Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Outline Indicative Conditionals, Strictly 1 Monotonic Patterns William Starr 2 New Data 3 A Strict Analysis Department of Philosophy will.starr@cornell.edu http://williamstarr.net 4 Assorted Curiosities April 6, 2019 William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 0 Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Conditionals Monotonic Patterns And Indicative Conditionals Antecedent Strengthening (AS) Antecedent Strengthening (AS) A → C ⊧ ( A ∧ B ) → C (1) a. If James Earl Ray didn’t kill MLK, someone else did. Example: Indicative (2) a. If Allie served tea, Chris came. b. If James Earl Ray hadn’t killed MLK, someone else b. So, if Allie served tea and cake, Chris came. would’ve. Subjunctive Counterexample (Stalnaker 1968; Adams 1975): a. If Allie served tea, Chris came. (3) b. # So, if Allie served tea and didn’t invite Chris, Chris came. William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 1 William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 2
Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns Monotonic Patterns Simplification of Disjunctive Antecedents Meet the Family Antecedent Monotonicity Simplification of Disjunctive Antecedents (SDA) If A → C ⊧ D and B ⊧ A, then B → C ⊧ D ( A ∨ B ) → C ⊧ ( A → C ) ∧ ( B → C ) • Conditional antecedents preserve consequence relations. Example: • Antecedent Monotonicity follows from Transitivity and the assumption that if A ⊧ B then ⊧ A → B (Starr 2019:n22) (4) a. If Allie served tea or cake, Chris came. b. So, if Allie served tea, Chris came; and, if Allie Transitivity served cake, Chris came. A → B , B → C ⊧ A → C Counterexample (Adams 1975; McKay & van Inwagen 1977): • Antecedent Monotonicity follows from Contraposition and (5) a. If Allie served only tea or only cake, she served only ‘Consequent Monotonicity’ (Starr 2019:n23) cake. b. # So, if Allie served only tea, she served only cake. Contraposition A → B ⊧ ¬ B → ¬ A William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 3 William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 4 Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References What to Say... Monotonic Patterns About Monotonic Patterns? Returning to the Counterexamples in Light of Indicative Felicity Antecedent Strengthening (AS) • Why are they sometimes good and sometimes bad? A → C ⊧ ( A ∧ B ) → C • Current accounts begin with an observation about the felicity of indicative antecedents Example revisited: a. Maybe Allie served tea and cake. If Allie served tea, (7) Indicative Felicity Chris came. An indicative conditional is only felicitous in contexts where its b. So, if Allie served tea and cake, Chris came. antecedent is mutually supposed to be possible. Counterexample revisited: (Stalnaker 1975; Adams 1975; Veltman 1986; Gillies 2010) a. Maybe Allie served tea and didn’t invite Chris. # If (8) (6) a. Allie definitely did not serve tea. Allie served tea, Chris came. b. # If Allie served tea, Chris came. b. # So, if Allie served tea and didn’t invite Chris, Chris came. William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 5 William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 6
Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns The Generalization Returning to the Counterexamples in Light of Indicative Felicity About Monotonic Patterns Simplification of Disjunctive Antecedents (SDA) ( A ∨ B ) → C ⊧ ( A → C ) ∧ ( B → C ) The Generalization Monotonic patterns sound compelling only when Indicative Example revisited: Felicity of conclusion is compatible with the truth (and a. Maybe Allie served tea, maybe she served cake. But, (9) Indicative Felicity) of the premises. if Allie served tea or cake, Chris came. b. So, if Allie served tea, Chris came; and, if Allie Terminology An argument pattern is said to satisfy Indicative served cake, Chris came. Felicity just in case the premises and conclusion Counterexample revisited: satisfy Indicative Felicity. a. Maybe Allie served only tea. #But, if Allie served (10) only tea or only cake, she served only cake. b. # So, if Allie served only tea, she served only cake. William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 7 William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 8 Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns Monotonic Patterns Two Explanations Two Explanations Variably-Strict Explanation (Stalnaker 1975) Strict Explanation 1 ‘Examples’ are semantically invalid but pragmatically 1 ‘Examples’ are compelling because monotonic patterns compelling ( reasonable inference ): any context which is are semantically valid. updated with a felicitous and true assertion of the 2 ‘Counterexamples’ sound bad because violation of premise, is one where the conclusion is true if felicitous. Indicative Felicity for conclusion leads to: • Pragmatical infelicity (Veltman 1986, 1985) 2 ‘Counterexamples’ exist because monotonic patterns are • Semantic presupposition failure (Gillies 2004, 2009) semantically invalid, and do not sound pragmatically • Equivocation via accommodation (Warmbr¯ od 1981) compelling because Indicative Felicity is not satisfied. • Key Prediction : any time Indicative Felicity is satisfied, • Key Prediction : any time Indicative Felicity is satisfied, a monotonic pattern will sound compelling. a monotonic pattern will sound compelling. William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 9 William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 10
Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Variably-Strict Analyses Basic Variably-Strict Analysis Of Conditionals Of Conditionals Basic Variably-Strict Analysis A → B is true in a world w , relative to f , just in case all f ( A , w ) -worlds are B-worlds. • f ( A , w ) are the A-worlds most similar to w . • Context Sensitivity : if w ′ is in context set c , w ′ ∈ f ( A , w ) . (Stalnaker 1975) William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 11 William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 12 Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Basic Strict Analysis Basic Strict Analysis Of Conditionals Of Conditionals Basic Strict Analysis A → B is true in a world w , relative to a space of accessible worlds R ( w ) , just in case all A-worlds in R ( w ) are B-worlds. • R ( w ) the information had by relevant agent’s in w . • Context Sensitivity : R ( w ) is the information ‘had’ by the conversationalists in w . William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 13 William Starr ∣ Indicative Conditionals, Strictly ∣ UConn 14
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