Exactly five voices

A predicable is something that can be predicated, that is, stated of a subject. Porphyry, in his Isagoge, defined and distinguished five kinds of predicables: genus, species, difference, property, and accident. This division of predicables was later accepted by logicians for a long time. [1] It is based upon a similar classification set forth by Aristotle in the Topics (a, iv–viii), which has “definition,” however, in place of “species.” [2]

Porphyry spent most of his book proving that his division of predicables was irreducible, that is, distinguishing each of his five ‘voices’ from the rest. Nevertheless, a good division must also be complete and rationally progressive, etc.; many requirements for a good division were recognized. [3] So, many derivations of the division of five predicables were written so as to make evident its good foundation. What follows is my listing of all such derivations that I have yet found.

Aristotle treated only statements of the form “A is B,” in which subject and predicate are both universal. He noted that in every true statement of this type the predicate either is convertible with the subject (i.e., “B is A” follows from “A is B”) or else it is not. If the predicate is convertible and states its essence, then it is the definition of the subject; whereas if it is convertible but does not state the essence, it is a property of the subject. On the other hand, if the predicate is not convertible with the subject but is part of the definition, it is the genus or differentia of the subject, for a definition always consists of genus and differentia. Finally, if the predicate is not convertible and is not part of the definition, it is an accident of the subject.

 — Encyclopaedia Brittanica, “Predicable” [2]

A universal term expresses either the essence of a thing or something added to the essence, In the former case, it expresses either the whole essence or only a part of it. If it denotes the whole essence, it is a species, and the beings to which it is applied are called individuals, as “man.”

If the universal denotes only a part of the essence, it denotes either the part common to other species, or the part by which the essence differs from them: in the first ease it is called genus, and in the second specific difference; thus, “animal” expresses what is common to both man and brute, and “rational” expresses the specific difference which distinguishes man from brute. If the universal denotes what is added to the essence, either this attribute cannot be separated from the essence, but is a necessary attendant of it, so that it is always found in the whole species and in that species only, in which case it is a property; or it can be separated without changing the essence, and then it is an accident; thus, “free will” is a property, “learning” is an accident of man. Genus, species, and difference are divided into highest, intermediates and lowest or proximate, as may be seen in the following diagram. [What follows is a diagram of the “Porphyrean tree”, omitted here.]

— Louis de Poissy, Elementary Course of Christian Philosophy [4]

§329. Again, when we say

(1) Some animals are men,

(2) Some men are black,

what is there to tell us that the predicate is to be regarded in the one case as a species and in the other as an accident of the subject? Nothing plainly but the assumption of a definition already known.

§330. But if this assumption be granted, the classification seems to admit of a more or less complete defense by logic.

For, given any subject, we can predicate of it either a class or an attribute.

When the predicate is a class, the term predicated is called a Genus, if the subject itself be a class, or a Species, if it be an individual.

When, on the other hand, the predicate is an attribute, the attribute predicated may be either the very attribute which distinguishes the subject from other members of the same class, in which case it is called the Difference, or it may be some attribute connected with the definition, i.e. Property, or not connected with it, i.e. Accident.

— St. George William Joseph Stock, Deductive Logic [5] [6]

[The number of universals] follows from the proportion of a substantial compound of which they are properly predicated, for what is truly predicated of another must name it totum, since it is impossible to predicate the part of the whole. However, a whole can be named for the whole, and also for a part, and thus the predicate can name the whole, either for a part, or for any other part, or for a part simultaneously with the whole.

One thing, therefore, can receive five predicates, if it is material. When the compound is named for its material, genus is predicated; when it is named for its formal principle, difference is predicated; when considering the genus with the difference, uniting matter and form, species is predicated; if it refers to accidents, caused by the principles of the species or genus, property is predicated, and if to accidents caused by the principles of an individual, accident is predicated.

We may demonstrate this in another way:

It may be said that, when some thing is predicated of another thing, it is totally or partially predicated.

What is totally predicated, is so predicated necessarily when it is of the quiddity of the thing, or contingently, when it is predicated in relation to the whole, not referring to its essence. In the first case, species is predicated – which is essentially, necessarily and totally predicated –, and difference is predicated, which is a constituent of the species. In the second case, property is predicated, which is a necessary accident of the species of thing to which it refers, but actually necessary of the subject that represents it.

When it is partially predicated, it may be predicated essentially or non-essentially. In the first case, genus is predicated, whether remote or proximate, which refers to the essence of a thing taken incompletely – since when you say that man is an animal, you say something of the essence, but incompletely.

In the second case, accident is predicated; only accident may, as such, be predicated both of the species and of the subject that represents it.

As these five possibilities are the only general ones that can be established regarding the predication of anything, the Porphyrean division of the five predicates is sufficiently explained and justified.

—  Mário Ferreira dos Santos, Isagoge de Porfírio [7]

[1] I am pretty sure of this, but I do not know what I could possibly cite in its favor. Can anyone recommend me a good historian of logic?

[2] https://www.britannica.com/topic/predicable

[3] See, for instance, Art. VII here: https://www3.nd.edu/~maritain/jmc/etext/cp01.htm

The listing of the requirements for a good division varies slightly between textbooks, and I should like to make another post, similar to this one, with a comparison of such listings.

[4] https://maritain.nd.edu/jmc/etext/cp01.htm

[5] https://etc.usf.edu/lit2go/189/deductive-logic/3898/part-2-chapter-6/

[6] A note on Stock’s name. He was not canonized; his first name was “St. George”, with the title included, cf. https://www.zinzin.com/observations/2012/who-was-st-george-william-joseph-stock/

[7] I have translated this myself, hopefully adequately. I have not attempted to do so very literally, but I have attempted to render the reasoning adequately and the technical terms properly. May Mário’s fans rebuke me if I have not done this.