USING VENN DIAGRAMS FOR CATEGORICAL SYLLOGISM VALIDITY

Venn Diagram

Visual tool for illustrating categorical syllogisms.

Categorical Syllogism

Logical argument with two premises and a conclusion.

Schema

Structured representation of syllogistic form.

AAA - 1

Specific syllogistic form with three universal affirmatives.

Diagramming Rules

Steps to visually represent syllogistic arguments.

Premise

Statement that supports the conclusion in syllogism.

Conclusion

Final statement derived from premises in syllogism.

Validity

Determination of whether an argument's conclusion follows.

Invalidity

Condition where conclusion does not logically follow.

Check Mark

Indicates a valid conclusion in analysis.

Question Mark

Indicates an invalid conclusion in analysis.

Categorical Syllogism

is a two premised deductive argument whose every claim is a categorical claim, and in which exactly three terms appear in the argument. Each term occurs exactly twice. Two terms appear in the conclusion and one term does not appear in the conclusion at all, but only in the premises.

True

True or False. Each of the three terms appear exactly twice in exactly two claims.

Some consumers are not Democrats.
All Americans are consumers.
Therefore
Some Americans are not Democrats

Major Term

The term that appears as the predicate in the conclusion of the argument

Minor Term

The term that appears as the subject in the conclusion of the argument

Middle Term

The term that appears in both premises of the argument but not in the conclusion

Major Premise

The premise which contains the major term

Minor Premise

The premise which contains the minor term

Major Premise, Top, Minor

In a Standard Form Categorical Syllogism, the _________ Premise goes on _____ of the _________ Premise.

Democrats, Americans, consumers, Some consumers are not Democrats, All Americans are consumers

Identify the Major Term, Minor Term, Middle Term, Major Premise, Minor Premise in this example: Some consumers are not Democrats. All Americans are consumers. Therefore
Some Americans are not Democrats.

False. The minor premise is on top and the major premise is underneath

True or False. This is in the standard form;
"All Americans are consumers.
Some consumers are not Democrats.
Therefore Some Americans are not Democrats." Why?

standard

Once a categorical syllogism is in __________ form, we can then determine its mood

1-5, 6

If a syllogism does not violate rules ______, but does violate rule #____, it is said to be conditionally valid.)

1. Draw the three overlapping circles.

Step 1 of Diagramming Syllogism

2. Identify the minor term, the major term, and the middle term.

Step 2 of Diagramming Syllogism

Label the minor term as the upper left-hand circle, the major term as the upper right-hand circle, and the middle term as the bottom center circle.

Step 3 of Diagramming Syllogism

4. Determine whether you need to shade and whether you need to place an X. Universals require shading; particulars require placing an X.

Step 4 of Diagramming Syllogism

5. Shade whatever needs to be shaded first. Then, afterwards, place an X if the argument contains a particular premise.

Step 5 of Diagramming Syllogism

6. Put your pencil down.

Step 6 of Diagramming Syllogism

False. You do not diagram he conclusion

True or False. You can diagram the Conclusion, the major and minor premises.

True

True or False. If the argument is invalid, the conclusion will NOT be diagrammed for you. But to be clear you do not diagram the conclusion directly; you only diagram the premises.

True

True or False. to know what the figure of the syllogism is, one must be certain that the syllogism is in Standard From

True

True or False. Mood and Figure can be used to classify all possible categorical syllogisms.

True

True or False. Note there are four different types of categorical claims, and each syllogism contains a total of three. So there are only 64 different possible Moods. (e.g. AAA, AAE, AAI, AAO, AEA, AEE, AEI, AEO, etc.)

True

True or False. Each mood can be configured in four different figures. That means there are only 256 possible standard form categorical syllogisms.

True

True or False. Of the 256, only 24 are valid forms.

True

True or False. Of the 24 valid forms, 15 are unconditionally valid, and 9 are conditionally valid.

True

True or False. Five rules apply to determine whether a syllogism is unconditionally valid

True

True or False. If a syllogism does not violate rules 1-5, but does violate rule #6, it is said to be conditionally valid.

Rule 1

Rule #___: In a valid categorical syllogism, the middle term must be distributed in at least one premise.

Rule 2

Rule #___: In a valid categorical syllogism, any term that is distributed in the conclusion must be distributed in the premises.

Rule 3

Rule #___: In a valid categorical syllogism, if the argument has a negative premise, it must have a negative conclusion.

Rule 4

Rule #___: In a valid categorical syllogism, if the argument has a negative conclusion, it must have a negative premise.

Rule 5

Rule #___: In a valid categorical syllogism, there cannot be two negative premises.

Rule 7

Rule #___: (Conditional Requirement) In a valid categorical syllogism, a particular conclusion cannot be drawn from two universal premises. (If one assumes existential import, the argument may be conditionally valid.)

Particular

The symbol "X" in venn diagram means __________.

Empty

Shading in the usage of venn diagram in categorical syllogism means __________.

Between S and P

"S-P" is sympolized by shading in __________.

Construct schema

The first step to prove validity of categorical syllogism using venn diagram is __________.

Never

The final step is to diagram the conclusion