Introductory Logic PHI 120

1. Presentation: “Basic Concepts Review " Introductory LogicPHI 120

2. Review of WFFs Identifying and Reading Sentences

3. WFFs Identifying Form

4. Sentential Logic • Simple WFFs • P, Q, R, S, …. • Complex WFFs • Negation (~Φ) • Conjunction (Φ&Ψ) • Disjunction (ΦvΨ) • Conditional (Φ->Ψ) • Biconditional (Φ<->Ψ) • and nothing else Learn these five forms especially!

5. Exercise: Seeing Form • ~Φ (negation) • ~P • ~(P & Q)

6. Exercise: Seeing Form • ~Φ (negation) • ~P • ~(P & Q) • Φ&Ψ (conjunction) • P & Q • ~P & ~Q

7. Exercise: Seeing Form • ~Φ (negation) • ~P • ~(P & Q) • Φ & Ψ (conjunction) • P & Q • ~P & ~Q • ΦvΨ (disjunction) • P v Q • (P & Q) v R

8. Exercise: Seeing Form • ~Φ (negation) • ~P • ~(P & Q) • Φ & Ψ (conjunction) • P & Q • ~P & ~Q • Φ v Ψ (disjunction) • P v Q • (P & Q) v R • Φ->Ψ (conditional) • P -> Q • P -> (Q <-> R)

9. Exercise: Seeing Form • ~Φ (negation) • ~P • ~(P & Q) • Φ & Ψ (conjunction) • P & Q • ~P & ~Q • Φ v Ψ (disjunction) • P v Q • P v (Q & R) • Φ -> Ψ (conditional) • P -> Q • P -> (Q <-> R) • Φ<->Ψ (biconditional) • P <-> Q • (P -> Q) <-> (R <->S)

10. WFFs Reading Sentences

11. The Key is Binding Strength Strongest ~ &and/orv -> <-> Weakest

12. Exercise: Reading Complex Sentences • P & (Q & R) What kind of sentence is this?

13. Exercise: Reading Complex Sentences • P & (Q & R) • Obviously an & (“ampersand”) kind of WFF • Φ&Ψ This is the form of a conjunction (or ampersand) kind of statement • Φ&Ψ is a binary. • It has a left side (Φ) and a right side (Ψ).

14. Exercise: Reading Complex Sentences • P & (Q & R) • Obviously an & (“ampersand”) kind of WFF • Φ & Ψ • Question • Look at the sentence as written: • What is the first conjunct (Φ)? • What is the second conjunct (Ψ)?

15. Exercise: Reading Complex Sentences • P & (Q & R) • Obviously an & (“ampersand”) kind of WFF • Φ & Ψ • Answer • Φ = P • Ψ = Q & R • This second conjunct is, itself, a conjunction (Q & R) • Q is the first conjunct • R is the second conjunct

16. Exercise: Reading Complex Sentences • P & (Q & R) • Obviously an & (“ampersand”) kind of WFF • Φ & Ψ • Answer • Φ = P • Ψ = Q & R • This second conjunct is, itself, a conjunction • Q is the first conjunct • R is the second conjunct • Why are there parentheses around the 2nd conjunct?

17. Exercise: Reading Complex Sentences • P & Q -> R What kind of sentence is this?

18. Exercise: Reading Complex Sentences • P & Q -> R • Could be an & (“ampersand”) or -> (“arrow”) kind of WFF • Φ&Ψ • Φ->Ψ • Question • Look at the sentence as written: • What is the weaker connective: the & or the ->?

19. Exercise: Reading Complex Sentences • P & Q -> R • Not obviously an & (“ampersand”) or -> (“arrow”) kind of WFF • Φ & Ψ • Φ -> Ψ • Answer • The -> binds more weakly than the & • You can break the sentence most easily here • Φ - “the antecedent”: P & Q • Ψ - “the consequent”: R

20. Exercise: Reading Complex Sentences () • P & Q -> R • Not obviously an & (“ampersand”) or -> (“arrow”) kind of WFF • Φ & Ψ • Φ -> Ψ • Answer • The -> binds more weakly than the & • You can break the sentence most easily here • Antecedent: P & Q • Consequent: R • Why are there no parentheses around the antecedent?

21. Exercise: Reading Complex Sentences • R <-> P v (R & Q) What kind of sentence is this?

22. Exercise: Reading Complex Sentences • R <-> P v (R & Q) • Either • Φ<->Ψ • ΦvΨ • Φ&Ψ • Question • Which is the main connective? Conjunction is embedded within parentheses.

23. Exercise: Reading Complex Sentences • R <-> P v (R & Q) • Either • Φ <-> Ψ • ΦvΨ • Φ & Ψ • Answer • Φ<->Ψ

24. Exercise: Reading Complex Sentences • R<->P v (R & Q) • What is first condition? • R • What is the second condition? • P v (R & Q) • Is this WFF a disjunction (v) or a conjunction (&)? • It is a v (a disjunction) • First disjunct: P • Second disjunct: R & Q • Question: can you see why are there parentheses around the second disjunct (R & Q)?

25. Grammar and Syntax - Non-Sense- Ambiguity- Well-formed formulas

26. Non-Sense Formula Exercise 1.2.1: v (page 8) A –> (

27. Ambiguous Formula Exercise 1.2.3: v (page 10) P -> R & S -> T

28. Well-Formed Formula Exercise 1.2.3: iii (page 10) P v Q -> R <-> S

29. Well-Formed Formula P v Q -> (R <-> S)

30. Sentential Logic • Simple WFFs • P, Q, R, S, …. • Complex WFFs • Negation (~Φ) • Conjunction (Φ&Ψ) • Disjunction (ΦvΨ) • Conditional (Φ->Ψ) • Biconditional (Φ<->Ψ) • and nothing else

31. The end.