introductory logic phi 120 presentation: “basic concepts review "
TRANSCRIPT
Introductory LogicPHI 120
Presentation: “Basic Concepts Review "
Review of WFFs
Identifyingand
Reading Sentences
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)
READING SENTENCESWFFs
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 2nd 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 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.