Towards a Teleological Model for Modals

Bridget Copley, SFL (CNRS/Paris 8)bridget.copley@sfl.cnrs.fr ∗

Paris Working Sessionson Modality, Goals, and Events

23-24 November 2010

(1) a. If you want to get a good macaron, you must/have to/should/oughtto go to Laduree.

b. To get a good macaron, you must/have to/should/ought to go toLaduree.

Ideas to be investigated in this talk:

• Fernando (2005), Nissenbaum (2005): A model that contains stringsof actions directed towards goals is superior to the existing possibleworlds accounts of anankastic conditionals.

• Copley and Harley (2010), Copley & Harley (in prep), Copley (in prep),provide such a theory. And in fact, the notion of a string of actiondirected towards a goal is needed elsewhere (non-culminating accom-plishments, progressives, frustratives, futures) and a model with thisnotion is superior to possible worlds accounts of these data.

• This model can be extended to account for teleological modality.

• (Research project: Are all modals underlyingly teleological?)

∗This talk builds on, and is inextricably intertwined with, joint work with Heidi Harley(University of Arizona): Copley and Harley (2010), Copley & Harley, in prep. Thanks toCNRS Federation de Recherche 2559 “Typologie et Universaux Linguistiques” for fundingthis project through the program “La causalite dans le langage et la cognition” (sfl-cause).

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1 The problem with teleological modality

A proposition is identified with the set of possible worlds where it is true;modal base m(w) is the set of worlds accessible from w (by some accessibilityrelation).

Suppose that the to-infinitive purpose clause is in some syntactic realizationan argument of the teleological modal.

(2) to p, must q is true in world w relative to a set of worlds m(w) iff allworlds in m(w) in which p is achieved also have q—i.e., m(w)∩ p ⊆ q

von Fintel & Iatridou 2005: Let m(w) be given by the ordering source andconversational background function of Kratzer (1991)

Nissenbaum (2005): Suppose the A train and the C train go to Harlem, andthe C train will have Pedro Martinez on it. You want to kiss Pedro Martinez.vF&I predict (3) to be true:

(3) #To go to Harlem, you have to kiss Pedro Martinez.

vF&I: q is an essential part of a way of achieving p relative to world w withmodal base m(w); P is a partial plan that lacks only q to bring about p

(4) for some set P of propositions, m(w)∩q∩⋂P ⊆ p but m(w)∩

⋂P 6⊆ p

Fernando (2005): But still, time doesn’t take care of itself.

(5) a. #To go to the Hotel California, you must die in the Hotel Califor-nia.

b. #To go to Harlem, you must visit the Apollo Theater.

This could be taken care of by taking propositions specified for times, andspecifying that the time index of p is after the time indices of q and of all thepropositions in P. But it seems we are really talking about chains of events.

Nissenbaum (2005): “eparkastic” conditionals

(6) #If you want to go to Harlem, you can kiss Pedro Martinez.

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(7) a. Varitek took the A train to get to Harlem.b. Rogers and Astaire practiced every day in order to dance profes-

sionally.

(8) a. #Those leaves turned colors to be attractive.b. #Brad was bleeding in order to prove a point.

Hard to escape the conclusion that the idea of doing something with a par-ticular goal in mind must be modeled.

(9) [[adjunct (in order) to go to Harlem]]a,w = λ e ∀ w’ such that w’ is com-patible with the goals relevant to e: Pro goes to Harlem at w’

Copley and Harley: put this notion into the model itself.

Physical and psychological issues:

(10) a. If you’re going to leave, you have to sign this first.b. If it’s going to snow, it has to get colder.

Must reconcile doing something with a goal in mind with the totally physicalversion in (10b)!

2 Copley & Harley 2010

“Power (lit. force) is being ableto break a bar of chocolate in fourpieces and only eat one.”

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2.1 Doing something with a goal

Non-culminating accomplishments:

(11) InalisN-pf-remove

kogen-I

angnom

mantas,stain,

perobut

naubusanrun-out-of

akonom-I

kaagadrapidly

nggen

sabon,soap

kayahence

hindinot

kogen-I

naalis.A-pf-remove

‘I tried to remove (lit. ’I removed’) the stain, but I ran out of soap,and couldn’t.’ (Tagalog)Dell (1987)

(12) k’ul’-un’-lhkanmake-TR-1SG.SU

tiDET

ts’la7-a,basket-DET

t’u7but

aoyNEG

t’u7just

kwDET

tsukw-sfinish-3POSS‘I made the basket, but it didn’t get finished.’ (St’at’imcets)Bar-El et al. (2005)

(13) kwDET

JohnJohn

naRL

kw’el-nt-ascook-TR-3ERG

taDET

skawtspotato

welhCONJ

hawNEG

k-asIRR-3CNJ

7iPART

huy-nexw-asfinish-LC-3ERG

‘John cooked a potato but never finished.’ (Skwxwu7mesh)Bar-El et al. (2005)

2.2 A force-situation framework

An event is to be understood as a force: an input of energy into an initialsituation that results in a result situation as long as nothing external to theinitial situation intervenes (ceteris paribus condition).

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Suppose that a situation s is a collection of individuals (x, y, z . . . ∈ De)and propositions about their properties (p, q, r . . . ∈ D〈s,t〉). The domain

of situations is Ds.

Cf. situation semantics (Barwise and Perry, 1983; Kratzer, 1989), dynamicsemantics/DRT (Heim, 1982; Kamp and Reyle, 1993; Beaver, 2001), propo-sitional dynamic logic (Fischer and Ladner, 1979).

A force is a function f from situations to situations (i.e., it is in D〈s,s〉. We’ll

use variables π, ρ, etc., to designate forces, and abbreviate type 〈s,s〉 as typef).

For any situation sn, there is a force fn such that fn is the net force of sn.

The successor situation sn+1 of a situation sn is found by applying the netforce of sn to sn.

From any force you can recover the initial situation (i.e., the one to which itis applied) and final situation: init(f), fin(f)

2.3 The net force and efficacy

How is the net force calculated? In general, by the cognitive system, not thegrammar.1

(14) John closed the door.

s0 = John, the door, open(the door)

John puts energy into s0 in a certain configuration.

1One exception already: The relative size of the agonist force as compared to anyantagonistic forces (Talmy, 2000; Wolff, 2007) seems to be relevant to determining thesource or agent of the force, which is of course relevant to the grammar.

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s1 = John, the door, closed(the door)

The net force is deterministic except when volitional entities are involved.

A situation s is efficacious if succeeds in proceeding via its net force to itssuccessor (i.e., all else is in fact equal and nothing else intervenes).

In English and other European languages, there is an efficacy presupposition.In languages with non-culminating accomplishments, there is no efficacy pre-supposition.

(15)

s0

s′0

f0

f ′0

s′1

s1

2.4 Non-spatiotemporal forces and the normal field

We are used to thinking of physical forces as contact forces that result in achange in the spatiotemporal properties of an object: where it is, whether itis moving or at rest, etc. In such cases, init(f) and fin(f) are situations thatdiffer only in the the spatiotemporal properties of an object. But actually,any physical change could be represented as a function from one situationto another. Consider a fruit ripening: init(f) includes the unripe fruit andfin(f) includes the ripe fruit. Insofar as ripening happens to all fruit unlessit is chilled, eaten while it is still green, etc., this case is less like pushing acup and more like gravity; fruit has a tendency to ripen.

This abstract kind of “force” could equally well be thought of as an input ofenergy, or as a “tendency” (Talmy, 1988, 2000, also Aristotle (Physics)).

In general, normal forces (e.g., gravitational forces, other natural laws, gen-eralizations about the tendency of individuals or classes of individuals, etc.to behave in a certain way) are assumed to arise as needed from a “normalfield” relativized to the topic situation. These are added up in the calculationof the net force.

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2.5 Predicate types

A force argument f can in general take the place of an event argument e. Soeventive predicates are now force predicates, type 〈f,t〉, or equivalently, type〈〈s,s〉,t〉. A situation argument s can in general refer to a state (though itmay also refer to an event...). So stative predicates are situation predicates,type 〈s,t〉. Propositions are also type 〈s,t〉 (cf. Copley (2008)).

2.6 Psychological forces

Predicates can be true by virtue of psychological forces as well as by virtueof spatiotemporal physical forces (Talmy, 1988, 2000; Wolff, 2007). For now,we are interested in intentions, though this will become more interesting inthe discussion of (10b) above.

Strictly speaking, psychological forces cannot be quite the same as physi-cal forces, since intentions involve the agent’s beliefs and thoughts. Wherephysical forces are type 〈s,t〉 (functions from situations to truth values), psy-chological forces should be type 〈s, 〈s, t〉〉 (functions from situations to setsof situations). (Variables F1, etc.)

Intentions are to be understood as net desires (calcuated in the cognitivesystem, not the grammar).

To jump the Davidsonian gap between the psychological and the physical(Davidson, 1963), we propose that the normal field includes a Law of RationalAction:

(16) Law of Rational Action: if a volitional entity intends somethingin a situation s and is not prevented by anything from acting in sucha way (according to his/her beliefs) as to achieve it, the being acts(exerts a force on s) in such a way, (according to his/her beliefs) toachieve it.

The LRA is itself a tendency of volitional entities, so when it is saturatedwith an entity and a situation, it is a force. This is why we say it is includedin the normal field.

Actually, any time there is a volitional agent, there is the agent’s intention,which is a psychological force. More about agents below but for now, we willwrite source(John, f) or source(John, F) to show that John is the source of

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either a physical force or an psychological force (=intention).

variable type (σ) kind of likevariables for

predicate(type 〈σ, t〉)

situations s0, s1, . . . s states p, q, . . .

physical forces f1, f2, . . .〈s, s〉

(abbr.: f)events π, ρ, . . .

psych. forces F1, F2 . . .〈s, 〈s, t〉〉(abbr.: F)

intentions Π, R, . . .

3 Teleological modality in a force-situation

framework

(17) a. If you want to get good macarons/To get good macarons,you must go to Laduree.

b. If you want to get good macarons/To get good macarons,you can go to Laduree.

s0

p

3.1 Rationale clauses with non-modal clause

(18) John went to Laduree [Pro to get good macarons.]

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Rationale clause adjoins to vP as per Nissenbaum’s proposal and is type 〈F,t〉( = 〈〈s, 〈s, t〉〉, t〉).

(19) (Copley & Harley in prep.)

a. [[ [vP John go to Laduree] ]] =λ f ∈ D〈s,s〉 . John-go-to-Laduree(f) & source(John, f)

where John-go-to-Laduree holds of f just in case f is a physicalinput of energy into a situation s where John goes and ends upat a situation s1 in which John is at Laduree

b. [[ [TP John went to Laduree] ]]=λ s . ∃ f : John-go-to-Laduree(f) & source(John, f) & f = net(s)& s < s0

(20) [[ [TP inf Pro to get good macarons] ]] =λ F ∈ D〈s, 〈s,t〉〉. Pro-to-get-good-macarons(F)

where Pro-to-get-good-macarons holds of F just in case F is anintention held in a situation s towards the proposition [Pro get goodmacarons].

(21a) is a new version of (19a), effected through a new denotation for v asin (21b):

(21) a. [[ [vP John go to Laduree] ]] =λ f ∈ D〈s,s〉 . John-go-to-Laduree(f) & source(John, f) & ∃F :

[Π(F) & source(John, F) & realize(f, F)]b. v = λπ ∈ D〈e,〈f,t〉〉 λx λΠ ∈ D〈F,t〉 λf . [π(x)](f) & ∃F : [Π(F)

& source(x, F) & realize(f, F)]

(22) realize(f, F) iff: f is a force generated by the Law of Rational Actionwith respect to F; given source(x1, F) and source(x2, f), x1 mustcontrol/have authority over x2, and init(f) = init(F)

(23) [[ [vP John go to Laduree Pro to get good macarons] ]] = λf . John-go-to-Laduree(f) & source(John, f) & ∃F : [John-to-get-good-macarons(F)& source(x, F) & realize(f, F) ]

(24) #The leaves turned colors to be attractive. (= (8a))

Note as well that things can go wrong and the sentence in (18) can still be

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true: suppose, e.g., John gets to Laduree and it is closed. What this meansis that he was the source of a force that ended up with a situation s1 that,from John’s earlier perspective, would count as a stop on the way to gettinggood macarons, but now it turns out not to be the case. In fact there wereno macarons to be had there, so it was not s1 that John got to but rather s’1(cf. the diagram in (15)). However, his action is still a John-go-to-Ladureeaction, and the rationale was still due to his intention to get macarons, sothe sentence is still true.

3.2 Anankastic/eparkastic conditionals

(25) a. If you want Pro to get good macarons, you must go to Laduree.b. If you want Pro to get good macarons, you can go to Laduree.

Let p = you want Pro to get good macaronsp’= Pro to get good macaronsq = you go to Laduree

The semantics of want (building in a sort of efficacy; is this a good idea?):

(26) a. [[you want Pro to get good macarons]] = λ s . source(you, F)& Pro-to-get-good-macarons(F) & the net force of s is an LRAforce obtained from F

b. [[want]] = λΠ λ x λ s . ∃F : source(x, F) & Π(F) & the net forceof s is an LRA force obtained from F

Let’s look at what p entails: the net force of s, whatever it may be (since avolitional entity may choose what it is to be), is obtained via the LRA withrespect to F, so it must be an f such that realize(f, F).

(27) a. [[if p, must π]] = λ s. ∀s’ causally accessible from s such thatp(s’) : [∀f such that f is a possible net force of s’ : [∃f : π(f)]From all causally accessible s′ such that p(s’): all causal chainsf include a substring f where π(f)

b. [[if p, can π]] = λ s. ∀s’ causally accessible from s such that p(s’): [∃f such that f is a possible net force of s’ : [∃f : π(f)]From all causally accessible s′ such that p(s’): there is a causalchain f that includes a substring f where π(f)

(28) [[(25a)]] = λ s . ∀s’ causally accessible from s such that you-want-to-

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get-good-macarons(s’) : [∀f such that f is a possible net force of s’ :[∃f : Pro-go-to-Laduree(f)]

(29) If it’s going to snow, it has to get warmer. (=(10b))

(30) [[(29) ]] = λ s . ∀s’ causally accessible from s such that it’s-going-

to-snow(s’) : [∀f such that f is a possible net force of s’ : [∃f :it-gets-warmer(f)]

(31) [[it’s going to snow]] = λ s . highest-entropy(s, [Pro to snow]) & thenet force of s is a force obtained from F

3.3 Rationale clause with modal

(32) a. To get good macarons, you must go to Laduree.b. To get good macarons, you can go to Laduree.

Nissenbaum and vF&I disagree about where to put the rationale clause; Iagree with the latter that it should be high.

We had a pretty good case for putting the heavy lifting in little v when therationale clause is adjoined to vP; where does it go now?

(33) #?To snow, it has to get colder.

4 Conclusions and musings

In this talk, I’ve presented some conclusions from recent literature on anankas-tic (and eparkastic) conditionals arguing that what is needed for teleologicalmodality is the notion of doing an action with the intent of achieving a goal.I’ve argued that the theory of Copley and Harley (2010) with some additionalmachinery for psychological forces, fits the bill.

Some other thoughts:

• Accessibility of one situation to another via forces is causal. In a sense,the physical forces (= events) are the accessibility relation. Various

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physical laws and the Law of Rational Action govern causal accessibil-ity.

• The work done by Kratzer’s ordering sources is no longer done in thegrammar at all, it is done in the cognitive system via the calculationof net forces and intentions (which are net desires).

• The physical universe wants only one thing: highest entropy.

• Forces and compositionality

– Montagovian semantics (Montague, 1974; Dowty, 1979; Heim andKratzer, 1998) operates from the hypothesis that the meaning ofa sentence is derived from the meanings of its parts and how theseparts are put together, with the heuristic that the rules for puttingparts together should be as simple as possible.

– In standard Montagovian models (e.g. Kratzer, 1996; Higginbotham,2000) there has to be a stipulated “CAUSE” relation, imposedwhen a type mismatch is detected between event-denoting sub-parts of the verb phrase.

– In our system, because a causing event is a function that takes itsfinal (result) situation as an argument, all components of the verbphrase are composed by functional application.

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