Categorical Proposition

1. Logic originated with the Greek philosophers. As far back as seven hundred years BC, they already had an understanding of good argument and used reasoning to draw abstract conclusions. This can be gleaned from fragments of their writings. But it was Aristotle who first developed a logical system. His comprehensive theory includes precise definitions, principles of reasoning, a system for exposing arguments, and rules for evaluating reasoning. The Aristotelian system is called categorical logic. It is also known as deductive logical system. It is a method for analyzing deductive argument which Aristotle called syllogisms. One of the requirements of categorical logic is that statement follows a certain form. They have to be categorical statements and must assert a relationship between one group of things and another.

Categories are classes or group of things. The words and phrases used to refer or name categories are called terms.

Statements in categorical logic assert a relationship between one category, the subject category, and another, the predicate category. The statement “all men are good” is thus to be interpreted as meaning that “all those belonging to the category of man belong to the category of good”. For Aristotle all statements can be expressed in terms of categories and the assertion of a relationship between categories. And all reasoning in categorical logic is reasoning about categories.

ORDINARY STATEMENT	CATEGORICAL STATEMENT
Some dogs bark.	At least one member of the class of dogs is a member of the class of animals that bark.
All spiders have eight legs.	All members of the class of spiders are members of the class of things having eight legs.
No bankers favor the withholding of interest on savings account.	No member of the class of bankers are members of the class of person favoring withholding interest on savings account.
Some of the people are not for the death penalty.	At least one member of the class of people is not a member of the class of those favoring the death penalty.

A categorical statement is also called a proposition. Its distinctive character is that it asserts that something is the case or that something is not the case. Its assertion has a truth-value, that is, it may either be true or false.

a. components and structure – A categorical proposition follows the standard subject-copula-predicate form. The subject is introduced be a quantifier which specifies how much of the subject class is included in or excluded from the predicate class. The copula is expressed in the third person, present tense, of the verb to be.

All students majoring in philosophy are required to take Metaphysics and Epistemology.

quantifier: all

subject term: students majoring in philosophy

copula: are

predicate term: required to take Metaphysics and Epistemology

b. quantity of the proposition – refers to the extension of the subject. A proposition could be either universal [if it refers to all the members of the class designated by the subject term] or particular [if it refers to some members of the class designated by the subject term].

c. quality of the proposition – could be either affirmative [if the predicate is asserted of the subject – AffIrmo] or negative [if the predicate is denied of the subject – nEgO].

d. distribution in the predicate – the predicate of an affirmative proposition is undistributed [does not refer to all the members of the class designated] while the predicate of the negative proposition is distributed [refers to all the members of the class designated].