Introduction to Logic Exam 1

All S is P

No S is P

Some S is P

Some S is P

Affirmative vs negative

Universal vs particular

• A & E
• Both of them cannot be true

• A & I
• E & O
• If the universal is true, the corresponding particular is true

• A & I
• Both of them cannot be false

• A & O
• E & I
• If one is true, the other must be false & vice versa

• Switch the subject and predicate terms
• Ex: "All cats are animals" → "All animals are cats" (invalid)
• Ex: "Some cats are animals" → "Some animals are cats" (valid)

• Change the quality of the statement
• Substitute the complement of the predicate in place of the predicate
• Ex: "All cats are animals" → "No cats are non animals"
• Ex: "Some cats are not red" → "Some cats are non red"

• Switch the subject and predicate terms
• Substitute the compliment for each
• Ex: "All circles are figures" → "All non figures are non circles"

• E: No S is P
• I: Some S is P

• A: All S is P
• E: No S is P
• I: Some S is P
• O: Some S is not P

• A: All S is P
• O: Some S is not P

• In a syllogism, the predicate of the conclusion
• Also appears in the major premise

• In a syllogism, the subject of the conclusion
• Also appears in the minor premise

In a syllogism, occurs in each premise

• Major premise
• Minor premise
• Conclusion

If the premises are true, the conclusion must be true

The types of sentences used in the order in which they appear

The positioning of the middle term

If it is a valid argument with true premises, then it is a sound argument

• M P
• S M
• S P

• P M
• S M
• S P

• M P
• M S
• S P

• P M
• M S
• S P

• Rule 1: A syllogism must have exactly three terms
• Rule 2: The middle term must be distributed at least once
• Rule 3: If a term is distributed in the conclusion, it must be distributed in the premise in which it occurs
• Rule 4: There cannot be two negative premises
• Rule 5: There can be a negative premise if and only if there is a negative conclusion & vice versa
• Rule 6: There cannot be two universal premises and a particular conclusion

To threaten someone instead of giving reasons in order to force him/her to accept a conclusion

To ignore reasons given for a conclusion and directs the attack against the author of those reasons

• To conclude that something is false if no one knows that it is true
• To conclude that something is true if no one knows that it is false

• Pleas to ignore a rational principle
• Ex: I should be awarded first place, even though I finished last, because I have short legs

To appeal to the majority

To appeal to authority as the final reason for accepting a conclusion

To draw general conclusions from too little evidence

• To give the wrong explanation for the occurrence of an event
• Ex: It is raining because someone danced for it
• Ex: Bad luck came along because of the black cat

To have an argument in which the premises of every valid deductive argument "contain" its conclusion

• To ask several questions with a single sentence
• Ex: "When did you stop beating your wife?" is at least four questions:
• 1) Do you have a wife?
• 2) Do you beat your wife?
• 3) Did you stop beating your wife?
• 4) When did you stop?

• Same as Rule 1 of the Six-Rule test
• Ex: "No news is good news. Rape, murder, and arson are no news; therefore, rape, murder, and arson are good news"

To reason that a whole has a characteristic because each of its parts has that characteristic

To claim that each of the parts has a characteristic because the whole does

• Definiendum
• Definiens

The concept being analyzed in a definition

The concepts in the analysis in a definition

An analysis of a complex concept

• Stipulative definition
• Dictionary definition
• Real definition

A definition in which emotions are influenced

• Also called a lexical definition
• These definitions are correct if they accurately reflect common usage

They're only correct if the analysis of concepts reflects accurately what we find in nature

A sentence whose application is often in doubt

A sentence that has several distinct senses