Categorical Statements: An Introduction

Readers of this blog know that I like to post something about logic every now and again, so this post briefly deals with categorical statements (also known as categorical propositions).

By "categorical," I mean statements that name/relate categories or classes of things like humans, dogs, cats, etc. We'll now examine four kinds of categorical statements:

1. Universal affirmative statements: an example is "All dogs are canines." Formally, this statement assumes the form, "All S is/are P." S is the subject while P is the predicate. Terms like "all," "no" and "some" are labeled quantifiers; are/are not bear the technical name, copula, in logic.

2. Universal negative statements: "No dogs are canines." The form of this statement is "No S are P."

3. Particular affirmative statements: "Some dogs are canines." The form here is "Some S are P."

4. Particular negative statements: "Some dogs are not canines." The form is "Some S are not P."

Statements like "All dogs are canines" and "No dogs are canines," we call contraries because they can be false at the same time, but they cannot simultaneously be true. On the other hand, "Some dogs are canines" and "No dogs are canines" not only are contrary statements, but they're contradictories. So are "All dogs are canines" and "Some dogs are not canines."

These categorical statements can be arranged into syllogisms, that is, arguments that have premises and a conclusion. Strictly speaking, syllogisms contain a major premise, minor premise, and conclusion.

Picture is courtesy of Wikimedia.org: public domain.