Logic Fundamentals: Argument Analysis & Reasoning

Understanding Statements

What is a Statement?

A statement is a declarative sentence capable of being either true or false.

Example: "Broccoli is a good source of vitamin A."

Non-Statements

Non-statements include:

• Questions (open-ended)
• Commands
• Exclamations
• Suggestions

Example: "Is it cold outside?"

Argument Structure: Indicators

Conclusion Indicators

Words that often signal a conclusion:

• Therefore
• Thus
• Consequently
• For this reason
• So

Premise Indicators

Words that often signal a premise:

• Since
• Because
• For
• For that reason
• In that
• As
• Given that

Deductive Argument Forms

Invalid Argument Example 1

This example demonstrates a common logical fallacy:

• Premise 1: All banks are financial institutions.
• Premise 2: Wells Fargo is a financial institution.
• Conclusion: Therefore, Wells Fargo is a bank.

This argument is invalid; the conclusion does not logically follow from the premises.

Disjunctive Syllogism (DS)

A valid deductive form:

• Premise 1: Either Split or Steal.
• Premise 2: Not Split.
• Conclusion: Therefore, Steal.

Modus Ponens (MP)

A valid deductive form:

• Premise 1: If Jane eats her dinner, then the family goes to the beach.
• Premise 2: Jane eats her dinner.
• Conclusion: Therefore, the family goes to the beach.

Modus Tollens (MT)

A valid deductive form:

• Premise 1: If Jane eats her dinner, then the family goes to the beach.
• Premise 2: The family does not go to the beach.
• Conclusion: Therefore, Jane does not eat her dinner.

Another example:

• Premise 1: If Bob cleans his room, then Bob gets ice cream.
• Premise 2: Bob does not get ice cream.
• Conclusion: Therefore, Bob does not clean his room.

Hypothetical Syllogism (HS)

A valid deductive form:

• Premise 1: If Jane eats her dinner, then the family goes to the beach.
• Premise 2: If the family goes to the beach, then the family rents kayaks.
• Conclusion: Therefore, if Jane eats her dinner, then the family rents kayaks.

Common Invalid Deductive Forms

Denying the Antecedent

This form is invalid:

• Premise 1: If A, then B.
• Premise 2: Not A.
• Conclusion: Therefore, not B.

Example:

• Premise 1: If Jane eats her dinner, then the family goes to the beach.
• Premise 2: Jane does not eat her dinner.
• Conclusion: Therefore, the family does not go to the beach.

Affirming the Consequent

This form is invalid:

• Premise 1: If A, then B.
• Premise 2: B.
• Conclusion: Therefore, A.

Example:

• Premise 1: If Jane eats her dinner, then the family goes to the beach.
• Premise 2: The family goes to the beach.
• Conclusion: Therefore, Jane eats her dinner.

Another example:

• Premise 1: If Bob cleans his room, then Bob gets ice cream.
• Premise 2: Bob gets ice cream.
• Conclusion: Therefore, Bob cleans his room.

Affirming a Disjunct

This form is invalid:

• Premise 1: Either A or B.
• Premise 2: A.
• Conclusion: Therefore, B.

Deductive vs. Inductive Reasoning

Deductive Arguments

Deductive arguments claim to guarantee the truth of their conclusion, assuming the premises are true.

Inductive Arguments

Inductive arguments claim that their conclusion probably follows from the premises.

Argument Validity and Soundness

Valid Arguments Defined

An argument is valid if it is impossible for the conclusion to be false, given that all the premises are true.

Invalid Arguments Defined

An argument is invalid if it is possible for the conclusion to be false, even if all the premises are true.

Example of a Valid Argument

• Premise 1: All television networks are media companies.
• Premise 2: NBC is a television network.
• Conclusion: Therefore, NBC is a media company.

Sound Arguments Defined

A sound argument is a valid argument with all true premises.

Assessing Inductive Argument Strength

Example of a Weak Inductive Argument

• Premise 1: When a lit match is slowly dunked into water, the flame is snuffed out.
• Premise 2: Gasoline is a liquid, just like water.
• Conclusion: Therefore, when a lit match is slowly dunked into gasoline, the flame will be snuffed out.

This is a weak inductive argument, as the conclusion is highly improbable despite the premises.