Phil 210 Exam 4 Study Guide

Syllogism

A deductive argument consisting of two premises and one conclusion.

Categorical Syllogism

A syllogism consisting of three categorical propositions and containing a total of three different terms, each of which appears twice of distinct propositions.

Major Term

The predicate of the conclusion.

Middle Term

Provides the middle ground between the two premises. The one that occurs once in each premise and does not occur in the conclusion.

Minor Term

The subject of the conclusion.

Major Premise

The premise that contains the major term.

Minor Premise

The premise that contains the minor term.

Mood

An attribute of a categorical syllogism that specifics the kind of propositions (A, E, I, O) of which it is composed.

Figure

An attribute of a categorical syllogism that specifics the location of the middle term.

Standard-form Categorical Syllogism

A categorical syllogism in which all three statements are standard-form propositions.

Has to meet the following four conditions:

1. All three statements are standard-form categorical propositions.

2. The two occurrences of each term are identical.

3. Each term is used in the same sense throughout the argument.

4. The major premise is listed first, the minor premise second, and the conclusion last.

Undistributed Middle

The middle term must be distributed at least once, and if it is not, then undistributed middle is committed.

Illicit Major

If a term is distributed in the conclusion, then it must be distributed in a premise. This occurs when the major term is distributed int he conclusion but not in the major premise.

Illicit Minor

If a term is distributed in the conclusion, then it must be distributed in a premise. This occurs when the minor term is distributed int he conclusion but not in the minor premise.

Exclusive Premises

Two negative premises are not allowed.

Drawing an affirmative conclusion from a negative premise

A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise.

Example

All crows are birds.

Some wolves are not crows.

Some wolves are birds.

Drawing a negative conclusion from affirmative premises

A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise.

Example

All triangles are three-angled polygons.

All three-angled polygons are three-sided polygons.

Some three-sided polygons are not triangles.

Critical Term

The term that must denote an actually existing thing in order for the syllogism to be valid from the Aristotelian perspective.

Example:

All mammals are animals.

All tigers are mammals.

Some tigers are animals.

From the Aristotelian viewpoint, mammals and tigers do denote actually existing things.

Figure 1 - AAI, EAO - S exists

Figure 2 - AEO, EAO - S Exists

Figure 3 - AAI, EAO - M exists

Figure 4 - AEO (S exists), EAO (M exists), AAI (P exists)

Reducing the number of terms

Testing categorical syllogisms in ordinary language sometimes requires that the number of terms be “reduced” to a total of three terms through the use of conversion, obversion, and contraposition.

Conversion and contraposition must never be used on statements for which they yield undetermined results. Conversion must never be used on A and O statements. Contraposition must never be used on E and I statements.

Ordinary Language Arguments

Inserting quantifiers, modifying subject and predicate terms, and introducing copulas. Restate the subject and predicate terms so that the premises correspond to the conclusion and identify an implicit factor shared at least two propositions and make it explicit (times, place, people, etc). The goal is to produce an argument consisting of three standard-form categorical repositions that contain a total of three different terms, each of which occurs twice in distinct propositions. Once translated, the argument can be tested by means of a Venn diagram or the rules for syllogisms. Since the task of translating arguments into standard-form syllogisms involves not only converting the component statements into standard form but adjusting these statements one to another so that their terms occur in matched pairs, a certain amount of practice may be required before it can be done with facility. In reducing the terms to three propositions and to express this common factor the strategic use of parameters.

Enthymeme

An argument expressed as a categorical syllogism that is missing a premise or conclusion.

Sorites

A chain of categorical syllogisms in which the intermediate conclusions have been omitted or left out.

Venn Diagrams

Hurley thinks this is the most intuitive and easiest-to-remember technique for testing the validity of categorical syllogisms.

Seven “Pointers”

1. Marks are made only for premises, not for the conclusion.

2. Universal premises are entered first.

3. Concentrate on the circles representing the two terms found in the proposition being diagrammed.

4. Remember that in particular statements “soem” means “at least one.”

5. When shading, be sure to shade all of the area in question.

6. If one part of the area in which an X goes is shaded, the X goes in the other part; if neither part is shaded, the X goes on the line separating the two parts.

7. An X should never be placed outside of the diagram or at the intersection of two lines.