohen 2 Revised 1/1/08
Fully explicit definitions
In a fully explicit definition, each definable term (definiendum) is replaced by its definiens. Thus,
the fully explicit definition of human will be:
Human =
df
rational sensitive animate material substance
This is obtained from the compressed definition above by successively replacing each definable
term (definiendum) in the definition with its definiens. Thus, we replace ‘animal’ in ‘human =
df
rational animal’ with its definiens and obtain ‘human =
df
rational sensitive living thing’. We then
do the same for the definiendum ‘living thing’ to get ‘human =
df
rational sensitive animate body’,
and finally, replacing ‘body’ with its definiens ‘material substance’ we obtain the fully explicit
definition above. A glance at the Tree of Porphyry shows that the complete definition of a
species consists of its differentia together with the differentiae of all of the genera under which it
falls. In this way, all the genera (except for the supreme genus) seem to disappear from the
definition, and thus, as Aristotle says (Metaph. Z.12, 1037b30) “there is nothing in the definition
except the first-named genus and the differentiae.”
There will be many differentiae because there is at least one differentia at each level: species,
genus, super-genus, super-super-genus, etc.
