Predicables - Amateur Logician

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Predicables (from Porphyry)

Five Relations for Predicating Universal Terms
1) Genus – wide class; where part of essence is shared with other species
2) Species – narrow class under a genus; expresses essence
3) Differentia (specific difference) – part of essence that makes it different
4) Property – not part of essence but necessarily results from essence
5) Accident – not part of essence and doesn’t necessarily result from essence

The question is How is the subject predicated?

Any subject can be predicated five general ways with universal terms. “This subject is _____.” Since logic is about the conceptual realm, classification falls under its traditional purview. It raises tricky metaphysical issues, though. Some of those issues will be addressed presently.

Porphyry (233-304 AD), a Neo-Platonist philosopher, worked off of Aristotle’s logic and wrote Introduction to the Categories. This is where we get “Porphyry’s Tree.”

Individuals can be collected together and then divided as groups in various ways. Sometimes this is arbitrary; sometimes this is not arbitrary.

Common sense tells us that there are things which are living and things which are not. Hence we can conceptually group together all living things as members of “living beings.” Within that group, we can divide members up into “animals” and “plants.” These are their own respective groups, yet they are united together in that they are composed of things which are living.

Elementary set theory is useful. For example, here are three sets: “animals,” “plants,” and “living beings.” A set is a collection of things. The set of “animals” contains all things which are animals. They are members of the set.

Set X is a subset of Set Y if and only if every member of Set X is also a member of Set Y. Thus, the set of “plants” is a subset of the set “living beings.”

Set X is a proper subset of Set Y if and only if (1) Set X is a subset of Set Y and (2) Set Y contains members that Set X doesn’t have. Thus, the set of “plants” is a proper subset of the set “living beings.”

Three Essential Predicables: Genus, Species, and Differentia

To understand predicables, a good place to begin is with the genus. It’s a class of things. In the language of set theory, a genus is a set. A genus is a relative term because it’s always related to species. A species is a class; but a species is always a proper subset of a genus.

“Living being” is a genus to the species “animal” and to the species “plant.”

Classes can be both a genus and a species. “Animal” is a species of the genus “living being.” However, “animal” is a genus to the species “man.”

Things can get more complex. Contemporary biology has “taxonomic ranks”: life, domain, kingdom, phylum, class, order, family, genus, and species. It uses the terms “genus” and “species” more narrowly than the traditional definitions found in logic. Nevertheless, these taxonomic ranks implicitly work on the relativity of the terms genus and species.

Subdivisions are hence possible. When the subdivisions have reached a point where no more division is possible, we have reached the lowest species — also called a infima species. (This is when any more division would result in dividing it up into separate individuals.) And insofar as there is a highest genus that cannot be a species, we have a summum genus. Things in-between, where a class acts as genus relative to some classes and a species relative to other classes, are called subalterns.

A differentia or specific difference is that which distinguishes a species from another species of the same genus. For example, “man” is a species of the genus “animal.” There are other species of “animal.” Man is different by his rationality. Thus, man’s differentia is rationality. That allows us to (objectively) classify man as different from the other animals.

Figuring out the specific difference isn’t always so easy or perfectly clear. Differences between things in our material world blur. And we have to recognize our ignorance. Sometimes we therefore have to settle for less than perfect classifications or definitions.

The Three Essential Predicables: Genus, Species, and Differentia
Examples. . .

“Socrates is an animal.”
Here is a predication of genus. This tells us about part of the essence of Socrates. Part of his essence, which he shares in common with some other species, is his animality.

“Socrates is a man.”
Here is a predication of species. This tells us about Socrates’s entire essence. He is a man, a human being.

(By understanding what it means to be human, we also understand that part of the essence of being a human is to be an animal and to be rational.)

“Socrates is rational.”
Here is a predication of differentia or specific difference. It’s about a part of Socrates’s essence that makes him different from other species that belong to the same genus that he does. Unlike other animals, he’s intelligent.

Notice that these three predicables deal with essences.

A Philosophical Detour on Essences

From an Aristotelian-Scholastic perspective, things in the world have “natures” or “essences.” Individuals are identifiable as “men,” “cats,” “gold,” “silver,” etc. precisely because they possess a nature. That is, they have features about them that make them what they are and not something else entirely. Natures are shared. Evey gold item shares the features that make gold be what it is.

Human beings can’t impose upon silver and gold their respective differences. We don’t dictate that silver’s atomic number is 47 or that 79 is gold’s. These are discoverable features. They are not “social constructs.” Gold and silver have a reality and a nature.

“Nature” and “essence” are nearly interchangeable terms in practice. In strict philosophy, though, they often are defined differently. An essence is a being’s innermost identity. A nature is the essence as expressed through activity.

A scientist learns about things in the world by how they act and interact.

Without things having a nature, science would be impossible!

Science is possible because we can observe natures. These natures behave in orderly ways. This order allows the world to be intelligible.

Two Non-Essential Predicables: Properties and Accidents

Remember, predicables are about five general ways to predicate a subject with a universal term. “This subject is _____.” It’s also important to note that predicables are about non-arbitrary groupings and non-arbitrary attributive specifications. There’s an objective fact of the matter that gold is one thing, for example, and silver is another thing.

Predication (with a universal term) of a subject can either be essential or non-essential.
— An essential predication deals with a subject’s genus, species, or differentia.
— A non-essential predicate is a property or accident of the subject.

When a predicate results from a subject’s essence, while still not being a part of that essence, it is a property. It’s an attribute that’s derived from the essence. In some sense, we could say it “flows from” or “follows from” the essence. It “accompanies” the essence.

Property as a Non-Essential Predicable
Examples. . .

“Socrates is a being who possesses a language.”
Possessing a language is a property because it’s a derivative of “rationality.” If Socrates wasn’t rational, then he couldn’t have a language.

“Euclidean triangles have their internal angles add up to 180 degrees.”
This is a property because it’s something that necessarily follows from the essence of a Euclidean triangle (which is a polygon of three sides). In fact, this property can be rigorously proved in mathematics.

Here’s a different example. . .
“Water is something which freezes at zero degrees Celsius.”
It’s arguably a property. First note, it’s clearly not the essence of water (which is its chemical makeup H₂O). Second, while it’s arguably a property, we obviously cannot derive this property like a proof in mathematics. We rather have to discover this property through empirical experimentation.

Finally, the last predicable is the accident. This predicate is not part of the subject’s essence and doesn’t necessarily follow from that essence.

Accidents are separable or inseparable.

A categorical proposition’s subject can either refer to a specific individual or a class of things. Separable and inseparable accidents take on different meaning depending on this.

The subject may be a specific individual (e.g., Socrates).
— An inseparable accident is constantly with the subject.
— A separable accident isn’t constantly with the subject.

Accident (of specific individuals) as a Non-Essential Predicable
Examples…

“Socrates is a man born in Athens.”
The predicate is an accident (as he may have been born elsewhere); it’s inseparable (as this fact cannot change).

“Socrates is talking.”
Talking is an activity. The predicate is an accident (as it is not of his essence to be talking); it’s separable (as he can talk and not talk at different times).

The subject may be a class of things or species (e.g., man).
— An inseparable accident is found in every member of the class.
— A separable accident is found only in a portion of the class.

For example, “some swans are white.”
White is a separable accident of swan.
Some swans are not white.
Thus, at most, white can only be a separable accident of the subject.

Alas, things can be murky. How is a property and an inseparable accident different? Truth be told, it’s not crystal clear in theory or practice. That’s why, I suspect, some traditional logic textbooks don’t mention the old division between “inseparable” and “separable.”

In Porphyry’s scheme of the predicables, a property is different by being unique to its own species. This is one way to approach the question.

Another example… “crows are black.”
Black would then be an inseparable accident.
Moreover, it makes sense to think of it as an accident, not a property, because if a crow was found to be white, this wouldn’t suggest that it belonged to a different species (or nature).

Logician Peter Coffey suggests that an inseparable accident is one that “we are unable to discover any necessary connexion between it and the specific nature of the class in question.”^[1]

For example, can we think of water without thinking about it freezing at zero degrees Celsius? So, should we claim this predicate is an inseparable accident instead of a property? (My preference, nevertheless, is to think of it as a property.)

It can be a question of how “certain” our knowledge is.
— If we have good or sufficient reason to think an attribute is somehow connected to the nature of a species, we can consider it a property.
— If we don’t know why an attribute seems always to accompany a species, we can consider it an inseparable accident.

As science progresses, then, what was once considered an “inseparable accident” can become a “property.”

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A Brief Note about Contemporary Analytical Philosophy

The late Saul Kripke (1940 – 2022) has pointed out a distinction between epistemological truths and metaphysical truths. The former can be broken down to truths known a posteriori or a priori. The latter can be broken down as truths that have necessity or contingency.

Epistemological Truths…
An “a priori” truth can be known before consulting experience, whereas “a posteriori” truth must be know through some particular experience.

Metaphysical Truths…
A true statement is “necessary” if it couldn’t have been false, whereas it is “contingent” if it could have been false.

Some parallels are present between this and Scholastic philosophy.
We can think about the predicables in terms of these distinctions.

“George resides in America.”
Separable Accident. | A Posteriori Contingency.

“Euclidean triangles are polygons.”
Genus (part of a Euclidean triangle’s essence). | A Priori Necessity.

“Water is H₂O.”
Species (as it is water’s essence). | A Posteriori Necessity.

“Saul Kripke is the son of Dorothy Kripke and Myer Kripke.”
A Posteriori Necessity.
No predicable, since the predicate is not a universal term.

Notice, some necessary truths are not a priori!
— Without Dorothy Kripke and Myer Kripke, Saul Kripke would not exist. Ergo, it’s a necessary truth about Saul Kripke that he was the son of those two.
— It is necessary that water is made of H₂O; otherwise, it would not be water. We discover this truth a posteriori.

Saul Kripke is an extremely important and well-known philosopher. Modal logic was developed by him. In many ways, he helped philosophers once again recognize the reality of essences and natures. He revived metaphysics!

[1] See The Science of Logic (volume 1) by Peter Coffey (p 87).