Cohen Carl - Introduction to Logic

Every standard-form categorical syllogism has exactly three terms, to wit:
The major term is the predicate term of the conclusion (P).
The minor term is the subject term of the conclusion (S).
The middle term is the term appearing in both premises but not in the conclusion (M).

The premise in which the major term appears is the major premise.
The premise in which the minor term appears is the minor premise.
A syllogism is in standard form when its three propositions are in exactly this order: major premise, minor premise, conclusion.

Every proposition in a categorical syllogism must be one of the following four:

The mood of a syllogism is determined by the types of its three propositions, AAA, EIO, etc.

The figure of a standard-form syllogism is determined by the position of its middle term:

1st: Middle term is the subject of the major premise and the predicate of the minor premise.

2nd: Middle term is the predicate of both premises.

3rd: Middle term is the subject of both premises.

4th: Middle term is the predicate of the major premise and the subject of the minor premises.

Any syllogistic form is completely determined by the combination of its mood and figure. There are exactly 15 valid forms of the categorical syllogism, each with a unique name:

Rules governing every valid categorical syllogism:

The syllogism must contain exactly three terms, used consistently.

The middle term of the syllogism must be distributed in at least one premise.

If either term is distributed in the conclusion, it must be distributed in the premises.

A valid syllogism cannot have two negative premises.

If either premise of the syllogism is negative, the conclusion must be negative.

From two universal premises no particular conclusion may be drawn.

Identify the problem

Devise preliminary hypotheses

Collect additional facts

Formulate a refined explanatory hypothesis

Deduce consequences from the refined hypothesis

Test the consequences deduced

Apply the theory

The Method of Agreement: The one factor or circumstance that is common to all the cases of the phenomenon under investigation is likely to be the cause (or effect) of that phenomenon.

A B C D occur together with w x y z.

A E F G occur together with w t u v.

(Note: A term is distributed when the proposition in which the term appears refers to all members of the class to which the term refers. Thus, in the proposition All humans are mortal the term humans is distributed, but the term mortal is not.)

INTRODUCTION TO
LOGIC

INTRODUCTION TO
LOGIC

FOURTEENTH EDITION

Irving M. Copi
University of Hawaii

Carl Cohen
University of Michigan

Kenneth McMahon
Hawaii Pacific University

In a republican nation, whose citizens are to be led by persuasion and not by force, the art of reasoning becomes of the first importance.

Thomas Jefferson

L ogic has sometimes been defined as the science of the laws of thought. This is inaccurate. Thinking is one of the processes studied by psychologists. If thought refers to any process that occurs in peoples minds, not all thought is an object of study for the logician. Thus, one may think of a number between one and ten without doing any reasoning about it. One may also remember, imagine, free-associate, or perform any of a number of mental processes. All reasoning is thinking, but not all thinking is reasoning. The laws that describe the movements of the mind are psychological laws rather than logical principles. To define logic in this way is to include too much.

Logic has also been called the science of reasoning. This is better, but reasoning is a kind of thinking in which inference takes place and conclusions are drawn from premises. This process is extremely complex, characterized by a combination of trial and error, occasionally illuminated by flashes of insight. Logicians are not concerned with the ways in which the mind arrives at its conclusions in the process of reasoning; they are concerned only with the correctness of the completed process: Does the conclusion reached