Let us articulate this Aristotelian structure of the predicables as follows:
One can see that the universal is placed in relation to the species (and not immediately to the individual) under two different aspects, such that there are four possible combinations. Along the line of extension, it can be reciprocable or not reciprocable with the subject; along the line of comprehension, it can be essential or not essential.
Let us return to our initial example. To the concept of 'man' can be attributed the concept of 'rational animal' in a reciprocable and essential way, therefore it is a definition, while one could attribute to the same subject the concept of 'risible' in a reciprocabile but not essential way. As far as the concept of 'animal', it is predicable of 'man' in an essential (determinable) but not reciprocable way, for which it is the genus, while 'white', with respect to man, is neither reciprocable nor essential, and therefore it is an accident. 'Rational', finally, pertains to the essence of 'man', but it is not reciprocable as intellectuality, of which rationality is a modality, because it pertains to other beings (God and seperate substances).
We should now examine briefly each of these predicables (Aristotle, Topics, A, 5, 102a31 - 32).
A translation of Fr Alain Contat's Logica