Lecture Notes for PHIL 240 - HNR-INTRODUCTION TO LOGIC at Texas A&M (A&M)

Notes Information

Material Type:Class Note
University:Texas A&M University
  • Constructive Dilemma
  • Either...or
  • Hypothetical
  • Conjunction
  • Inference Rules
  • On the Ground
  • Conditional
  • Rule of Thumb
  • Hypothetical Syllogism
  • Modus Ponens
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8.1: Implicational Rules of Inference Comment: The focus of the rest of the course will be on systems of natural deduction, in which one uses a set of inference rules to demonstrate, step by step, that the conclusion of an argument follows from the premises. Advantages of Natural Deduction ? Generally less cumbersome than truth tables. ? Reflects more closely the way we actually reason. Definition (sorta): A proof is a series of "steps" that leads, by way of valid inference rules, from the premises of a symbolic argument to its conclusion. An inference rule is valid if and only if, any statement that follows from a set of statements by means of the rule must be true if all of the statements in the set are true. Implication Rules Rule 1: Modus ponens (MP) p ? q p ? q 1. If it's either raining or snowing, the ground is wet. (R?S) ? W 2. It's either raining or snowing. R?S So, 3. The ground is wet. W Rule 2: Modus tollens (MT) p ? q ?q ? ?p 1. If it's either raining or snowing, the ground ...

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