Journal of Semantics Advance Access originally published online on May 3, 2005
Journal of Semantics 2005 22(3):231-280; doi:10.1093/jos/ffh025
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© The Author 2005. Published by Oxford University Press. All rights reserved.
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Conditional Truth and Future Reference
Northwestern University
Correspondence: STEFAN KAUFMANN, Department of Linguistics, Northwestern University, 2016 Sheridan Road, Evanston, IL 60208-4090 USA, e-mail: kaufmann{at}northwestern.edu
This paper proposes a compositional model-theoretic account of the way the interpretation of indicative conditionals is determined and constrained by the temporal and modal expressions in their constituents. The main claim is that the tenses in both the antecedent and the consequent of an indicative conditional are interpreted in the same way as in isolation. This is controversial for the antecedents of predictive conditionals like ‘If he arrives tomorrow, she will leave’, whose Present tense is often claimed to differ semantically from that in their stand-alone counterparts, such as ‘He arrives tomorrow’. Under the unified analysis developed in this paper, the differences observed in pairs like these are explained by interactions between the temporal and modal dimensions of interpretation. This perspective also sheds new light on the relationship between ‘non-predictive’ and ‘epistemic’ readings of indicative conditionals.
1 Some speakers, including an anonymous reviewer, find that (2a) requires the presence of a temporal adverbial like ‘tomorrow’. Others believe that the future reference time may be supplied contextually (Steedman 2002).
2 Transitive: if i 
j and j k then i k. Serial: For all i there is a j such that i j. Euclidean: if i j and i k then j k. See Fagin et al. (1995); Stalnaker (2002).
3 The resulting logic depends on the properties of the accessibility relation; specifically, S5 for 
and KD45 for .
4 In Kaufmann (2002), I called this notion the ‘presumption of settledness’. An anonymous reviewer found this term confusing, since the intention is that it is the question of ‘whether 
’ that is settled, not the proposition ‘that ’.
5 This paper is not committed to a particular analysis of aspect (or Aktionsart); the framework should be compatible with any account of the constraints that it contributes. One candidate would be Gennari's (2003) proposal that the Present induces a future reference time with all aspectual classes and that the co-temporal interpretation of statives is inferable via their ‘superinterval property’.
6 I use the term ‘epistemic’ here in its linguistic sense. In this sense, ‘epistemic’ modals are opposed to ‘root’ (e.g., deontic) modals (Jackendoff 1972; Hofmann 1976; Brennan 1993). There is some potential for confusion, since these ‘epistemic’ modals may have epistemic, doxastic or metaphysical readings in the logical sense. I should also mention at this point that I do not intend the same analysis to apply to root modals. They appear to be embedded under epistemic modals of the kind I discuss here, hence semantically in the nuclear scope of the operator I introduce in the next section. Related to this is the observation that they do not seem to scope out of conditional consequents (Frank 1996; Zvolenszky 2002).
7 I will not be dealing with ‘must’, which has been characterized as adding to the assertion the claim that it is supported by the available evidence only in some ‘indirect’ fashion (Veltman 1986; Stone 1994; Westmoreland 1995). I believe that this is basically correct; I will not discuss ‘must’ any further because the meaning just described makes it an evidential, placing it outside the scope of this paper.
8 In my view, this analysis does not entail a commitment to a syntactic analysis of the bare Present which actually includes a morpheme meaning ‘Ø’. Perhaps the universal modal force is simply a default way of interpreting non-modalized sentences. On the other hand, phenomena like emphatic do-support do lend some support to the idea that there might be some syntactic motivation for this analysis.
9 One could include at this point a means for incorporating contextually given reference times. To add a reference interval rs, (18a) is changed to ‘
PRES
= 
ij.i 
j 
rs(j)’, where rs is a variable of type 
s, t
that is locally free but contextually bound; similarly for (18b).
10 Also like tenses, these arguments can be subject to contextually provided restrictions. This happens, for instance, in sequences of conditionals: Even if (b) is true in isolation, it is odd in the context of (a), where it tends to be interpreted as (c).
- a. If I win a million, I will quit my job.
- b. If I quit my job, I will be poor.
- c. If I win a million and quit my job, I will be poor.
- b. If I quit my job, I will be poor.
11 For lack of space, I cannot discuss this reinterpretation in full detail. I only note that I believe the modal base (e.g., ‘According to the schedule...’) enters the nuclear scope of Ø, and that the whole sentence is still interpreted with respect to, for instance, the speaker's beliefs.
12 The detailed semantic analysis of this operator is an ongoing endeavor. See Condoravdi (2003) for alternatives to some aspects of my proposal.
13 An earlier version of this paper offered a probabilistic treatment at this point. The change is due to space constraints and does not constitute a retraction of the earlier account.
14 The term ‘relative likelihood’ was applied to such pre-orders by Halpern (1997, 2003).
15 The temporal component attributed to WOLL in Definition (32) ignores the forward-shifting effect it has on the reference interval even without the Present tense, as observed in Past-tense ‘would’. To take it into account, we would need an explicit representation of the reference time (see Footnote 9). Part of the meaning of WOLL would then consist in an extension of this reference time into the future. The intersective meaning of the tenses would ensure that this indefinitely extended reference interval is cropped at speech time with the Past tense but left intact with the Present (see also Condoravdi 2003). I will not explore this matter further here. Definition 32 suffices for my purposes.
An anonymous reviewer suggests that ‘will’ necessarily shifts the reference time forward. I am not sure if such a strong claim is warranted. The temporal behavior of ‘will’ resembles in some respects that of the bare Present. The fact that for the truth of (ia) it is not sufficient that John be crying now, is paralleled in the fact that (ia') must have a future reference time. But like the bare Present, ‘will’ can occur with present reference times in stative sentences; cf. (ib,b'). This suggests that the reason why (ia) cannot have a present reference time has to do with the aspectual properties of the predicate, not (only) the semantics of ‘will’.
- (i) a. John will cry. a'.?John cries.
- b. John will be in his office (now). b'.John is in his office (now).
- c. John will be in his office tomorrow. c'. ?John is in his office tomorrow.
- b. John will be in his office (now). b'.John is in his office (now).
16 There may well be languages in which the word for ‘tomorrow’ has such a logophoric use, but English is not one of them.
17 Or, if one prefers Garrett's (2001) term, ‘time of enlightenment’. It also resembles Crouch's (1993) ‘temporal deictic center’.
18 Here and below, the labels NYT and WSJ indicate the corpora in which the examples are attested (New York Times and Wall Street Journal, respectively).
19 The example of Thomason's on which (58a) is based is (ia):
- (i) a. If my wife is deceiving me, I will believe that she is not.
- b. If I find out that my wife is deceiving me, I will believe that she is not.
- c. If my wife is deceiving me (currently), I believe that she is not.
- b. If I find out that my wife is deceiving me, I will believe that she is not.
(ia) does not pose a problem on its predictive reading, despite the fact that the conditions on doxastic states deprive the speaker of the ability to conceive of the possibility that a sentence he believes to be false may be objectively true. For (ia) is a conditional prediction about future beliefs which the speaker may not yet have at present.
(ic), on the other hand, is predicted by my account to be necessarily either false or infelicitous (due to vacuity). Whether this prediction is right or not, I believe that it is peripheral to the topic of this paper.
20 As opposed to the ‘Peircean’ interpretation relative to and the doxastic one relative to ; see Burgess (1979) for a discussion of this terminology.
21 Wekker (1976), who claims that non-volitional ‘will’ does not exist in conditional antecedents because he found no instances in his 600,000-word corpus, adopts Leech’s opinion about ‘will/shall + Progressive’ (p. 118) for other contexts.
22 The non-veridicality of the context may be related to this phenomenon. Palmer (1979; 150) noted similar effects in questions: (ia,b) are volitional and deontic, respectively, but these connotations are absent in (ic,d).
- (i) a. Will you come to the party? c. Will you be coming to the party?
- b. Shall I come to the party? d. Shall I be coming to the party?
- b. Shall I come to the party? d. Shall I be coming to the party?
- (ii) a. I/you/she won't come to the party.
- b. I/you/she won't be coming to the party.
- b. I/you/she won't be coming to the party.
23 (69) is a variant of an example from Leech (1971) which was also used, apparently independently, by Close (1980). I changed the consequent of (69), as well as (70) below, because my analysis does not cover imperatives. Leech's version is (b), Close's is (a):
- (i) a. If you will be alone on Christmas Day, let us know about it.
- b. If you will be alone on Christmas Day, let us know now.
- b. If you will be alone on Christmas Day, let us know now.
24 Recall that just as nothing requires the modal bases of antecedent and consequent to be the same, nothing requires them to be different either. Here they are given as a and b, respectively, because this is the most natural interpretation. In principle, the consequent could have the speaker's modal base as well, although it requires some effort to think of a scenario in which the conditional would then be true. ‘His’ letting ‘us’ know would still require his expecting in addition to the speaker's.
The superscripts on
25 These include open vs. closed (Funk 1985); conditional vs. hypothetical (Dudman 1989); hypothetical vs. interactional (Garrett 2001); doesn't-will vs. didn't-did (Bennett 1995; Edgington 1995); and sometimes forward-looking vs. backward-looking.
26 The latter case motivates Edgington's (1995) observation that there is ‘no ideal, objective thing to think’ about a conditional, the falsehood of whose antecedent is settled.
27 This is part of a larger pattern in the interaction between modal and temporal dimensions in the interpretation of modals. For instance, Condoravdi (2002) explains the observation that (ia,b) can only have epistemic interpretations, whereas (ic) is not so constrained, in terms of the same interaction between epistemic and metaphysical modal bases.
- (i) a. He may be sick (now).
- b. He may have been sick (last week).
- c. He may get sick.
- b. He may have been sick (last week).
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