Introductory Logic PHI 120

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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

This is Introductory Logic PHI 120 Sections 001 - 024

Introductory LogicPHI 120Presentation: Basic Concepts Review "1Review of WFFsIdentifyingandReading Sentences2Identifying FormWFFs3Sentential LogicSimple WFFsP, Q, R, S, .Complex WFFsNegation (~)Conjunction ( & )Disjunction ( v )Conditional ( -> )Biconditional ( ) and nothing elseLearn these five forms especially!4Exercise: Seeing Form~ (negation)~P~(P & Q)Exercise: Seeing Form~ (negation)~P~(P & Q) & (conjunction)P & Q~P & ~QExercise: Seeing Form~ (negation)~P~(P & Q) & (conjunction)P & Q~P & ~Q v (disjunction)P v Q(P & Q) v RExercise: Seeing Form~ (negation)~P~(P & Q) & (conjunction)P & Q~P & ~Q v (disjunction)P v Q(P & Q) v R -> (conditional)P -> QP -> (Q R)Exercise: Seeing Form~ (negation)~P~(P & Q) & (conjunction)P & Q~P & ~Q v (disjunction)P v QP v (Q & R) -> (conditional)P -> QP -> (Q R) (biconditional)P Q(P -> Q) (R S)Reading SentencesWFFsThe Key is Binding Strength

Strongest~& and/or v->

WeakestExercise: Reading Complex SentencesP & (Q & R)What kind of sentence is this?Exercise: Reading Complex SentencesP & (Q & R)Obviously an & (ampersand) kind of WFF & This is the form of a conjunction (or ampersand) kind of statement & is a binary.It has a left side () and a right side ().Exercise: Reading Complex SentencesP & (Q & R)Obviously an & (ampersand) kind of WFF & QuestionLook at the sentence as written:What is the first conjunct ()?What is the second conjunct ()?Exercise: Reading Complex SentencesP & (Q & R)Obviously an & (ampersand) kind of WFF & Answer = P = Q & RThis second conjunct is, itself, a conjunction (Q & R)Q is the first conjunctR is the second conjunctExercise: Reading Complex SentencesP & (Q & R)Obviously an & (ampersand) kind of WFF & Answer = P = Q & RThis second conjunct is, itself, a conjunctionQ is the first conjunctR is the second conjunctWhy are there parentheses around the 2nd conjunct?Exercise: Reading Complex SentencesP & Q -> RWhat kind of sentence is this?Exercise: Reading Complex SentencesP & Q -> RCould be an & (ampersand) or -> (arrow) kind of WFF & -> QuestionLook at the sentence as written:What is the weaker connective: the & or the ->?Exercise: Reading Complex SentencesP & Q -> RNot obviously an & (ampersand) or -> (arrow) kind of WFF & -> Answer The -> binds more weakly than the &You can break the sentence most easily here - the antecedent: P & Q - the consequent: RExercise: Reading Complex SentencesP & Q -> RNot obviously an & (ampersand) or -> (arrow) kind of WFF & -> 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?( )Exercise: Reading Complex SentencesR P v (R & Q)What kind of sentence is this?Exercise: Reading Complex SentencesR P v (R & Q)Either v & QuestionWhich is the main connective?Conjunction is embedded within parentheses.Exercise: Reading Complex SentencesR P v (R & Q)Either v & Answer

Exercise: Reading Complex SentencesR P v (R & Q)What is first condition?RWhat 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)?- Non-Sense- Ambiguity- Well-formed formulasGrammar and SyntaxNon-Sense FormulaExercise 1.2.1: v (page 8)

A > (Ambiguous FormulaExercise 1.2.3: v (page 10)

P -> R & S -> TWell-Formed FormulaExercise 1.2.3: iii (page 10)

P v Q -> R SWell-Formed FormulaP v Q -> (R S)Sentential LogicSimple WFFsP, Q, R, S, .Complex WFFsNegation (~)Conjunction ( & )Disjunction ( v )Conditional ( -> )Biconditional ( ) and nothing else30The end.