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Introductory Logic PHI 120 Presentation: “Basic Concepts Review "

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Presentation: “Basic Concepts Review ". Introductory Logic PHI 120. Review of WFFs. Identifying and Reading Sentences. WFFs. Identifying Form. Sentential Logic. Simple WFFs P , Q , R , S , …. Complex WFFs Negation ( ~ Φ ) Conjunction ( Φ & Ψ ) Disjunction ( Φ v Ψ ) - PowerPoint PPT Presentation

### Transcript of Introductory Logic PHI 120

Introductory LogicPHI 120

Presentation: “Basic Concepts Review "

Review of WFFs

Identifyingand

IDENTIFYING FORMWFFs

Sentential Logic

• Simple WFFs1. P, Q, R, S, ….

• Complex WFFs2. 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 & 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)

The Key is Binding Strength

Strongest~

& and/or v->

<->Weakest

1. P & (Q & R) What kind of sentence is this?

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).

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)?

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

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 2nd conjunct?

2. P & Q -> R What kind of sentence is this?

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 ->?

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

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?

( )

3. R <-> P v (R & Q) What kind of sentence is this?

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.

3. R <-> P v (R & Q)– Either• Φ <-> Ψ• Φ v Ψ• Φ & Ψ

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 FormulaExercise 1.2.1: v (page 8)

A –> (

Ambiguous FormulaExercise 1.2.3: v (page 10)

P -> R & S -> T

Well-Formed FormulaExercise 1.2.3: iii (page 10)

P v Q -> R <-> S

Well-Formed Formula

P v Q -> (R <-> S)

Sentential Logic

• Simple WFFs1. P, Q, R, S, ….

• Complex WFFs2. Negation (~Φ)3. Conjunction (Φ & Ψ)4. Disjunction (Φ v Ψ)5. Conditional (Φ -> Ψ)6. Biconditional (Φ <-> Ψ)– and nothing else

The end.