Categorical Syllogism

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CATEGORICAL SYLLOGISM


By Najnin Jahan



Chapter Outline


  1. Introduction
  2. Learning Objectives
  3. Syllogism and Categorical Syllogism
    1. Meaning of Syllogism and Categorical Syllogism
    2. Three Terms of syllogism
    3. Mood of a Standard Syllogism
    4. Figures of a Standard Syllogism
  4. Summary
  5. Key Points
  6. Glossary
  7. Practice Test
  8. Reference and Further Readings





Introduction


The chapter deals with one of the important non-mixed syllogisms “categorical syllogism”. A syllogism is said to be categorical when the argument consisting of three categorical propositions contains exactly three terms. Each of these terms occurs in exactly two of the constituent propositions. The premises and conclusion of a standard categorical syllogism are all standard-form categorical propositions and are arranged in a specified standard order. To specify that order, in this chapter, the logician’s special names for the terms and premises of categorical syllogisms have been explained.




Learning Objectives
After reading this chapter, you are expected to learn about:


  • Explain the term of syllogism;
  • Differentiate between syllogism and categorical syllogism;
  • Describe the Mood of a Standard Syllogism; and
  • Illustrate the Figures of a Standard Syllogism.




Syllogism and Categorical Syllogism


Syllogism is a widely used term in logic. In the previous chapter we mentioned the meaning of syllogism. It has, however, been defined in this chapter as a deductive argument in which a conclusion is inferred from two premises. For brevity, in this section we shall refer to categorical syllogisms simply as “syllogisms” even though there are other kinds of syllogisms that will be discussed in later units. In this section we will try to make you understand the meaning, terms, mode, figures etc of categorical syllogism. A categorical syllogism is a deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs in exactly two of the constituent propositions.


Meaning of Syllogism and Categorical Syllogism


A syllogism is a deductive argument in which a conclusion is inferred from two premises. A categorical syllogism is a deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs in exactly two of the constituent propositions.

A categorical syllogism is said to be in standard form when its premises and conclusion are all standard-form categorical propositions and are arranged in a specified standard order. To specify that order, it will be useful to explain the logician’s special names for the terms and premises of categorical syllogisms.

Three Terms of Syllogism


The conclusion of a standard-form syllogism is a standard-form categorical proposition that contains two of the syllogism’s three terms. The conclusion is always used to identify the terms of the syllogism.

  • Major Term: The term that occurs as the predicate of the conclusion is called the “major term” of the syllogism.
  • Minor Term: The term that occurs as the subject term of the conclusion is called the “minor term” of the syllogism.
  • Middle Term: The third term of the syllogism, which does not occur in the conclusion, appearing instead in both premises, is called “middle term”.

Let’s make the terms clear with an example.

No heroes are cowards.
Some soldiers are cowards.
Therefore some soldiers are heroes.
Here,
Soldiers= Minor term
Heroes= Major term
Cowards= Middle term (which does not appear in the conclusion)

The premises of a standard-form syllogism are named after the terms that appear in them. The major and minor terms must each occur in a different one of the premises. The premise containing the major term is called the “major premise” and the premise containing the minor term is called the “minor premise”. In the syllogism given above,

Major premise= No heroes are cowards.
Minor premise= Some soldiers are cowards.

Dear learners, earlier we said that a syllogism is in standard form when its premises are arranged in a specified order. Let’s see the order,

  1. Major premise
  2. Minor premise
  3. Conclusion



Mood of Standard-form Syllogisms


The mood of a standard-form syllogism is determined by the types(identified by letter: A,E,I or O) of the standard-form categorical propositions it contains. The mood of every syllogism is represented by three letters, in a specific order:

First letter= Type of the syllogism’s major premise
Second letter= Type of its minor premise
Third letter= Type of its conclusion



For example, in the illustrative syllogism given above, the major premise is an E proposition, the minor premise is an I proposition, and the conclusion is an O proposition. So the mood of that syllogism is EIO.

Figure of Standard-form Syllogism


But the mood of a standard-form syllogism does not completely characterize its form. Consider the following two syllogisms:

All great scientists are college graduates.
A. Some professional athletes are college graduates.
Therefore some professional athletes are great scientists.
and
All artists are egotists.
B. Some artists are paupers.
Therefore some paupers are egotists.

Both are of mood All, but they are of different forms. We can bring out the difference in their forms most clearly by displaying their logical “skeletons”; Abbreviating

the minor terms by S
the major terms by P
the middle terms by M; and

The forms or “skeletons” of these two syllogisms are

All P is M All M is P
A. Some S is MB. Some M is P
Some S is M Some S is P.

In the first, labeled A, the middle term is the predicate term of both premises; while in the second labeled B, the middle term is the subject term of both premises.

These examples show that, although the form of a syllogism is partially described by a statement of its mood, syllogisms having the same mood may differ importantly in their forms, depending on the relative positions of their middle tems. We may completely describe the form of a syllogism, however, by stating both its mood and its figure, where the figure indicates the position of the middle term in the premises. It is clear that syllogisms may have four and only four possible different figures. The middle term may be the subject term of the major premise and the predicate term of the minor premise, or it may be the predicate term of both premises, or it may be the subject term of both premises, or it may be the predicate term of the major premise and the subject term of the minor premise.These different possible positions of the middle term constitute the first, second, third, and fourth figures, respectively. They are schematized in the following array, where only the relative positions of the terms are shown, and reference to mood is suppressed by not representing either quantifiers or copulas:

M-P P-M M-P P-M
S-M S-M M-S M-S
Therefore S-P Therefore S-P Therefore S-P Therefore S-P
1st Figure 2nd Figure 3rd Figure 4th Figure

We give a complete description of the form of any standard-form of syllogism by naming its mood and figure. Thus any syllogism of mood AOO in the second figure (named more briefly as AOO-2) will have the form

All P is M
Some S is not M
Therefore Some S is not M


Results




Key Points

The key points of this chapter are as follows:


  • Syllogism
  • Deductive Reasoning
  • Categorical Syllogism
  • Major terms and Premises
  • Minor Terms and Premises
  • Middle Terms and Premises,and
  • Figure




Glossary


Categorical:Not modified or restricted by reservations.

Deductive Reasoning:Reasoning from the general to the particular (or from cause to effect).

Figure:The figure indicates the position of the middle term in the premises.

Major Term:The term in a syllogism that is the predicate of the conclusion.

Major Premise:The premise of a syllogism that contains the major term (which is the predicate of the conclusion).

Middle Term:The term in a syllogism that is common to both premises and excluded from the conclusion.

Minor Term:The term in a syllogism that is the subject of the conclusion.

Minor Premise:The premise of a syllogism that contains the minor term (which is the subject of the conclusion).

Syllogism: Deductive reasoning in which a conclusion is derived from two premises.




Practice Test


Long Answer Type Questions
1. Rewrite each of the following syllogisms in standard form, and name its mood and figure.

No nuclear-powered submarines are commercial vessels, so no warships are commercial vessels, since all nuclear-powered submarines are warships.




Self-Assessment Questions (SAQs)

Put tick (√) mark on the correct answer:

1. What type of argument is called a syllogism?
a) Deductive (b) Inductive (c) Invalid (d) None

2. How many terms does a categorical syllogism contain?
a) Exactly three (b) Two (c) Exactly Four (d) Below three

3. Which of the following term does not appear in the conclusion?
a) Major term (b) Minor term (c) Middle term (d) None

4. How many letters are there in the mood of a syllogism?
a) Two (b) Four (c) One(d) Three



Answers to SAQs


1. (a) 2. (a) 3. (c) 4. (d)




References and Further Readings


Copi, I.M and Cohen, C (1996). Introduction to Logic.Prentice -Hall of India Private Limited, New Delhi.Ninth Edition.

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