An Invitation to Modal Logic:Lecture 1Philosophy 150Eric PacuitStanford UniversityNovember 26, 2007Eric Pacuit: Invitation to Modal Logic, Philosophy 150 1Setting the StageMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.list of sentences (premises followed by a conclusion)Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Is the argument valid?Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.formal proofsMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Truth-tables, first-order structuresEric Pacuit: Invitation to Modal Logic, Philosophy 150 2Setting the StageMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.list of sentences (premises followed by a conclusion)Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Is the argument valid?Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.formal proofsMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Truth-tables, first-order structuresEric Pacuit: Invitation to Modal Logic, Philosophy 150 2Setting the StageMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.list of sentences (premises followed by a conclusion)Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Is the argument valid?Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.formal proofsMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Truth-tables, first-order structuresEric Pacuit: Invitation to Modal Logic, Philosophy 150 2Setting the StageMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.list of sentences (premises followed by a conclusion)Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Is the argument valid?Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.formal proofsMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Truth-tables, first-order structuresEric Pacuit: Invitation to Modal Logic, Philosophy 150 2Setting the StageMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.list of sentences (premises followed by a conclusion)Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Is the argument valid?Much of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.formal proofsMuch of this course has focused on techniques to evaluatearguments.Arguments have been analyzed from both syntactic andsemantic perspectives.Truth-tables, first-order structuresEric Pacuit: Invitation to Modal Logic, Philosophy 150 2Setting the Stage: Two LogicsBoolean Logic (BL)ILanguage: P ∧ Q, P → (Q ∨ ¬R), etc.IProof-Theory: ∧-elim, ∧-intro, ∨-elim, etc.ISemantics: Truth-tablesFirst-Order Logic (FOL)ILanguage: x = y, ∀x∃y (F (x) → (G (x, y) ∧ ¬R(y))), etc.IProof-Theory: ∀-elim, ∀-intro, etc.ISemantics: First-order structuresEric Pacuit: Invitation to Modal Logic, Philosophy 150 3Setting the Stage: Two LogicsBoolean Logic (BL)ILanguage: P ∧ Q, P → (Q ∨ ¬R), etc.IProof-Theory: ∧-elim, ∧-intro, ∨-elim, etc.ISemantics: Truth-tablesFirst-Order Logic (FOL)ILanguage: x = y, ∀x∃y (F (x) → (G (x, y) ∧ ¬R(y))), etc.IProof-Theory: ∀-elim, ∀-intro, etc.ISemantics: First-order structuresEric Pacuit: Invitation to Modal Logic, Philosophy 150 3Setting the StageDo we need the quantifiers?Yes!All men are mortalSocrates is a manSocrates is mortalEric Pacuit: Invitation to Modal Logic, Philosophy 150 4Setting the StageDo we need the quantifiers? Yes!All men are mortalSocrates is a manSocrates is mortalEric Pacuit: Invitation to Modal Logic, Philosophy 150 4Setting the StageThere are some valid arguments that cannot be formalized usingeither boolean or first-order logic.Plan for today: highlight a number of such arguments.Eric Pacuit: Invitation to Modal Logic, Philosophy 150 5Setting the StageThere are some valid arguments that cannot be formalized usingeither boolean or first-order logic.Plan for today: highlight a number of such arguments.Eric Pacuit: Invitation to Modal Logic, Philosophy 150 5Plan for the next 6 classes11/26: Motivating Examples11/28: Motivating Examples, Basic Modal Logic I11/30: Basic Modal Logic II12/3: Basic Modal Logic III12/5: Dynamics in Logic I12/7: Dynamics in Logic IIEric Pacuit: Invitation to Modal Logic, Philosophy 150 6Problems with the material conditionalModern Modal Logic began with C.I. Lewis’ dissatisfaction withthe material conditional (→).Eric Pacuit: Invitation to Modal Logic, Philosophy 150 7Problems with the material conditionalThe Material ConditionalX Y X → YT T TT F FF T TF F TEric Pacuit: Invitation to Modal Logic, Philosophy 150 8Problems with the material conditionalThe Material ConditionalX Y X → YT T TT F FF T TF F TEric Pacuit: Invitation to Modal Logic, Philosophy 150 8Problems with the material conditionalThe Material ConditionalX Y X → YT T TT F FF T TF F TEric Pacuit: Invitation to