Four kinds of Categorical Proposition

As we know, Aristotle’s philosophical method was all about categories - what went in what category and what didn’t. Any statement that describes what goes in which category (and what doesn’t) we call a categorical proposition. Aristotle described four kinds of categorical proposition:

1. All S are P —e.g. All dogs are mammals

2. No S are P —e.g. No dogs are fish

3. Some S are P —e.g. Some dogs are aggressive

4. Some S are not P —e.g. Some dogs are not aggressive

(S stands for Subject, and P stands for Predicate. Predicate just means description or category.)

Syllogisms

If we combine two of these Categorical Propositions together in the right way, we can discover new conclusions. For example, look at the following:

1. All dogs are mammals

2. All mammals are animals

What’s the logical conclusion? — All dogs are animals.

We can use the symbol ∴ for therefore, so we can write:

1. All dogs are mammals

2. All mammals are animals

3. ∴ All dogs are mammals

Features of a Categorical Syllogism

You’ll notice a few things about all these syllogisms:

1. A syllogism is made up of three Categorical Propositions. (In a syllogism, the first two propositions are premises and one is a conclusion)

2. Each proposition contains two terms (a subject and a predicate). In the proposition all dogs are animals, dogs is the subject term, and animals is the predicate term.

3. The syllogism contains three terms in total. As well as the subject and predicate, there is a term that is shared between the first two premises called the middle term.

4. So in the following syllogism, the middle term is mammals.

• All mammals are animals

• All dogs are mammals

• ∴ All dogs are animals.

5. So, to recap: 

• The shared term is called the middle term.

• The subject of the conclusion is called the subject.

• The predicate of the conclusion is called the predicate.

6. You might also notice that we can rearrange the subject, middle, and predicate terms. (Though the conclusion is always subject then predicate). Aristotle described three figures. There are 256 possible arrangements for syllogisms but only 24 are valid (i.e. make sense). Aristotle identified the following 11 which are unconditionally valid.

Eleven valid forms of the Categorical Syllogisms

#logic