Introductory Logic - PowerPoint Presentation

Slide1

Introductory LogicPHI 120

Presentation: “Basic Concepts Review "Slide2

Review of WFFsIdentifyingandReading SentencesSlide3

Identifying FormWFFsSlide4

Sentential LogicSimple WFFsP,

Q

,

R

,

S

, ….

Complex WFFsNegation (~Φ)Conjunction (Φ & Ψ)Disjunction (Φ v Ψ)Conditional (Φ -> Ψ)Biconditional (Φ <-> Ψ) and nothing else

Learn these five forms especially!Slide5
Exercise:

Seeing Form~Φ (negation)~P

~

(P & Q)Slide6
Exercise:

Seeing Form~Φ (negation)

~P

~(P & Q)

Φ

&

Ψ (conjunction)P & Q~P & ~QSlide7
Exercise:

Seeing Form~Φ (negation)

~P

~(P & Q)

Φ

&

Ψ

(conjunction)

P & Q~P & ~QΦ v Ψ (disjunction)P v Q(P & Q) v RSlide8
Exercise:

Seeing Form~Φ (negation)

~P

~(P & Q)

Φ

&

Ψ

(conjunction)

P & Q~P & ~QΦ v Ψ (disjunction)P v Q(P & Q) v RΦ -> Ψ (conditional)P -> QP -> (Q <-> R)Slide9
Exercise:

Seeing Form~Φ (negation)

~P

~(P & Q)

Φ

&

Ψ

(conjunction)

P & Q~P & ~QΦ v Ψ (disjunction)P v QP v (Q & R)Φ -> Ψ (conditional)P -> QP -> (Q <-> R)Φ <-> Ψ (biconditional)P <-> Q

(P -> Q) <-> (R <->S)Slide10

Reading SentencesWFFsSlide11
The Key is

Binding Strength

Strongest

~

&

and/or

v-><->WeakestSlide12

Exercise: Reading Complex SentencesP & (Q & R)What kind of sentence is this?Slide13

Exercise: Reading Complex SentencesP & (Q & R)Obviously an

&

(“ampersand”) kind of WFF

Φ

&

ΨThis is the form of a conjunction (or ampersand) kind of statementΦ & Ψ is a binary.It has a left side (Φ) and a right side (Ψ).Slide14

Exercise: Reading Complex SentencesP & (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)?Slide15

Exercise: Reading Complex SentencesP & (Q & R)Obviously an & (“ampersand”) kind of WFFΦ

&

Ψ

Answer

Φ

= P

Ψ

= Q & RThis second conjunct is, itself, a conjunction (Q & R)Q is the first conjunctR is the second conjunctSlide16

Exercise: Reading Complex SentencesP & (Q & R)

Obviously an & (“ampersand”) kind of WFF

Φ

&

Ψ

Answer

Φ

= PΨ = Q & RThis second conjunct is, itself, a conjunctionQ is the first conjunctR is the second conjunctWhy are there parentheses around the 2nd conjunct?Slide17

Exercise: Reading Complex SentencesP & Q -> RWhat kind of sentence is this?Slide18

Exercise: Reading Complex SentencesP & Q -> RCould be an & (“ampersand”) or -> (“arrow”) kind of WFF

Φ

&

Ψ

Φ

-> ΨQuestionLook at the sentence as written:What is the weaker connective: the & or the ->?Slide19

Exercise: Reading Complex SentencesP & Q -> RNot 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 hereΦ - “the antecedent”: P & QΨ - “the consequent”: RSlide20

Exercise: Reading Complex SentencesP & Q -> RNot 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 hereAntecedent: P & QConsequent: RWhy are there no parentheses around the antecedent?( )Slide21

Exercise: Reading Complex SentencesR <-> P v (R & Q)What kind of sentence is this?Slide22

Exercise: Reading Complex SentencesR <-> P v (R & Q)EitherΦ <->

Ψ

Φ

v

ΨΦ & ΨQuestionWhich is the main connective?Conjunction is embedded within parentheses.Slide23

Exercise: Reading Complex SentencesR <-> P v (R & Q)Either

Φ

<->

Ψ

Φ

v

ΨΦ & ΨAnswerΦ <-> ΨSlide24

Exercise: Reading Complex SentencesR <-> 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: PSecond disjunct: R & QQuestion: can you see why are there parentheses around the second disjunct (R & Q)?Slide25

- Non-Sense- Ambiguity- Well-formed formulas

Grammar and SyntaxSlide26

Non-Sense FormulaExercise 1.2.1: v (page 8)A –> (Slide27

Ambiguous FormulaExercise 1.2.3: v (page 10)P -> R & S -> TSlide28

Well-Formed FormulaExercise 1.2.3: iii (page 10)P v Q -> R <-> SSlide29

Well-Formed FormulaP v Q -> (R <-> S)Slide30

Sentential LogicSimple WFFsP,

Q

,

R

,

S

, ….

Complex WFFsNegation (~Φ)Conjunction (Φ & Ψ)Disjunction (Φ v Ψ)Conditional (Φ -> Ψ)Biconditional (Φ <-> Ψ) and nothing elseSlide31
The end.