SYLLOGISM
​What is a syllogism, or a categorical syllogism, or a syllogistic argument?
Encyclopedias have long sections on the term. Gordon Clark’s definition from the Glossary of his Logic is a good one.
Syllogism – An argument composed of two premises and a conclusion, with the predicate of the conclusion in one, the subject of the conclusion in the other, and a third term in the two premises. (Logic, Glossary, PB, p.123)

The syllogism’s elements consist of three and only three propositions. Two of the propositions are reasons (premises) in support of the third proposition, the conclusion. These propositions share three terms in a definite arrangement.

The subject of the conclusion of the argument is the minor term, the predicate of the same proposition is the major term, and the middle term is in both premises but never in the conclusion.
The premise with the predicate term of the conclusion is the major premise.
The premise with the minor term, either as subject or predicate, is the minor premise.

A syllogism has 3 propositions: the major premise, placed 1st, the minor premise, placed 2nd, and the conclusion (placed 3rd).

• The major term located in the major premise and in the conclusion (the conclusion’s predicate term). 
• The minor term is located in the minor premise and in the conclusion (the conclusion’s subject term).
• The middle term is located in the major premise and the minor premise, never in the conclusion.

Dr. John W. Robbins' excellent essay on why one should study logic may be accessed by clicking on his link in the Resources side bar. His essay is worth separate treatment in a future blog for it is an example of Dr. Robbins' brilliant, clear thinking and writing on a subject that is denigrated throughout academia and public schools. This brief post, owing much to Dr. Robbins' essay, is an abbreviated version of the Preview Page of The Logic Classroom.
Why Study Logic?
FIRST
To the question what is more basic than the three R’s of Reading, wRiting, and aRithmetic, we answer THOUGHT. To engage in any one of the three activities, you must think! Thinking, correctly done, follows rules. We think incorrectly, when we neglect those rules.  The rules for correct thinking and methods for avoiding mistakes in reasoning belong to the subject of logic.
​SECOND
The study of logic trains the mind to distinguish logical from emotional (psychological) appeals, which may be offered in support of a conclusion or a position. To opt for a course of action by confusing an emotional appeal with a logical appeal is to fall victim to incorrect thinking. It is a fallacy to accept an emotional inference as a necessary inference. Logic is the irreplaceable means for correct thinking and avoiding fallacious reasoning.
THIRD
The structure of man’s mind is the same as his Creator’s. God is not insane; He is a rational being, and the structure of God’s mind is logic. For these reasons, we say not only that logic is irreplaceable and universal, but logic is necessary and fixed. It is not one scheme of things among others. It is not optional. Man’s mind was formed on the principles of identity, excluded middle, and non-contradiction.
To repeat.
Three reasons for the study of logic are:

• Correct thinking requires it;
• Discerning minds necessarily depend on it; and
• Man is a rational being created in the image of his Creator.

As described in the previous post, Logic is the study of necessary inference. Its elements are propositions that form arguments. A proposition is the meaning of a declarative sentence. An argument is composed of propositions some of which are premises and one of which is the conclusion. Premises are reasons given to support the conclusion of an argument or a position. Arguments are classified as either inductive or deductive. With Deductive Argument, we ask: "Does this conclusion follow as a necessary consequence from these premises?" If the answer is affirmative, the Deductive Argument is valid; otherwise, the argument is invalid. Deductive Arguments are either valid or invalid. If the argument is not invalid, then it is valid. If the argument is not valid, then it is invalid.

Logic is Universal, Necessary, and Irreplaceable.
Man’s mind was formed on the principles of identity, excluded middle, and non-contradiction. These three laws or principles are the basis for all intelligible thought. Without them, all rational discourse vanishes. (Upcoming: Blogic Post on the Laws of Logic.)

​Dr. John W. Robbins' excellent essay on why one should study logic may be accessed by searching The Trinity Foundation web page. His essay is worth separate treatment in a future blog for it is an example of Dr. Robbins' brilliant, clear thinking and writing on a subject that is denigrated throughout academia and public schools. This brief post, owing much to Dr. Robbins' essay, is an abbreviated version of the Preview Page of The Logic Classroom.
Why Study Logic?
FIRST
To the question what is more basic than the three R’s of Reading, wRiting, and aRithmetic, we answer THOUGHT. To engage in any one of the three activities, you must think! Thinking, correctly done, follows rules. We think incorrectly, when we neglect those rules.  The rules for correct thinking and methods for avoiding mistakes in reasoning belong to the subject of logic.

Logic is the science of necessary inference. An inference is the drawing of a conclusion from premises by logical methods. The adjective "necessary" in necessary inference or necessary consequence means that the conclusion is inescapable. An argument consists of one or more propositions in support of another proposition. The propositions in support of the other proposition are premises; the proposition supported by the other propositions is the conclusion. The familiar argument about Socrates illustrates the relation between premises and conclusion in deductive argument.

1. All Men are Mortal.
2. Socrates is a Man.
3. .:. Socrates is Mortal.

The last proposition, the conclusion, is supported by the conjunction of the first two propositions, the premises.