# Categorical propositions and individuals in Aristotelian term logic

If I understand the Stanford Encyclopedia article on the subject, there are two types of terms used in syllogistic propositions, the universal and the individual, and only universal terms can serve as predicate terms, while both individual and universal terms can be subjects.

My question concerns categories, the use of the phrase "categorical proposition," and their relation to individual terms. Are individuals also considered categories in their own right, and is a proposition with an individual subject like "Aristotle is a philosopher," lacking one of the universal or particular AEIO affirmatives and denials, also considered a categorical proposition? Or should one only refer to propositions containing a universal subject and AEIO predication as a categorical proposition?

The SEP article only uses the phrase "categorical sentence" to describe propositions with universal subjects and AEIO predication. However, the wikipedia article on Categorical Propositions gives as its first example a proposition with an individual subject and no AEIO predication: "Midshipman Davis serves on H.M.S. Invincible."

• The SEP article seems to suggest otherwise: "However, he notes that when the subject is a universal, predication takes on two forms: it can be either universal or particular. These expressions are parallel to those with which Aristotle distinguishes universal and particular terms, and Aristotle is aware of that, explicitly distinguishing between a term being a universal and a term being universally predicated of another. Whatever is affirmed or denied of a universal subject may be affirmed or denied of it it universally (...), in part (...), or indefinitely (...)." – epictetus Jan 18 '13 at 17:18
• Can you be more specific? Also, the subject is particular here (Aristotle) and not universal, and so whatever it is that the above is meant to say does not apply here. – danielm Jan 18 '13 at 17:23

## 2 Answers

"Aristotle is a philosopher" is an instance of Iab. Iab is equivalent to "b is predicated of some a". In your case, "philosopher is predicated of Aristotle" because Aristotle is "some a", i.e., an individual. – danielm

To elaborate on why I don't think that interpretation is correct: if "Aristotle is a philosopher" is an instance of Iab (N.B. that the article places predicate first and subject second in abbreviations), that would mean we could translate the sentence to "Some Aristotle are Philosophers," which doesn't appear to make sense. Additionally, according to the article, Aristotle argued the soundness of three different conversions, one of which was Iab → Iba. That would mean we should be able to convert "Some Aristotle are Philosophers" to "Some Philosophers are Aristotle." However, the article specifically identifies such a sentence as erroneous due to its predicate containing an individual term:

Universal terms are those which can properly serve as predicates, while particular terms are those which cannot.

This distinction is not simply a matter of grammatical function. We can readily enough construct a sentence with “Socrates” as its grammatical predicate: “The person sitting down is Socrates”. Aristotle, however, does not consider this a genuine predication. He calls it instead a merely accidental or incidental (kata sumbebêkos) predication. Such sentences are, for him, dependent for their truth values on other genuine predications (in this case, “Socrates is sitting down”).

• Oh, I see. I'm not familiar with the notation (I didn't know it was particular to categorical syllogisms), but I see you're right. No, Aristotle is a particular not a universal. In this case, something like the second substance "human" or an accidental property such as "philosopher" which are said-of (or predicated) Aristotle would be universals. "Aristotle is a philosopher" is not a categorical sentence. – danielm Jan 18 '13 at 22:05

After reading another entry on the same subject from the Internet Encyclopedia of Philosophy and rereading the relevant portion of the original article, I think I have my answers.

Apparently Aristotle treated sentences with individual terms as their subjects as if they were universal affirmatives (Aab) or negatives (Eab), so a sentence like "Aristotle is a philosopher" would be translated as "All (of) Aristotle is a philosopher."

Individuals belong to Aristotle's first category, the so-called "primary substances."