Indicative Conditionals, Strictly

Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Outline

1 Monotonic Patterns William Starr

2 New Data

3 A Strict Analysis Department of Philosophy [email protected] http://williamstarr.net 4 Assorted Curiosities April 6, 2019

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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 (O) b. If James Earl Ray hadn’t killed MLK, someone else (2) a. If Allie served tea, Chris came. would’ve. Subjunctive (X) b. So, if Allie served tea and cake, Chris came. Counterexample (Stalnaker 1968; Adams 1975): (3) a. If Allie served tea, Chris came. b. # So, if Allie served tea and didn’t invite Chris, Chris came.

William Starr S Indicative Conditionals, Strictly S UConn 1 William Starr S Indicative Conditionals, Strictly S 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 (4) a. If Allie served tea or cake, Chris came. assumption that if A ⊧ B then ⊧ A → B (Starr 2019: n22) 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

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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:

Indicative Felicity (7) a. Maybe Allie served tea and cake. If Allie served tea, 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. (Stalnaker 1975; Adams 1975; Veltman 1986; Gillies 2010) Counterexample revisited: (8) a. Maybe Allie served tea and didn’t invite Chris. # If (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 S Indicative Conditionals, Strictly S UConn 5 William Starr S Indicative Conditionals, Strictly S 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 Example revisited: Monotonic patterns sound compelling only when Indicative (9) a. Maybe Allie served tea, maybe she served cake. But, Felicity of conclusion is compatible with the truth (and if Allie served tea or cake, Chris came. Indicative Felicity) of the premises. 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. (10) a. Maybe Allie served only tea. #But, if Allie served only tea or only cake, she served only cake. b. # So, if Allie served only tea, she served only cake.

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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: 2 ‘Counterexamples’ exist because monotonic patterns are • Pragmatical infelicity (Veltman 1986, 1985) semantically invalid, and do not sound pragmatically • Semantic presupposition failure (Gillies 2004, 2009) compelling because Indicative Felicity is not satisﬁed. • Equivocation via accommodation (Warmbr¯od1981)

• 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.

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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 an A-world is the in context set c, w ′ ∈ f (A, w). (Stalnaker 1975)

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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.

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(11) a. If the coin came up heads or tails, maybe it came up Variably-Strict vs. Strict Analyses heads. Debate between variably-strict and strict analyses comes to: b. # If the coin came up tails, maybe it came up heads. 1 Compelling monotonic patterns are better explained (12) pragmatically. (Variably-Strict) a. Maybe the coin came up tails. But, if the coin came up heads or tails, maybe it came up heads. 2 Compelling monotonic patterns are better explained b. # If the coin came up tails, maybe it came up heads. semantically. (Strict) • Unlike (10), premise is not infelicitous when conjoined • (Shared) Key Prediction: any time Indicative Felicity is w/conclusion’s presupposition. satisﬁed, a monotonic pattern will sound compelling. • So (11) is a counterexample to the ‘Key Prediction’ of both strict and variably-strict analyses.

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Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References New Counterexamples New Counterexamples AS and Epistemic Possibility AS and Probably

(15) a. If Allie served tea, Chris probably came. (13) a. If Allie served tea, maybe Chris came. b. # If Allie served tea and Chris didn’t come, Chris b. # If Allie served tea and Chris didn’t come, maybe probably came. Chris came. (16) a. Maybe Allie served tea and Chris didn’t come. But, (14) a. Maybe Allie served tea and Chris didn’t come. But, if Allie served tea, Chris probably came. if Allie served tea, maybe Chris came. b. # If Allie served tea and Chris didn’t come, Chris b. # If Allie served tea and Chris didn’t come, maybe probably came. Chris came. • Premise is not infelicitous when conjoined w/conclusion’s • Unlike (8), premise is not infelicitous when conjoined presupposition. w/conclusion’s presupposition. • So (15) is a counterexample to the ‘Key Prediction’ of So (13) is a counterexample to the ‘Key Prediction’ of • both strict and variably-strict analyses. both strict and variably-strict analyses. • See Lassiter (2018) for related counterexamples to SDA.

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Limited Antecedent Weakening • Parallel counterexamples exist for Trans, Contraposition → → ⊧ ( ∨ ) → • This style of counterexample exists for all monotonic A C, B C A B C patterns • Shared validity in strict/variably-strict analyses • While not depending on a violation of Indicative Felicity • (Shared) Key Prediction: any time Indicative Felicity is Simpliﬁcation of Disjunctive Antecedents (SDA) satisﬁed, a monotonic pattern will sound compelling. (A ∨ B) → C ⊧ (A → C) ∧ (B → C) • This is false. • Only valid on strict analysis • Where should we look for a better analysis?

• Other patterns favor a strict analysis: The Disjunctive Equivalence 1 Embedded Monotonic Patterns (A ∨ B) → C ⊧ ⊧ (A → C) ∧ (B → C) 2 ‘Preserving Antecedents’ as in Import-Export • Only valid on strict analysis

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Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Embedded Monotonic Patterns Embedded Monotonic Patterns The Disjunctive Equivalence More Generally

(17) a. If Allie served tea, then if Bill brought honey or Chris brought sugar, everyone was happy. • Embedded cases exist for other monotonic patterns A → ((B ∨ C) → H) • E.g. contraposition b. If Allie served tea, then if Bill brought honey, • Old-style counterexamples lurk here too everyone was happy. (18) a. If Chris came then if Allie served only tea or only A → (B → H) cake, she served only cake. b. # If Chris came then if Allie served only tea, she • Easily predicted by strict analysis via: served only cake. 1 The Disjunctive Equivalence 2 Substitution of equivalent consequents • These facts favor strict analyses where Indicative Felicity 3 Consequent weakening is treated as a semantic presuppposition cf. Veltman (1986); Gillies (2009); Stalnaker (1975) • Not predicted by pragmatic variably-strict analysis: • • Conditional in consequent of (17) not asserted

William Starr S Indicative Conditionals, Strictly S UConn 21 William Starr S Indicative Conditionals, Strictly S UConn 22 Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Preserving Antecedents Preserving Antecedents Antecedent Preservation Antecedent Preservation Antecedent Preservation (AP) ⊧ A → (B → A) Antecedent Preservation (AP) • Valid on strict analysis; not variably-strict analysis. ⊧ A → (B → A) Example: • Valid on strict analysis; not variably-strict analysis. (19) If Allie served tea, then if Chris came Allie served tea. New counterexample: Familiar counterexample: (21) # If the coin maybe came up heads, then if the coin (20) # If the coin came up heads, then if the coin came up came up tails, the coin maybe came up heads. tails it came up heads. nH → (¬H → nH)

• Both explained on strict analysis w/semantic approach to • So there’s still work to be done for strict analysis Indicative Felicity • No explanation of (19) on variably-strict analysis

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Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Preserving Antecedents Basic Dynamic Semantics Import-Export Just Information

Classical Picture

Import-Export • Sentences (relative to contexts) refer to regions of logical A → (B → C) ⊧ ⊧ (A ∧ B) → C) space W • Valid on strict analysis; not variably-strict analysis. • Interpreters use utterances of them to shift to region of logical space within region referred to Example: (22) a. If Allie bet, then if the coin came up heads, she won. Dynamic Picture (Veltman 1996; Heim 1982) b. If Allie bet and the coin came up heads, she won. Assign each φ a function [φ] encoding how it changes s ⊆ W : s[φ] = s′ (I.e.: [φ](s) = s′) • No explanation of (22) on variably-strict analysis • Meaning as information update potential. • s as mutual information.

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Dynamic Informational Semantics (Veltman 1996) Where s ⊆ W : Dynamic Strict Conditional v1 (Gillies 2003, 2009) 1 s[A] = {w ∈ s S w(A) = 1} ⎧ ⎪ s if s[φ] ⊧ ψ s[φ → ψ] = ⎨ 2 s[¬φ] = s − s[φ] ⎪ ⎩⎪ ∅ otherwise 3 s[φ ∧ ψ] = (s[φ])[ψ] • Tests that all φ-worlds in s are ψ-worlds. 4 s[φ ∨ ψ] = s[φ] ∪ s[ψ] Epistemic Modals (Veltman 1996) Support (Basic Logical Concept) 1 s[nφ] = {w ∈ s S s[φ] ≠ ∅} s ⊫ φ ⇐⇒ s[φ] = s 2 s[ φ] = {w ∈ s S s ⊧ φ} • s supports φ just in case any information φ can provide is already part of s.

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Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References The Dynamic Analysis The Dynamic Analysis Conditionals, Epistemic Modals Dynamic Strawsonian Consequence

Dynamic Strict Conditional w/Presupposition ⎧ ⎪ s if ∃w ∈ s∶ w ⊧ φ & s[φ] ⊧ ψ ⎪ Strawsonian Dynamic Consequence s[φ → ψ] = ⎨ ∅ if ∃w ∈ s∶ w ⊧ φ & s[φ] ⊭ ψ ⎪ ⎪ φ1, . . . , φn ⊧ ψ ⇔ ∀s∶ if s[φ1]⋯[φn][ψ] is defined, then ⎪ ∄ ∈ ∶ ⊧ ⎩ Undefined if w s w φ s[φ1]⋯[φn] ⊧ ψ • Presupposes that φ is true in some w ∈ s. • Tests that all φ-worlds in s are ψ-worlds. • s’s w/failed presuppositions don’t count toward validity (Strawson 1952: 173-9, von Fintel 1999a, Beaver 2001) • Semantic presupposition for old-style counterexamples, • Non-Strawsonian Definition: no conditional validities! embedded variations • This presupposition: prevents (nA ∧ ¬A) → (nA ∧ ¬A) from being a counterexample to numerous validities

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(13) a. If Allie served tea, maybe Chris came. (3) a. If Allie served tea, Chris came. A → nC b. # So, if Allie served tea and didn’t invite Chris, b. # If Allie served tea and Chris didn’t come, maybe Chris came. Chris came. (A ∧ ¬C) → nC • s0 = {wAIC, waIC, waic};

• Contextually excluded: wAic, wAIc, wAiC, waiC • s0 = {wAC, wAc, waC, wac}

• s0[A → C] = s0, since s0[A] ⊧ C. • s0[A → nC] = s0, since s0[A] ⊧ nC

• But s0[A → C] is undeﬁned. • s0[(A ∧ ¬C) → nC] = ∅, since s0[A ∧ ¬C] ⊭ nC

• So states like s0 don’t count for/against consequence. • So s0[A → nC] ⊭ (A ∧ ¬C) → nC • Beauty of Strawsonian Dynamic Consequence at work! • Hence: A → nC ⊭ (A ∧ ¬C) → nC • Why? Because of how n works.

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Persistence (Veltman 1985; Groenendijk et al. 1996) Miserly (Veltman 1985) φ is persistent just in case s′ ⊧ φ if s ⊧ φ and s′ ⊆ s. φ is miserly just in case s′ ⊭ φ if s ⊭ φ and s′ ⊆ s. • Support for φ persists after more information comes in. • s continues to withhold support of φ even after s is enriched with more information. • nA is not persistent. • Moving from s to s′ can eliminate A-worlds. • B and A → B are not miserly. ′ • Moving from s to s can eliminate ¬B-worlds. Fact (Starr) If the main consequents are persistent, then antecedent Fact (Starr) preservation and all monotonic patterns other than If the main consequents are miserly, then contraposition and contraposition are valid. (Given semantics/logic above.) modus tollens are valid. (Given semantics/logic above.)

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Unrestricted Validities Miserly Validities 1 Identity: ⊧ φ → φ For miserly ψ: 2 Modus Ponens: φ → ψ, φ ⊧ ψ 1 Contraposition: φ → ψ ⊧ ¬ψ → ¬φ

3 Deduction Equivalence: φ ⊧ ψ ⇐⇒ ⊧ φ → ψ ⊧ 2 Modus Tollens: φ → ψ, ¬ψ ⊧ ¬φ 4 Import-Export: φ1 → (φ2 → ψ) ⊧ (φ1 ∧ φ2) → ψ See Veltman (1986) and Yalcin (2012) for MT Persistent Validities • counterexamples w/non-miserly ψ For persistent ψ:

1 Antecedent Strengthening: φ1 → ψ ⊧ (φ1 ∧ φ2) → ψ Conditional/Modal Interactions (Gillies 2010)

2 SDA: (φ ∨ φ ) → ψ ⊧ (φ → ψ) ∧ (φ → ψ) ⊧

1 2 1 2 1 φ → nψ ⊧ n(φ ∧ ψ)

⊧ 3 Transitivity: φ → φ , φ → ψ ⊧ φ → ψ ⊧ 1 2 2 1 2 (φ → ψ) ⊧ φ → ψ ⊧ φ → ψ 4 Antecedent Preservation: ⊧ ψ → (φ → ψ)

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Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Dynamic Analysis Assorted Curiosities Review Truth, ‘Probably’ and Subjunctives

1 Informational support as basic logical concept 2 Dynamic Strict Conditional, Epistemic Modals + Presupp. 3 Strawsonian Dynamic Logic • Modus Ponens, Identity, Import-Export, Deduction Equivalence valid {w}, △, ⊲ 4 Addresses old-style counterexamples to monotonic patterns and AP 5 New counterexamples explained: • AS, SDA, Trans, AP only valid when main consequent is persistent • CP, MT only valid when main consequent is miserly 6 Captures embedded monotonic patterns, AP

William Starr S Indicative Conditionals, Strictly S UConn 37 William Starr S Indicative Conditionals, Strictly S UConn 38 Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References What Happened to Truth-Conditions? What Happened to Truth-Conditions? Two Questions A Basic Application

Truth-Conditions Just as Good? (Gillies 2009) • Chris just had a brief glimpse at two shapes x and y. φ → ψ = {w S C(w) ∩ φ ⊆ ψ } C C Cφ • She thinks there was both a triangle and a square. J K J K J K • All the contextually-live φ-worlds are ψ-worlds • Given Chris’ information, is it correct for her to • C(w) is the set of live worlds with respect to w assert/believe: • Cφ(w) = C(w) ∩ φ C , for all w (23) If x is a triangle, y is a square. J K • My judgment: Correct. • Modus ponens requires assuming that for all w, w ∈ C(w). • As it turns out, x and y are both squares. • This assumption is inconsistent with interpreting C(w) as • Given Chris’ information and the actual state of things, is agents’ information. it correct for her to assert/believe (23)? • My judgment: Probably, but some ambivalence. • That interpretation is essential for basic applications.

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Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References What Happened to Truth-Conditions? Truth from a Dynamic Perspective The Point Truth and Perfect Information Key Points about (23) d’Alembert (1751) on Truth 1 We do have simple judgments about whether some “The universe... would only be one fact and one great truth information supports a conditional belief/assertion. for whoever knew how to embrace it from a single point of 2 Those judgments can occur even if that information is view.” (d’Alembert 1995: 29) false in world of evaluation. 3 When we learn what the world of evaluation is, our Truth, Propositions (Starr 2010) judgments can change. w ⊧ φ ⇐⇒ {w}[φ] = {w} φ = {w S w ⊧ φ} J K • Point 1 suggests judgments reﬂect contextual information alone — no ‘world of evaluation’. Classical Consequence (Starr 2010) ( ) • Judgments are not a product of both w and C w φ1, . . . , φn ⊧Cl ψ ⇐⇒ ∀w ∶ {w}[φ1]⋯[φn] ⊧ ψ • Point 2 incompatible w/requiring w ∈ C(w) for all w. • Classical logic is the logic of perfect information • Can point 3 be explained on the dynamic approach?

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• Sentences can be evaluated from a range of uncertain (informational) perspectives. • Interaction of quantificational operators and conditionals • That’s a matter of the information supporting the entails choice: sentence. 1 if-clauses are just restrictors (Lewis 1975; Kratzer 1986) • Can also be evaluated from a range of certain (worldly) 2 Conditionals have trivalent truth-conditions perspectives. (Jeffrey 1963; Belnap 1970; McDermott 1996; Huitink 2008) • That’s a matter of a world making the sentence true. • Option 2 faces serious logical difficulties. Either: • As in (23) after evaluation world is revealed. • ¬(φ → ψ) ⊧ φ is valid (Huitink 2008; Jeffrey 1963) • From semantics and truth definition it follows that: • Modus ponens is invalid (McDermott 1996: 31) Truth-Conditions for Indicative Conditionals • The account here has no such logical difficulties — logic is not beholden to truth-conditions. 1 φ → ψ is true in w if φ ∧ ψ is true in w. • But it can appeal to those truth-conditions in defining 2 φ → ψ is false in w if φ ∧ ¬ψ is true in w. quantificational operators! 3 Otherwise, φ → ψ’s truth-value is undefined.

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Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Semantics for ‘Probably’ What about Subjunctives? Adapting Yalcin (2012) Antecedent Preservation Failure?

⎧ Antecedent Preservation (AP) ⎪ sPr if Pr({w ∈ s∶ w ⊧ φ}S{w ∈ s∶ w ⊧ φ or w ⊭ φ}) > 0.5 s [△φ] = ⎨ Pr ⎪ ⊧ A → (B → A) ⎩⎪ ∅Pr otherwise New indicative counterexample: • Update clause for atomics must also change to conditionalize Pr ; disjunction tricky. (21) # If the coin maybe came up heads, then (even) if the coin came up tails, the coin maybe (also) came up heads.

Interesting Consequences nH → (¬H → nH) 1 φ → △ψ ⊧ ⊧ △(φ → ψ) • Consider its subjunctive counterpart, in context where we 2 sPr ⊧ △(A → B) ⇐⇒ Pr( B S A ) > 0.5 don’t know outcome of past coinﬂip. J K J K 3 △φ is neither persistent nor miserly. (24) If the coin could have come up heads, then (even) if the See also de Finetti (1936), Milne (1997), Rothschild (2014). coin came up tails, the coin could (also) have come up heads. n⊲ H → (⊲ ¬H → n⊲ H) (Starr 2014)

William Starr S Indicative Conditionals, Strictly S UConn 45 William Starr S Indicative Conditionals, Strictly S UConn 46 Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References What about Subjunctives? What about Subjunctives? Counterfactual Expansion And New Counterexamples?

Counterfactual Expansion ⊲ (Starr 2014) ′ ′ sf [⊲ A] = {w S ∃w ∈ s ∶ w ∈ f (w, A)}f • w ′ is among the A-worlds closest to some w ∈ s Allie didn’t host, or serve anything. • w ′ may be outside s (cf. Iatridou 2000; von Fintel 1999b) (25) a. If Allie had served only tea or only cakes, she could have served only tea. • sf [n⊲ H → (⊲ ¬H → n⊲ H)] amounts to testing that: b. So, if Allie had served only cakes, she could (also) • sf [n⊲ H][⊲ ¬H] ⊧ n⊲ H have served only tea. • sf [n⊲ H] tests that sf [⊲ H] ≠ ∅. • If passed, next step is sf [⊲ ¬H]. • At least much better than indicative counterparts! • This expands to include most-similar ¬H-worlds. • n⊲ H can persist after updating with ¬H • So new-style counterexamples may not exist for subjunctives...

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Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Conclusion Indicative Conditionals, Strictly

Highlights 1 New counterexamples to monotonic patterns • That satisfy Indicative Felicity! Thank you! 2 Problem for variably-strict and strict analyses alike. 3 Presuppositional dynamic strict analysis provides compelling diagnosis of countrexamples new and old • Differs from Gillies (2009) and Veltman (1986) (Slides available at http://williamstarr.net/research) 4 Also provides promising approach to: • Trivalent truth-conditions for indicatives • Modal/quantifier/conditional interaction • Unified analysis of indicatives and subjunctives

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J. Groenendijk, et al. (1996). ‘Coreference and Modality’. In S. Lappin (ed.), The E. W. Adams (1975). The Logic of Conditionals. D. Reidel, Dordrecht. Handbook of Contemporary Semantic Theory, pp. 179–213. Blackwell Publishers, D. Beaver (2001). Presupposition and Assertion in Dynamic Semantics. CSLI Oxford. Publications, Stanford, California. I. R. Heim (1982). The Semantics of Definite and Indefinite Noun Phrases. Ph.D. N. Belnap (1970). ‘Conditional Assertion and Restricted Quantification’. Nôus thesis, Linguistics Department, University of Massachusetts, Amherst, 4(1):1–12. Massachusetts. J. L. R. d’Alembert (1995). Preliminary Discourse to the Encyclopedia of Diderot. J. Huitink (2008). Modals, Conditionals and Compositionality. Ph.D. thesis, Radboud University of Chicago Press, Chicago. Originally published in 1751. University Nijmegen, Nijmegen. B. de Finetti (1936). ‘La Logique de la Probabilité’. Actes du CongrésInternational S. Iatridou (2000). ‘The Grammatical Ingredients of Counterfactuality’. Linguistic de Philosophie Scientifique 4:31–9. Inquiry 31(2):231–270. A. S. Gillies (2003). ‘Epistemic Conditionals and Conditional Epistemics’. Unpublished R. C. Jeffrey (1963). ‘On Indeterminate Conditionals’. Philosophical Studies manuscript, Harvard University. 14(3):37–43. A. S. Gillies (2004). ‘Epistemic Conditionals and Conditional Epistemics’. Noûs S. Kaufmann (2005). ‘Conditional Predictions’. Linguistics and Philosophy 38(4):585–616. 28(2):181–231. A. S. Gillies (2009). ‘On Truth-Conditions for “If” (but Not Quite Only “If”)’. A. Kratzer (1986). ‘Conditionals’. In Proceedings from the 22nd Regional Meeting of Philosophical Review 118(3):325–349. the Chicago Linguistic Society, pp. 1–15, Chicago. University of Chicago. A. S. Gillies (2010). ‘Iffiness’. Semantics and Pragmatics 3(4):1–42. D. Lassiter (2018). ‘Complex Sentential Operators Refute Unrestricted Simplification of Disjunctive Antecedents’. Semantics & Pragmatics 11(9):Early Access.

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W. B. Starr (2010). Conditionals, Meaning and Mood. Ph.D. thesis, Rutgers D. K. Lewis (1975). ‘Adverbs of Quantiﬁcation’. In E. L. Keenan (ed.), Formal University, New Brunswick, NJ. Semantics of Natural Language, pp. 3–15. Cambridge University Press, Cambridge, England. W. B. Starr (2014). ‘A Uniform Theory of Conditionals’. Journal of Philosophical Logic 43(6):1019–1064. M. McDermott (1996). ‘On the Truth Conditions of Certain “If”-Sentences’. The Philosophical Review 105(1):1–37. W. B. Starr (2019). ‘Counterfactuals’. In E. N. Zalta (ed.), Stanford Encylcopedia of Philosophy. Metaphysics Research Lab, Stanford University, spring 2019 edn. T. J. McKay & P. van Inwagen (1977). ‘Counterfactuals with Disjunctive Antecedents’. Philosophical Studies 31:353–356. P. F. Strawson (1952). Introduction to Logical Theory. Methuen, London. P. Milne (1997). ‘Bruno de Finetti and the Logic of Conditional Events’. The British F. Veltman (1985). Logics for Conditionals. Ph.D. dissertation, University of Journal for the Philosophy of Science 48(2):195–232. Amsterdam, Amsterdam. D. Rothschild (2014). ‘Capturing the relationship between conditionals and F. Veltman (1986). ‘Data Semantics and the Pragmatics of Indicative Conditionals’. conditional probability with a trivalent semantics’. Journal of Applied In E. C. Traugott, A. ter Meulen, J. S. Reilly, & C. A. Ferguson (eds.), On Non-Classical Logics 24(1-2):144–152. Conditionals. Cambridge University Press, Cambridge, England. R. Stalnaker (1968). ‘A Theory of Conditionals’. In N. Rescher (ed.), Studies in F. Veltman (1996). ‘Defaults in Update Semantics’. Journal of Philosophical Logic Logical Theory, pp. 98–112. Basil Blackwell, Oxford. 25(3):221–261. R. Stalnaker (1975). ‘Indicative Conditionals’. Philosophia 5:269–286. Page references K. von Fintel (1999a). ‘NPI Licensing, Strawson Entailment Context Dependency’. to reprint in Stalnaker (1999). Journal of Semantics 16(2):97–148. R. C. Stalnaker (1999). Context and Content: Essays on Intentionality in Speech and K. von Fintel (1999b). ‘The Presupposition of Subjunctive Conditionals’. In Thought. Oxford University Press, Oxford. U. Sauerland & O. Percus (eds.), The Interpretive Tract, vol. MIT Working Papers in Linguistics 25, pp. 29–44. MITWPL, Cambridge, MA.

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Import-Export A → (B → C) ⊧ ⊧ (A ∧ B) → C) K. Warmbr¯od(1981). ‘An Indexical Theory of Conditionals’. Dialogue, Canadian Philosophical Review 20(4):644–664. We have a very wet match that is unlikely to light if struck, S. Yalcin (2012). ‘A Counterexample to Modus Tollens’. Journal of Philosophical but will deﬁnitely light if thrown in the campﬁre. Logic 41(6):1001–1024. (26) a. If the match lights, it will light if you strike it. b. If you strike the match and it lights, it will light.

• (26a) seems false, while (26b) seems logically true.

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Monotonic Patterns New Data A Strict Analysis Assorted Curiosities References Import-Export Kaufmann (2005: 213) Counterexample

Import-Export A → (B → C) ⊧ ⊧ (A ∧ B) → C)

We had a very wet match that was unlikely to light if struck, but would deﬁnitely have light if thrown in the campﬁre. We don’t remember what happened to it. (27) a. If the match lit, then if it was struck, it lit. b. If the match was struck and it lit, then it lit.

• Much less clear that (27a) is false. • Tentative conclusion: original counterexample is due to future tense/discourse relations/word-order.

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