Compositionality in counterfactuals
Atle Grønn
November 1, 2006
Forum for teoretisk lingvistikk
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Introduction I (modality)
(1) That must be my secretary.
• [[M U ST ]] w c (ModalBasew c )(p) = 1 iff wc ∈ {w|
T
M B(w) ⊆ p}
• One context which makes (1) true:
MBepistemic (wc ) = {Somebody is knocking on my door, I smell perfume,
etc...}
• A version of the Samaritan paradox:
(2) If I cheat on my wife, I must seek foregiveness.
(3) If I cheat on my wife, she must go to jail.
• On a deontic interpretation, (3) is usually not considered a true sentence
in our culture, but...:
• MBdeontic (wc ) = {”You don’t kill”, ”You don’t cheat on your wife”, ”Seek
foregiveness for your sins”...}
T
• wc ∈ {w| M B(w) ⊆ (A → C)}, since
T
• {”You don’t kill”, ”You don’t cheat on your wife”, ”Seek foregiveness
for your sins” ...} ⊆ ¬A ∨ C
• Kratzer-style improvement:
• OrderingSourcedeontic(wc ) = {”You don’t kill”,
”Seek foregiveness for your sins”...}
,
”You don’t cheat on your wife”
• MBcircumstantial (wc ) = {Your secretary is flirting heavily ...}
• Basic idea: ”must” induces universal quantification over possible worlds
in which the antecedent is added to the modal base and as many facts
as possible hold in the ordering source. These ”best” possible worlds are
worlds in which you seek foregiveness, but your wife does not go to jail.
Hence, in wc (2) is true and (3) is untrue.
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Introduction II (counterfactuals)1
2
(4) If the USA were to throw its nukes into the sea tomorrow, there would
be war. (Lewis)
• Kratzer:
– Modal base = W (i.e. MB is empty)
– Ordering Source: totally realistic
• ”If A were the case, then C would be the case” is true in world w iff the
A-worlds that are as similar to w as they can be are C-worlds.
• Stalnaker/Heim: [[(1)]] w c = 1 iff ∀w′ ∈ SIM(wc )(A) → C(w′ )
• What about tense? ... Ippolito, Arregui, Hacquard ... von Stechow ...
Grønn (?)
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Data
3.1
Norwegian
(Faarlund et al. 1997):
(5) Hvis han visste det, sa han det nok.
(6) Hadde jeg tid, gikk jeg på kino i morgen.
(7) Bad du han komme, gjorde han det sikkert
(8) Hvis jeg hadde vært i ditt sted, ville jeg ha gjort det.
(9) Hadde vi hatt råd, skulle vi ha kjøpt den bilen.
(10) Hadde dei sett deg no, ville dei ha vorti rasande.
(11) Hvis jeg hadde vært i ditt sted, hadde jeg gjort det.
(12) Hadde vi hatt råd, hadde vi kjøpt den bilen.
(13) Hadde dei sett deg no, hadde dei vorti rasande.
(14) I så fall kunne det / være / ha vært / vært / en god løsning.
(15) I så fall / hadde / ville / det kunnet være en god løsning.
(16) I så fall ville det kunne / ha vært / vært / en god løsning.
(17) I så fall ville det / ha kunnet / kunnet / være en god løsning.
(18) I så fall ville det beste / være / ha vært / vært / å kjøpe en ny.
(19) I så fall hadde det beste villet være å kjøpe en ny.
1 I am grateful to Arnim von Stechow for many highly stimulating discussions on this topic.
All errors are mine.
2
3.2
French
(20) Si j’avais 20 ans de moins je partirais vivre ailleurs. (internet)
If I were 20 years younger, I would move somewhere else.
(21) Le coup de boule n’aurait étonné personne s’il était venu de Cantona
par exemple. (internet)
The headbutting wouldn’t have surprised anyone if it hade come from
Cantona for instance.
3.3
Russian
(22) Esli by segodnja u menja byli den’gi, ja by vse ich potratil na knigi.
(internet)
If BY-SUBJUNCTIVE today with me BE-PAST money, I BY-SUBJUNCTIVE
all them SPEND-PAST-PF on books.
If I had money now, I would spend them all on books.
3.4
Other languages: English, German ...
(23) Wenn Frantz krank sein würde, würde er zu Hause sein. (von Stechow)
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Previous accounts
4.1
(Ogihara 2000)
(24) If John had given flowers to Mary TOMORROW[F ] , she would have
been pleased.
Problems...:
(25) (Charlie died a month ago before ever going to New York and both Lucy
and Sally know it. Lucy and Sally are talking about him and Lucy says
that she believes that if Charlie had gone to New York today, he would
have met his friends. Sally disagrees and she utters:)
No. If Charlie had gone to New York TOMORROW[F ], he would have
met his friends. (Ippolito)
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4.2
(Ippolito 2003)
(26) If Per stopped smoking today, he would feel much better.
(27) (*Per stopped smoking many years ago.) If Per stopped smoking TOMORROW[F ],
he would feel much better.
(28) Per stopped smoking yesterday. If he had stopped smoking TOMORROW[F ] ,
he could have participated in the experiment.
Structure for ”one-past counterfactual”:
[[[PerfP PERF[AspP ∀⊆ [[WOLL A]C]]]]] w c ,t c
Truth-conditions:
[[If Per stopped smoking today, he would feel much better.]] w c ,t c = 1 iff
∃t′ :RightBoundary(tc , t′ ) ∧ ∀t′′ ⊆ t′ [∀w′ [w′ is metaphysically accessible from
wc at t′′ ∧ ∃t′′′ t′′ s.t. it is true in w′ at t′′ that Per will stop smoking today
at t′′′ ∧ ¬∃w′′ [w′′ is metaphysically accessible from wc at t′′ and s.t. it is true
in w′′ at t′′ that Per will stop smoking today ∧ w′′ is overall more similar to wc
than w′ ]] → ∃t′′′′ t′′ s.t. it is true in w′ at t′′ that Per will feel much better at
t′′′′ ].
Structure for ”two-past counterfactual”:
[[[TP PAST[PerfP PERF[AspP ∀⊆ [[WOLL A]C]]]]]] w c ,t c
Truth-conditions:
[[If Per had stopped smoking today, he would have felt much better.]] w c ,t c = 1 iff
∃t′ :RightBoundary(t5 , t′ ) ∧ ∀t′′ ⊆ t′ [∀w′ [w′ is metaphysically accessible from
wc at t′′ ∧ ∃t′′′ t′′ s.t. it is true in w′ at t′′ that Per will stop smoking today
at t′′′ ∧ ¬∃w′′ [w′′ is metaphysically accessible from wc at t′′ and s.t. it is true
in w′′ at t′′ that Per will stop smoking today ∧ w′′ is overall more similar to wc
than w′ ]] → ∃t′′′′ t′′ s.t. it is true in w′ at t′′ that Per will feel much better at
t′′′′ ], defined only if t5 ≺ tc .
Problems...:
(29) If he had known her since she was a child, he would have known that
she was allergic to penicillin. (Arregui 2005)
(30) If you had lived in this house since 1963, you would have qualified for a
rent subsidy.
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4.3
(Arregui 2005)
• Counterpart relations amongst individuals (Lewis) – modal talk about
individuals is understood in terms of non-modal claims about counterparts
of individuals.
(31) The winner of the presidential elections could have lost.
In some possible world a counterpart of the actual world winner has the
non-modal property of losing (i.e. the sentence does not claim that the
winner in the possible world lost in that possible world.)
• ”Similarity in the past counts for more”
• would-conditionals make de re hypothesis about the past.
(32) She doesn’t love him. If she loved him, she wouldn’t have married him.
If the past had led to ”she loves him”, it would also have led to ”she
won’t marry him”.
• [[woll]] : λP λQλt∀w′ [t ⊳ w′ ∧ P (t′ )(w′ ) → Q(t′ )(w′ )], where t′ is a contextually salient non-past time and the temporal argument of the modal will
be saturated by the c-commanding past tense. (Arregui 2005, 51) (⊳ =
”part of”)
(33) If Nixon had pushed the button, there would have been a nuclear holocaust.
• Worlds in which somebody cuts the cable seconds before Nixon pushes
the button are pretty similar to wc but are discarded from the domain of
quantification because their spatio-temporal match with wc is smaller...
(cf. Lewis)
4.4
Arregui: aspectual difference
(34) A: Don’t worry about looking after my plants. They died yesterday.
B: I’m sorry, but also a bit relieved. If your plants had died next week,
I would have been very upset.
(35) A: I’m worried about my plants.
B: I can see what is going wrong. They simply don’t have enough light.
If they had enough light, they would be fine.
(36) A: Don’t worry about looking after my plants. They died yesterday.
B: I’m sorry, but also a bit relieved. # If they died next week instead,
I would be very upset.
• The first case quantifies over worlds in which there is an event of A’s
plants dying next week that contain a counterpart of the actual past. The
relevant past counterparts cannot include an event of A’s plants dying.
(Arregui 2005, 147)
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• The Perfect (”to have died”) and states (”to have enough light”) are predicates of times... (the perfect binds off the event variable)
• Simple past morphology doesn’t give the modal access to worlds that differ
from the actual world w.r.t. the plants’ death. A silent deictic perfective
aspectual head anchors the antecedent clause proposition to worlds that
are like the actual world w.r.t. the time of the plants’ death.
• [[⊘perfective ]] : λP λtλw[P (e)(w) ∧ e ⊂ t], where e is a contextually salient
event, cf. (Arregui 2005, 186). Events are individuals with their counterpart relations... The quantificational domain of the modal is thus restricted to possible worlds in which there is a counterpart of the actual
world event (which is sensitive to the temporal location of the actual world
event).
4.5
(Hacquard 2006)
• Ordering of functional heads:
Modepis - T - CF - ASP - Modcirc
• Against Condoravdi’s metaphysical/counterfactual reading of ”might” (Hacquard 2006, 93):
(37) They might still have won the game.
At a past time there was a possibility that they would win the game (but
they didn’t).
• Stalnaker/Hacquard: It doesn’t make sense to talk about a universal or
existential counterfactual modal.
• ”might have” involves an epistemic ”might” on top of a counterfactual
modal.
• Further evidence from the morphology of French counterfactuals (imparfait/conditionnel)
(38) Ils ont pu gagner. (epistemic)
(39) Ils auraient pu gagner.
They could-CF win.
• ”It is possible that they would have won”: POSSepis >CF
• ”They would have been able to win”: CF>POSScirc
(40) Ils auraient dû gagner contre l’Italie, mais Zidane a perdu la tête. (EPIS>CF)
They should have won against Italy, but Zidane lost his mind.
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(41) S’ils n’avaient pas fait match nul avec la Suisse, ils auraient dû gagner
contre l’Italie pour arriver en demi-finale. (CF>CIRC)
If they hadn’t drawn against Switzerland, they would have had to win
against Italy, in order to get to the semi-finals.
Compare:
(42) Si Darcy ne s’était pas tordu la cheville, ils auraient gagné.
If Darcy hadn’t twisted his ankle, they would have won.
(43) Si Darcy ne s’était pas tordu la cheville, ils auraient dû gagner.
If Darcy hadn’t twisted his ankle, they should have won.
The latter case contains an epistemic modal on top of CF, hence the winning
event is less certain (cf. It must be raining vs. it is raining).
(44) Il aurait répondu. (Hacquard 2006, 97)
He have-FUT-ipf answered.
• Input to tense (PAST*):
λt′ [∀w ∈ METw c : ∃t′′ [t′′ = [t′ , ∞){t′ ≺ tc } ∧ ∃e[e in w ∧ e ⊆ t′′ ∧ answer (e, w)]]]
• In all metaphysically accessible worlds, there is some time t′′ , future to
some salient past time t′ , such that there is an event of him answering at
t′′ .
• What gets spelled out as would (Eng.) / le conditionnel (Fr.) is the combination of a universal modal which quantifies over metaphysical worlds
and a future, which introduces a new (open) time interval.
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5
Dislocation (separating morphology from semantics)
(45) Wolfgang played tennis on every Sunday. (von Stechow)
= For every Sunday in PASTc there is a time t at which Wolfgang plays
tennis.
6= There is a past time on every Sunday at which Wolfgang plays tennis.
6= For every Sunday, there is a time before it s.t. Wolfgang plays tennis
at that time.
6
Minimalist Feature theory – an illustration of
”multiple agree” (SOT)
(46) PAST*[i-PAST] Mary said [u-past] that she was [u-past] in the opera.
• Sequence of tense: The embedded past tense carries the feature [u-past]
which is checked by the PAST* operator in the matrix [i-PAST].
• The embedded past is pronounced at PF, but is deleted at LF.
• Every uninterpretable feature must be checked by an interpretable feature.
• Interpretable features can check more than one uninterpretable feature
(multiple agree).
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7
Ingredients in a compositional analysis of counterfactuals
• notational convention: [UPPER CASE LETTERS] = interpretable features (at LF)
• notational convention: [lower case letters] = u-features = uninterpretable
features (at LF), pronounced at PF.
• Common feature of past tense and counterfactuality: distancing or remoteness w.r.t the evaluation time/world (Iatridou 2000)
• wc = the context/evaluation world (distinguished variable)
• tc = the context/evaluation time (distinguished variable)
• [[Rpast ]] = λP λwλt.P (w)(t)[only defined for t ≺ tc ] =
λP λwλt.P (w)(t){t ≺ tc }2
• [[Rcf ]] = λP λwλt.P (w)(t)[only defined for w 6= wc ] =
λP λwλt.P (w)(t){w 6= wc }
• Counterfactuality is decomposed into the operators SIM and MUST:
• SIM only occurs in the antecedent (Stalnaker 1968).
• [[SIMw c ]] = λP λwλt.P (w)(t) & ¬∃w′ [P (w′ )(t) & w′ < w c w]
• [[MUST]] = λP λQλt.∀w[P (w)(t) → Q(w)(t)]
• ”Two-past” counterfactuals require an embedded perfect in the antecedent,
consequent or both:
• [[P*]] = λP λwλt∃t′ [P (w)(t′ ) & t′ ≺ t]
2 At a later stage λt... is reduced through the presence of a temporal adverbial – denoting
an interval in the past – or by default existential closure.
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(47) Esli by segodnja u menja byli den’gi, ja by vse ich potratil na knigi.
(internet)
If BY-SUBJUNCTIVE today with me BE-PAST money, I BY-SUBJUNCTIVE
all them SPEND-PAST-PF on books.
If I had money now, I would spend them all on books.
Analysis of ”one-past” Russian
λw.M (w)(tc ){w 6= wc } & ¬∃w′ [M (w′ )(tc ) & w′ < w c w] ⊆ λw.B(w)(tc ) {w 6= wc }
λt[λw.M (w)(t){w 6= wc } & ¬∃w′ [M (w′ )(t) & w′ < w c w]] ⊆
[λw.B(w)(t) {w 6= wc }]
tc
[PRES]
λwλt.B(w)(t) [only defined for w 6= wc ]
”by” (subjunctive particle)
[i-REMOTE]
λQλt.∀w[M (w)(t)[...] → Q(w)(t)]
MUST⊆
[CF]
”l” (tense morphology) VP: λwλt.B(w)(t)
[u-remote]
λwλt.M (w)(t) [only defined for w 6= wc ]
&¬∃w′ [M (w′ )(t) & w′ < w c w]
SIM
[CF]
”esli” (if)
λwλt.M (w)(t) [only defined for w 6= wc ]
”by” (subjunctive particle)
[i-REMOTE]
”l” (tense morphology)
[u-remote]
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VP: λwλt.M (w)(t)
Standard analysis of aspect both in antecedent and consequent:
λwλt∃e[P (e)(w){w 6= wc } & e ⊆ t]
”by” = [[Rcf ]]
[i-REMOTE]
”l” (tense morphology)
[u-remote]
λwλt∃e[P (e)(w) & e ⊆ t]
[[PF*]] = λQλwλt∃e[Q(e)(w) & e ⊆ t]
[i-PF]
perfective morphology
[u-pf]
VP: λwλe.P (w)(e)
No overt perfect morphology, but free interpolation of [[P*]] both in antecedent and consequent:
λwλt∃e∃t′ [P (e)(w){w 6= wc } & e ⊆ t′ & t′ ≺ t]
”by” = [[Rcf ]]
[i-REMOTE]
”l” (tense morphology) λwλt∃e∃t′ [P (e)(w) & e ⊆ t′ & t′ ≺ t]
[u-remote]
[[P*]]
[PERF.PART]
λwλt∃e[P (e)(w) & e ⊆ t]
[[PF*]] = λQλwλt∃e[Q(e)(w) & e ⊆ t]
[i-PF]
perfective morphology
[u-pf]
VP: λwλe.P (w)(e)
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8
Back to Germanic
(48) Hadde jeg hatt penger (nå / den gang), hadde (ville) jeg kjøpt den bilen.
• Remember: Germanic is SOT, Slavic is non-SOT.
• Idea: For hypothetical possibilities in the present/future, a covert operator
Rcf checks all instances of past tense morphology. Implementation ...?
• Structure for (48)...:
[TP Rcf [i−REMOTE ] [MP [if A[u−REMOTE ]...[u−REMOTE ], WOLL C [u−REMOTE ]...[u−REMOTE ]]]]
References
Ana Arregui. On the Accessibility of Possible Worlds: The Role of Tense and
Aspect. PhD thesis, UMass, Amherst, 2005.
Jan Terje Faarlund, Svein Lie, and Kjell Ivar Vannebo. Norsk referansegrammatikk. Universitetsforlaget, Oslo, 1997.
Atle Grønn. Relative past and the syntax-semantics interface in Russian. Proceedings of FDSL-6, Potsdam, to appear.
Atle Grønn. A compositional theory of counterfactuals. Antwerpen, talk at
Chronos7, 2006.
Valentine Hacquard. Aspects of Modality. PhD thesis, MIT, 2006.
Sabine Iatridou. The grammatical ingredients of counterfactuality. Linguistic
Inquiry, 31(2):231–270, 2000.
Michaela Ippolito. Quantification over times in subjunctive conditionals.
Tübingen, ms., 2003.
Toshiyuki Ogihara. Counterfactuals, temporal adverbs, and association with
focus. In Proceedings of SALT X, Cornell University, 2000. CLS Publications.
Philippe Schlenker. Conditionals as definite descriptions. Research on Language
and Computation, 2(3):417–462, 2004.
Robert Stalnaker. A theory of conditionals. In N. Rescher, editor, Studies in
logical theory, pages 98–112. Blackwell, Oxford, England, 1968.
Arnim von Stechow. Interpretiertes Tempus: Temporale Orientierung von
Modalen. Neue Beiträge zur germanistischen Linguistik, 2005.
Arnim von Stechow. Types of iF/uF-agreement. paper presented at the ESSLLIworkshop Concord Phenomena at the Syntax-Semantics Interface, Malaga,
2006.
Hedde Zeijlstra. On the syntactic flexibility of formal features. In Th. Biberaurer, A. Holmberg, and I. Roberts, editors, The limits of parametric variation.
Benjamins, Amsterdam, 2006.
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