Lecture on Deductive Reasoning, Validity, and Soundness

Introduction

• Importance of writing out thoughts, ideally in standard logical form.
• Examples of topics for philosophical discussion: political issues, concepts of humanity and animality.
• Writing helps clarify and refine thoughts. Philosophical writing is about constant revision.

Sources for Assignments

• No strict requirement: No minimum or maximum number of sources needed.
• Cite properly: Use MLA, Chicago, APA, or your favorite format consistently.
• Short argumentative paper, not a research paper.
• Importance of reviewing the assignment and asking questions in advance.

Overview of Deductive Reasoning

• Focus on fallacies and deductive patterns.
• Validity: Testing inferential strength - connections among premises leading to a conclusion.
  • Not about factual truth but logical consistency.

• An argument is valid if the premises can't all be true without the conclusion also being true. • An argument is valid if the truth of all its premises forces the conclusion to be true. • An argument is valid if it would be inconsistent for all its premises to be true and its conclusion to be false. • An argument is valid if its conclusion follows with certainty from its premises. • An argument is valid if it has no counterexample, that is, a possible situation that makes all the premises true and the conclusion false. Chris A. Kramer (2024) 566 zoom JUN

Testing Validity

• Formal Fallacies: Applies to deduction, invalid if conclusion does not necessarily follow from the premises.
• Inductive Weakness: In induction, even if premises are true, they don't necessarily support the likelihood of the conclusion being true.

Concepts of Validity and Soundness

• Validity: Impossible for premises to be true and conclusion false.
• Soundness: If valid and all premises are true, then sound.
• Use the thought experiment approach to assume the premises are true for testing validity.

Practical Examples

1. Example: Wet Person

   • Person is soaking wet, leading to the conclusion it is raining.
   • Inductive argument: Conclusion follows with high probability but not necessarily.
   • Highlight of deductive vs. inductive reasoning.

2. Examples of Arguments

   • Fish are religious, anything religious is a dog, therefore, fish are dogs.
   • Illustrates validity irrespective of truth.

Testing Validity with Hypotheticals

• Using Euler Diagrams: Representing relationships visually to test conclusions.
• Consistent Forms: Identifying valid argument patterns like modus ponens.
  • Valid arguments preserve truth if premises are true.

Logical Fallacies in Depth

• Affirming the Consequent: If P then Q; Q; therefore P (Invalid)
• Denying the Antecedent: If P then Q; Not P; therefore not Q (Invalid)
• Misinterpretations can lead to invalid arguments despite potentially true premises.

Real-World Testing

• Examples: Santa Claus, Serial Killers
  • Illustrate the disconnect between logical form and factual truth.
• Context Matters: Background knowledge influences inductive inferences.

Complex Examples

• Disjunctive Syllogism: Either P or Q; Not Q; therefore P (Valid form)
• Fallacy of Undistributed Middle: Misleading connections between categories.

Relevance to Everyday Scenarios

• Practical Takeaway: Understand validity and soundness to evaluate arguments effectively.
• Importance of context and definitions: Clarity in defining terms and context enhances arguments' strength.

Conclusion

• Emphasis on starting with testing validity before moving to soundness.
• Practice: Regularly write, revise, and test arguments logically.
• Remember: Validity concerns logical form, not factual accuracy.