Categorical Statements: Definition, Standard Form & Translation

Instructor: David White
Categorical statements are used to aid in deductive reasoning, but they can be a little complicated. Through this lesson, you will learn how to define these statements and explore the various ways in which they can be constructed.

What Is a Categorical Statement?

One of the more challenging things about writing and public speaking is that we tend to use more words than are necessary to make our point. In some cases, like teaching, this is done intentionally to complicate subjects or concepts in order to provide a well-balanced or fully developed argument. Other times, though, people might try to complicate an argument and just end up being vague or clouding their point.

One of the best ways to simplify an argument or draw a conclusion is through the use of categorical statements. These are statements that indicate how two sets of things, like people or animals, relate to each other. An example of a categorical statement is 'all golden retrievers are dogs.' In general, the categorical statement splits things into two groups: what it is and what it is not.

Categorical statements may seem incredibly reductive, but they exist for a very important reason. Broadly, they are part of what's known as deductive reasoning, which is the process of drawing a conclusion based on statements or ideas that are assumed to be true. In reality, how golden retrievers came into being and where they fit in the canine world is complex and would require a lot of time to explain, which is probably more information than a person needs to conclude that they are dogs. Given that, the categorical statement allows you to skip over the complicated parts by saying that they fit into this category (dogs) because they don't fit into any other category (everything that's not dogs).

Terms, Subject, and Predicate

As I've said, categorical statements can be very effective because they take incredibly complex things and break them down into categorical terms, which are the groups that a thing fits into. In general, categorical terms are nouns, like people, animals, or places, that are defined by their opposite, which is every group that they are not. For example, Americans are humans because they aren't cars, houses, or trees.

In a categorical statement, the terms are broken down into two groups: the subject, which is the first group in the statement; and the predicate, which is the larger group. In my previous statement about golden retrievers, for example, 'golden retrievers' is the subject and 'dogs' is the predicate. It's important to know, however, that simply having a subject and predicate in the sentence doesn't make it a categorical statement; that requires two other pieces.

First, these two sets have to be connected by using a copula, which in the case of standard categorical statements is always going to be 'are.' In order to finish the statement, you also need the quantifier, which is going to be 'none', 'all', or 'some.' The quantifier refers to how many of the subject you're talking about.

The copula and quantifier may not seem as significant as the subject or predicate, but they are in fact what make it a categorical statement. The statement 'golden retrievers can't be cats,' for example, has a subject (golden retrievers) and a predicate (cats), but it's not a categorical statement. In order to make it one, I would have to rephrase it by saying 'no golden retrievers are cats.' What makes the latter a categorical statement, besides the essential pieces, is that it provides information about both the subject and the predicate. By making it a categorical statement, you know that not only are golden retrievers not cats, but also that cats are not golden retrievers.

The Four Types of Statements

Given that categorical statements have a subject, a predicate, and three possible qualifiers, there can only be four types of statements, which are referred to as 'A, E, I, and O':

The 'A' statement is the universal affirmative in which all of the subject (referred to as 'S') is also the predicate (which is referred to as 'P'). For example, 'all whales are mammals' can be shortened to 'all S are P.'

The 'E' statement, known as the universal negative, is the opposite of 'A' in which none of the subject is a part of the predicate. 'No people are cars,' for example, would be 'no S are P.'

The third option, known as the 'I' statement, is the middle ground that indicates at least one member of the subject is also a part of the predicate. For example, 'some snakes are poisonous snakes' could be indicated by saying 'some S are P.'

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