Past as past approaches are conceptually very attractive. They have the poten- tial to maintain the standard meanings for the simple past and the perfect. This is interesting, because changing this meaning, particularly introducing a lexical ambiguity would complicate the lexicon. Additionally, one would like to maintain the standard meanings, because in many sentences they make the correct predic- tions. We have said above, that the price to be payed for a conservative lexical semantics is to give up the syntactic analysis sketched in figure 6.1 on page 162. But why should we adopt this analysis? One has to admit that this analysis was
rather naive and might very well be wrong. Furthermore, what does commit us to a logical form that mirrors surface structure? Issues like quantifier raising have forced us to become used to the idea that this does not always have to be the case.
Despite its attractiveness, there are only few semanticians that have tried to give substance to the past-as-past approach. One reason is that the alternative past-as-modal approach has a lot of intuitive appeal. But this is certainly also the consequence of the difficulties one has to face when one tries to work out a past- as-past proposal. It is easy to come up with suggestions for different structures for conditional sentences, but much more difficult to find one that explains the puzzle of the missing interpretation. One of the few works following the past-as- past hypothesis is Tedeschi (1981). The essential idea behind his approach is that the simple past in subjunctive conditionals does not apply to the eventualities described in antecedent and consequent, but to the conditional as a whole. Hence, the semantical structure of such a conditional looks rather as follows.
Tedeschi’s interpretation rule for subjunctive conditionals
A subjunctive conditional with the tenseless propositions p in the antecedent and q in the consequent is assigned the following logical form:
P (p ≻ F (q)),
where P and F are logical operators shifting the evaluation time back- ward (P) and forward (F) respectively, and ≻ a conditional connective, whose meaning still has to be defined.
From a compositional perspective, this proposal is not very convincing. It is not clear why the past operator is in the position superordinating the conditional. Furthermore, the approach is bound to an analysis of the simple past as a senten- tial operator. Many students of tense in English have argued that this is not the way English tenses work (see, among others, Kamp & Reyle 1993). However, the underlying idea, that subjunctive conditionals are conditionals evaluated in the past has a long tradition in the literature of conditionals. It is actually the leading idea of all past-as-past approaches. It is also very often taken as a basis for the semantic meaning of would have conditionals by authors that want to derive the counterfactuality of these conditionals as conversational implicature (see Condo- ravdi 2002, Ippolito 2003, and many others). But also philosophers have found it very attractive, for instance, to describe the difference between indicative and subjunctive conditionals (see Adams 1975, 1976, and Skyrms 1980, 1981, 1984, 1994).
Before we discuss more past-as-past approaches in detail, let us first clarify this common idea for the meaning of conditionals. The basic claim is that the class of conditionals can be split into those evaluated with respect to possibilities
admissible at the utterance time4 (the indicative conditionals, for some authors
also the would conditionals), and conditionals evaluated with respect to sets of possibilities accessible at some past time point (would have conditionals, for some authors also would conditionals). Let us call the first group present conditionals and the second group past conditionals. Two sets of possibilities are generally considered relevant for the evaluation of conditionals.5 In one case the condi-
tional is read epistemically. In this case, the possibilities are the possible worlds consistent with what some agent believes/knows at some time-point. According to the other reading, the conditional makes reference to the ontic (metaphysic) alternatives. Ontic alternatives are also represented by a set of possible worlds. But this time these worlds do not represent what is known or believed by some agent, but what is settled about some world. Intuitively, a fact is settled, if it is no longer open to manipulation, it cannot be changed. A central claim or observation about settledness is that it depends on time: while the past and the present of a world are settled, the future is – to some extent – still open. Kamp (1978) illustrates this difference with two games, GOF6 and GOP7. GOF works
as follows. It is played by two players A and D. A makes some claim about the immediate future and D has to respond by saying wether the claim is correct or not. It is easy to see that player A has a winning strategy in this game: the player just makes some claim about some fact concerning the future that is under his control. For instance, that he will scratch his nose in a minute. Then D has no chance to get the answer right. The rules of GOP are similar to those of GOF. The only difference is that this time A has to make a claim about the immediate past. Now, it is not that easy for A to win. The reason is – or that is the claim – that A has no control about the past. The past is already settled.
The standard formalization of the notion of settledness or the ontic alterna- tives follows the branching futures an approach introduced by Kamp (1978) and Thomason (1985). According to this formalization, time is a linear structure and worlds are complete histories, interpretation functions defined for the whole time line. Let T be the set of times and M be the set of complete histories over T . To model settledness, an accessibility relation ∼= between worlds is introduced that at a certain time relates all those worlds that share the same history up to this time point. Hence, ∼= is a 3-place relation on T × W × W , such that (i) for all t, ∼=t is an equivalence relation, and (ii) for any w1, w2 ∈ W and t1, t2 ∈ T , if
w1 ∼=t2 w2 and t1 < t2, then w1 ∼=t1 w2. These conditions warrant that the set of
worlds w′ that stand in the relation ∼=
t to a world w decreases over time. At each
t the relation ∼=t splits the set of all worlds into equivalence classes that become
smaller and smaller over time. Finally, one demands that if w ∼=t w′ and P is a
4Adams (1975, 1976) suggests that these conditionals have to be evaluated with respect to
a present epistemic probability distribution.
5Kratzer (1979, 1981) proposes many more. 6Game Of the Future
atomic proposition letter, then ∀t′ < t : t′ ∈ w(P ) ⇔ t′ ∈ w′(P ). This condition
assures that the worlds standing in the relation ∼=t do in fact interpret the past
up to t identically.
Based on the relation ∼= we can now give a rough formalization of the evalua- tion strategy for past conditionals described above. We will call this the back-shift interpretation rule of past conditionals.
The back-shift interpretation rule for past conditionals
A past conditional with antecedent A and consequent C is true in w0
at t0 if
∃t < t0∀w : (w0Rw & A(w)(t)) ⇒ C(w)(t),
where R is either an epistemic accessibility relation or the ontic ac- cessibility relation ∼=.
To illustrate this approach to conditionals with an example, consider again the Kennedy example we have discussed in Chapter 5.
(104) a. If Oswald didn’t kill Kennedy, someone else did.
b. If Oswald hadn’t killed Kennedy, someone else would have.
Most people agree with the first, indicative conditional, but deny the second, subjunctive conditional. An approach along the lines sketched above could now explain the difference in truth conditions as follows. Interpreters that share the intuitions just described believe that Kennedy is dead, but they may have doubts concerning whether Oswald was indeed the murderer. The first conditional is an epistemic present conditional, evaluated with respect to the epistemic alterna- tives of this interpreter at the utterance time. The interpreter does believe that Kennedy is dead. Hence, in all worlds consistent with his beliefs where Oswald did not kill Kennedy someone else has to be the murderer. The second condi- tional is an ontic past conditional, evaluated with respect to ontic alternatives accessible at some past time.8 We go back in the actual world to some time when
the antecedent was still not settled and look at all those ontic alternatives where the antecedent turns out to be true. If the interpreter believed in a conspiracy theory concerning the death of Kennedy, then there would be some past time – probably the time at which the conspiracy was set up – at which in all futures where Oswald does not kill Kennedy, somebody else does. Hence, the second conditional comes out as true. However, the type of normal interpreter that we refer to here does not believe in conspiracies. Hence, he would find no past time were all futures in which the antecedent turns out to be false, the consequent becomes true. Thus, the conditional is predicted to be false.
Let us now come back to the puzzle of the missing interpretation. The aspect of this analysis that makes it so attractive to proponents of a past-as-past hypothesis is that it allows for at least some of the past markers in subjunctive conditionals to keep their temporal meaning. They are taken to express the back-shift of the evaluation time of the conditional. The question is whether we can provide some plausible compositional semantics for conditionals that produces the described back-shift interpretation rule for subjunctive conditionals. Furthermore, we have to see whether this approach can completely explain the puzzle of the missing interpretation.
One past-as-past approach that tries to answer these questions has been brought forward by Ippolito (2003). She builds on the theory for condition- als introduced by Kratzer (1979, 1981). Kratzer proposes that conditionals are modal statements. Modals, on the other hand, are according to Kratzer (1979, 1981) interpreted as quantifiers over possible worlds. They take two arguments denoting sets of possible worlds, a restrictor and a nucleus and then make a state- ment about the relation between these two sets. It is proposed that antecedents or if-clauses restrict the first argument, while the consequent describes the nu- cleus. According to this theory, a conditional has the logical structure described in figure 6.2. Kratzer proposes that the modal is not always explicitly present in a conditional, but is in standard conditionals the covert modal Must, interpreted as universal quantifier.9 HH HH HH HHHH @ @@ HH HHH Modal Restrictor Antecedent Nucleus Consequent
∀w : (Restrictor(w) & Antecedent(w)) ⇒ Consequent(w) Figure 6.2: Kratzer’s approach to conditionals
Ippolito (2003) only aims at accounting for would have conditionals that refer to the present or future. She calls these conditionals mismatched past conditionals. Remember, that in these conditionals both the simple past and the perfect seem to miss their temporal interpretation. Central for the approach of Ippolito (2003) is the claim that in a modal quantificational structure the past can be interpreted
9Kratzer seems to assume for all conditionals discussed here, also those with will and would
either in the restrictor or in the nucleus. She then proposes that in the case of mismatched past conditionals, it is interpreted in the restrictor. The restrictor is a time and world dependent accessibility relation. The simple past restricts the interpretation of the temporal variable of this accessibility relation to some time interval in the past.10 According to her, this leaves the antecedent and the consequent as tenseless propositions. The structure Ippolito proposes for mismatched past conditionals is sketched in figure 6.3, together with what apears to be the meaning assigned to these sentences.11
HH HH HH HHHH @ @@ HH HH HHH HHH HHH must
hhsti, hhsti, tii
Restrictor hs, hi, hstiii Antecedent hsti Consequent hsti w s t[past] i
A mismatched past conditional with antecedent A and consequent C is true in world w0 at time t0, if the following holds:
∃t < t0∀w : [w ∼=tw0 & A(w) ⇒ C(w)]
Figure 6.3: Ippolito’s approach to conditionals
The central problem of this approach is that it provides no explanation for why in a modal quantificational structure the past can be interpreted either in the restrictor or in the nucleus. Furthermore, Ippolito (2003) leaves unclear how four markers of past time reference – simple past and perfect in antecedent and simple past and perfect in consequent – are interpreted as one past operation, or, in other worlds, why interpreting one past feature on the restrictor turns the antecedent and the consequent into tenseless propositions. It seems reasonable that one instance of the past referring morphology may somehow apply to the restrictor. But if this is what she means, which one is the chosen one? And what happens to the others?
There exists a proposal very similar in spirit to Ippolito (2003), but worked out much more systematically and precisely: Condoravdi (2002). Actually, Condo-
10Ippolito (2003) proposes a standard interpretation for the simple past: it imposes restric-
tions on the interpretation of the temporal variables to which it applies, the variable has to be interpreted as some time before the utterance times. She also assumes that the perfect is in some contexts interpreted this way.
11Ippolito (2003) assumes that mismatched past conditionals always refer to the ontic modal
ravdi is also not primarily interested in accounting for the puzzle of the missing interpretation. Instead, she wants to account for some aspects of the (non-root) meaning of the modals may, might, will, would, particularly when combined with the perfect, as in (105). But in combination with Kratzer’s approach to condition- als, her theory can be extended to a proposal about the meaning of conditionals. (105) Peter might have won the game.
Because, in contrast to Kratzer, Condoravdi (2002) treats will and would as modals, many more conditionals than in the original approach of Kratzer now become explicitly modalized. The driving idea in Ippolito’s proposal, that in modal structures some past feature can be interpreted either in the restrictor or in the nucleus of the modal, is also central for Condoravdi’s approach. But now it is explained as a consequence of a structural ambiguity of the scoping relation between modal and perfect: the perfect can just as well scope over the modal as under it. Under the modal it applies to the phrase in scope of the modal, which describes the nucleus of the quantifying structure. Over the modal it shifts the evaluation time of the restrictor of the modal backward. This is all worked out in a detailed compositional semantics. Below, in figure 6.4, the two logical forms Condoravdi proposes for sentences like (105) are given, together with the meanings she proposes for the simple present, the perfect, and the modals.12 The
interpretation of the present tense and the perfect follows standard lines. The modals are analyzed as quantifiers over possible worlds. Their domain, the modal base MB, is contextually given. Condoravdi distinguishes two modal bases for the non-root readings of the modalities: an epistemic modal base and an ontic modal base.13 They follow the description given above. The meanings she proposes for
might/may and would/will combine a standard modal meaning with a temporal meaning: the modalities expand the evaluation time for the property of times in their scope forward. The last line in figure 6.4 describes the meaning Condoravdi (2002) predicts for (105) if the perfect scope over the modal.
In how far can this approach account for the puzzle of the missing interpre- tation? It is important to realize that – contrary to Ippolito’s proposal – the structural ambiguity proposed applies only to the perfect and not to the past tense. Condoravdi can account for why it may sometimes look as if the perfect loses its interpretation in would have conditionals or modalities for the past. If the perfect scopes over the modal, then the evaluation time of the modal, more par- ticularly the modal base, is shifted to the past. But because the modal expands
12We ignore here an important feature of her approach. Condoravdi distinguishes in her
ontology sorted eventualities. Basic untensed sentences denote properties of eventualities. This enables her to account for some very intriguing facts about differences in interpretation between eventive and stative predicates. However, we simplify matters here and interpret basic untensed sentences as properties of times. The reason is that the facts Condoravdi accounts for with this event apparatus are only peripheral for the discussion at hand.
@ @@ @ @ @ @@ HH HHH @ @@ Modal MB
Peter win the game PRES PERF @ @@ @ @@H HH HH @ @@ Modal MB
Peter win the game PRES
PERF
PRES : λP λw.AT (now, w, P ),
PERF : λP λwλt.∃t′ : t′ < t & AT (t′, w, P ),
might/may : λMBλP λwλt.∃w′ ∈ MB(w)(t) & AT ([t, −), w′, P ),
would /will : λMBλP λwλt.∀w′ ∈ MB(w)(t) ⇒ AT ([t, −), w′, P ),
AT (t, w, P ) : ∃t′ : t′ ⊆ t & P (w)(t′)
(where P s a property of times, M B is a time-sensitive accessibility relation, and [t, −) is the time-interval starting with t and without right boundary).
[[(105)]] = λw.∃t < now ∃w′ : [w′ ∼=
tw & AT ([t, −), w′, P eter win the game)]
Figure 6.4: Condoravdi’s approach to non-root modals
the evaluation time for the property of times in its scope forward, this property might actually refer to the present or the future. However, this approach says nothing about the surface past tense markings on the modalities might and would and why they appear not to be interpreted as past tenses. Actually, if you look at the trees given in figure 6.4, you see that according to Condoravdi’s proposal these modals are not semantically interpreted as bearing a past tense. Instead they are analyzed as carrying present tense.14 In a handout, Condoravdi (2003)
proposes that the past morphology on might must (and on would can) be inter-