Introductory Logic PHI 120 Presentation: “Basic Concepts Review "

Review of WFFs Identifying and Reading Sentences

IDENTIFYING FORM WFFs

Sentential Logic Simple WFFs 1.P, Q, R, S, …. Complex WFFs 2.Negation (~Φ) 3.Conjunction (Φ & Ψ) 4.Disjunction (Φ v Ψ) 5.Conditional (Φ -> Ψ) 6.Biconditional (Φ Ψ) – and nothing else Learn these five forms especially!

Exercise: Seeing Form ~Φ (negation) –~P–~P – ~(P & Q)

Exercise: Seeing Form ~Φ (negation) – ~P – ~(P & Q) Φ & Ψ (conjunction) – P & Q – ~P & ~Q

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

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)

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)

READING SENTENCES WFFs

The Key is Binding Strength Strongest ~ & and/or v -> Weakest

Exercise: Reading Complex Sentences 1.P & (Q & R) What kind of sentence is this?

Exercise: Reading Complex Sentences 1.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).

Exercise: Reading Complex Sentences 1.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)?

Exercise: Reading Complex Sentences 1.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

Exercise: Reading Complex Sentences 1.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 2 nd conjunct?

Exercise: Reading Complex Sentences 2.P & Q -> R What kind of sentence is this?

Exercise: Reading Complex Sentences 2.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 ->?

Exercise: Reading Complex Sentences 2.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

Exercise: Reading Complex Sentences 2.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? ( )

Exercise: Reading Complex Sentences 3.R P v (R & Q) What kind of sentence is this?

Exercise: Reading Complex Sentences 3.R P v (R & Q) – Either Φ Ψ Φ v Ψ Φ & Ψ – Question – Which is the main connective? Conjunction is embedded within parentheses.

Exercise: Reading Complex Sentences 3.R P v (R & Q) – Either Φ Ψ Φ v Ψ Φ & Ψ – Answer Φ Ψ

Exercise: Reading Complex Sentences 3.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)?

- NON-SENSE - AMBIGUITY - WELL-FORMED FORMULAS Grammar and Syntax

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

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

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

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

Sentential Logic Simple WFFs 1.P, Q, R, S, …. Complex WFFs 2.Negation (~Φ) 3.Conjunction (Φ & Ψ) 4.Disjunction (Φ v Ψ) 5.Conditional (Φ -> Ψ) 6.Biconditional (Φ Ψ) – and nothing else

The end.