PHIL-1290-LECTURE4-FINAL

Chapter 1: Introduction to Deductive Reasoning

• Introduction to Deductive Reasoning

  • Focus on deductive reasoning or deduction.

  • Core notion: logical entailment.

• What is an Argument?

  • Sequence of assertions (premises) supporting a conclusion.

  • Different types of arguments lend support in different ways.

• Deductive Arguments

  • Support conclusions via entailment.

  • Premises guarantee the truth of the conclusion.

• Examples of Valid Deductive Arguments

  • "All bachelors are unmarried, Steven's a bachelor, therefore Steven is unmarried."

  • "Kai Lin's either from China or Taiwan; not China, so Taiwan."

  • More complex example: "If more asylum seekers than host countries exist, we need a developed system. There are more asylum seekers; thus, we need this system."

• Non-Deductive Arguments

  • Do not lend support via entailment.

  • Example: Enrollment predictions based on past data do not entail the conclusion.

Chapter 2: Testing for Valid Deductive Arguments

• Imagining Consequences

  • If premises true, can conclusion be false?

  • Consider conceivable worlds for testing entailment.

• Different Tests for Entailment

  • Test 1: Imagine premises true, can the conclusion be false?

  • Test 2: Assume conclusion false, can premises all be true?

Chapter 3: Validity of Deductive Arguments

• What Makes an Argument Valid?

  • Truth of premises guarantees truth of conclusion.

• Importance of Form

  • Validity based on the relationship between premises and conclusion.

• Examples of Valid Arguments

  • Different content but share the same form (disjunctive syllogism).

Chapter 4: Common Valid Argument Forms

• Valid Argument Forms

  • Modus Ponens: If P, then Q; P; therefore Q.

  • Modus Tollens: If P, then Q; not Q; therefore not P.

  • Disjunctive Syllogism: P or Q; not P; therefore Q.

  • Hypothetical Syllogism: If P, then Q; if Q, then R; therefore if P, then R.

Chapter 5: Understanding Soundness

• Soundness Defined

  • Argument must be valid and all premises true.

• Example of Soundness

  • "All mammals give live birth; platypus are mammals; thus, platypus give live birth." (Sound only if premises are true)

Chapter 6: Addressing Invalid Arguments

• Recognizing Invalid Arguments

  • Affirming the Consequent: Invalid form that fails tests for validity.

  • Denying the Antecedent: Another common fallacy.

Chapter 7: Conclusion and Recap

• Overview of Deductive Reasoning

  • Focus on entailment, validity (truth of premises necessitating conclusion), soundness (valid + true premises), and logical forms.

  • Introduction to symbolic logic for formalizing arguments.