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Logic: The Language of Philosophy

Logic: The Language of Philosophy. What is Logic?. Logic is the study of argumentation In Philosophy, there are no right or wrong opinions, but there are arguments that are better than others. What is an “Argument”?.

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Logic: The Language of Philosophy

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  1. Logic: The Language of Philosophy

  2. What is Logic? • Logic is the study of argumentation • In Philosophy, there are no right or wrong opinions, but there are arguments that are better than others.

  3. What is an “Argument”? • Argument: a set of statements consisting of at least two premises and at least one conclusion. • Premises: reasons supporting the conclusion • Conclusion: the statement you are trying to prove

  4. Philosophers write arguments like this: • Socrates is a man. (premises) • All men are mortal --------------------------- 3. Socrates is mortal (conclusion)

  5. Arguments must be valid and sound • An argument is valid when the premises guarantee the conclusion • This is not subjective • An argument is sound if (1) it is valid; and (2) the premises are true

  6. Argument Forms I. Modus Ponens (“Affirming Mode”) P→Q 1. If the ground is wet, then it was raining. P 2. The ground is wet. ------- ------------------------------------------------------ Q 3. Therefore, it was raining.

  7. Modus Tollens • Latin for “Denying Mode” P→Q 1. If the ground is wet, then it was raining. ~Q 2. It was not raining ------- ----------------------------------------------------- ~P 3. Therefore, the ground is not wet.

  8. Common Errors P→Q P→Q ~P Q -------- --------- ~Q P Affirming the Consequent Denying the Antecedent

  9. Denying the Antecedent P→Q 1. If Socrates is French, then Socrates is mortal ~P 2. Socrates is not French -------- ------------------------------------------------------------------ ~Q 3. Socrates is not mortal NOT VALID!

  10. Affirming the Consequent P→Q 1. If Socrates is French, then Socrates is mortal. Q 2. Socrates is mortal. -------- -------------------------------------------------------------------- P 3. Socrates is French NOT VALID!

  11. Chain Reasoning P  Q 1. Nellie is a dog. Q  R 2. A dog is a mammal. -------- ----------------------------- P  R 3. Nellie is a mammal.

  12. Disjunctive Syllogism P  Q 1. Either the maid did it or the butler did it. ~P 2. The maid did not do it. -------- ------------------------------------------------------ Q 3. Therefore, the butler did it.

  13. Hypothetical Syllogism P→Q 1. If Jim comes to the party, then Chris will come too. Q→R 2. If Chris comes to the party, then Pat will come too. ------- ------------------------------------------------------------- P→R 3. Therefore, if Jim comes to the party, Pat will come too.

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