Abstract

Kripke (1990/2009) argues that the presupposition triggered by the additive particle too is anaphoric in nature, an influential thesis with important ramifications for the theory of presupposition. This article reexamines the empirical evidence and proposes an alternative explanation, leaving too with only its traditional existential presupposition.

The year 2009 finally saw the publication of Kripke 1990/2009, which has had a significant impact on the literature on presupposition over the past quarter century. I want to offer some comments on its central empirical thesis: namely, that the presupposition triggered by the additive particle too is anaphoric in nature. Consider (1).

(1)

  • a.

    Peter drinks.

  • b.

    [John]F drinks, too.

The traditional view (see, e.g., Karttunen and Peters 1979) held that too in (1b), where it associates with the focused element John, triggers the ‘‘existential’’ presupposition that someone other than John drinks, so that a context updated with (1a) admits (1b). Kripke argues that such an existential presupposition is not enough, and that too is anaphoric, requiring a parallel proposition (1a) in the active discourse context, such that the focused associate (John) is referentially distinct from its counterpart ( Peter).

Kripke presents two arguments in support of this thesis. First, in an out-of-the-blue context, (2) is odd.

(2) #[Peter]F had dinner in New York last night, too.

This is not explained on the traditional view since a mere ‘‘existential’’ presupposition that someone other than Peter had dinner in New York last night would always be trivially satisfied. Kripke’s anaphoric approach correctly predicts that (2) cannot be used without a preceding parallel proposition.

The second argument is based on the distinctness effect in examples like (3) and (4).

(3) If Herb comes to the party, then [the boss]F will come to the party, too.

(4) If Herb and his wife both come to the party, then [the boss]F will come, too.

(3) conveys that Herb is not the boss; (4) conveys that both Herb and his wife are not the boss. Kripke argues convincingly that the existential presupposition theory might be able to explain this distinctness effect in the case of (3), but fails on (4). For (3), the explanation might run as follows. The sentence is taken to presuppose that, if Herb comes to the party, someone other than the boss does. Why should a speaker take this implication for granted? Obviously, because the speaker takes it that Herb is someone other than the boss. Hence, this is what an utterance of (3) presupposes. However, as Kripke points out, this reasoning does not explain why (4) implies that neither Herb nor his wife is the boss: for the antecedent clause to entail the existential presupposition that someone other than the boss will come, it is enough that Herb and his wife are not identical.

Kripke does not provide an implementation of his proposal, beyond suggesting that the anaphoric properties of too should be compared with those of pronominals. Nonetheless, it seems plausible that an anaphoric treatment of too can explain the distinctness effect in both (3) and (4): if too introduces an anaphor that finds its antecedent in the if-clause, we can state the requirement that the boss and its counterpart Herb and his wife must be disjoint in reference. The details depend, of course, on the exact implementation. The literature contains several implementations of Kripke’s proposal, which I will discuss below as the need arises.

The goal of this article is to argue that the evidence in favor of Kripke’s anaphoric approach, and against the traditional existential approach, is unconvincing. I will show that Kripke’s observations are explained by two independently motivated constraints, in combination with the traditional existential presupposition. Along the way, I will also point out empirical problems for existing implementations of Kripke’s view. Finally, I will provide direct counterevidence to the anaphoric approach. The conclusion will be that there is no evidence favoring the anaphoric approach over the existential approach, and some evidence favoring the existential approach. As a result, Kripke’s observations can no longer be relied on to support the conclusions that have been based on them in the presupposition literature.

The remainder of the article is organized as follows. Section 1 discusses Kripke’s argument from (4) and shows that the data can be explained along the lines suggested in Beaver 2001. It also shows that existing implementations of Kripke’s approach in fact do not explain (4). Section 2 discusses Kripke’s argument from (2) and argues that the data follow from familiar constraints on deaccenting. Section 3 shows that, on top of the independently motivated constraints adopted thus far, we still need to assume that too triggers a presupposition. Section 4 takes the argument one step further and provides evidence suggesting that the existential approach is superior to the anaphoric approach.

1 The Argument from Distinctness

Recall the examples in (3) and (4), where the boss is distinct from Herb and his wife.

(3) If Herb comes to the party, then [the boss]F will come to the party, too.

(4) If Herb and his wife both come to the party, then [the boss]F will come, too.

As explained above, Kripke (1990/2009) demonstrates that the distinctness of the boss from both Herb and his wife in (4) does not follow from the existential presupposition commonly attributed to the additive particle. In this section, I will argue that an alternative explanation is available. Specifically, I will argue that the distinctness effect is a conversational implicature; it is not due to a presupposition, and neither is it triggered by too. I will also argue that Kripke’s anaphoric approach itself does not seem to explain the distinctness effect.1

I propose that the correct explanation is the one suggested by Beaver (2001:94n15): ‘‘I would favour a Gricean explanation of the distinctness implication, whereby each clause of a sentence or discourse is normally required to be informative.’’ In, say, (3) the consequent of the conditional is interpreted in a local context (the one resulting from updating the preceding discourse with the antecedent of the conditional) that entails that Herb comes to the party; in that context, the consequent is uninformative if Herb is the boss. I am not even sure that we need a condition of local informativeness for the present examples. The idea is that if Herb or his wife is the boss, then because in (3) and (4) the consequent of the conditional follows from the antecedent, the conditional sentences are uninformative, on a par with (5).

(5) #If Herb comes to the party, then [Herb]F will come to the party, too.

Since uninformativeness can only be avoided if Herb and his wife are not (known to be) the boss, this is what the sentences conversationally implicate.

Beaver presents one argument in favor of this view: that (6) shows that the distinctness implicature is defeasible.

(6)

  • If Clark is at the party, then Superman is definitely there too, since Clark is Superman!

  • (Beaver 2001:94n15)

Unfortunately, this argument is not entirely convincing. One reason is that the literature on the substitutivity of pairs like Clark/Superman provides analyses that would allow one to escape the conclusion that distinctness is defeated in (6). For instance, Zimmermann (2005) proposes that while Clark and Superman always refer to the same individual, only a speaker who believes they are distinct can felicitously use both names. A speaker who knows that Clark and Superman are identical can only use both names by pretending to be an ignorant speaker, thereby performing a ‘‘counterfactual speech act.’’ An utterance of the conditional sentence in (6) by an ignorant speaker could presuppose the nonidentity of Clark and Superman, which would be satisfied by his or her background assumptions. Likewise, an informed speaker could pretend, counterfactually, to accept this presupposition, before updating the common ground with the identity statement.

Moreover, Soames (2009) discusses examples like (7), which can even be used as part of a discourse aimed at establishing the identity of Hesperus and Phosphorus.

(7) The heavenly body, Hesperus, that is seen in the evening is a planet, and the heavenly body, Phosphorus, that is seen in the morning is too.

Rather than dismissing the distinctness presupposition hypothesis, however, Soames entertains the possibility that the distinctness presupposition is conversationally canceled here (probably not an option for Beaver). Another option is, in effect, to weaken the presupposition to the requirement that it is not known to the hearer whether the focused element and its counterpart are identical.2

I want to present some less problematic arguments in favor of Beaver’s view. First of all, the distinctness requirement remains in force when too is removed.

(8)

  • a.

    Herb will come to the party, and the boss will come to the party.

  • b.

    Herb and his wife will come to the party, and the boss will come to the party.

  • c.

    If Herb comes to the party, then the boss will come to the party.

These examples also imply that Herb and his wife are not the boss. The examples therefore attest to an independent principle causing a distinctness effect; it is unclear how we could prevent this principle from explaining (3) and (4) as well. In other words, (3) and (4) cannot profitably be used to demonstrate the properties of the additive particle, because the distinctness effect they show also obtains in the absence of the additive particle. The conversational implicature postulated by Beaver explains the distinctness effect both in (8) and in (3) and (4).3

Second, if the distinctness requirement follows from a conversational ban on uninformative statements, we expect it to be lifted in situations that call for tautologies, such as Logic or Math 101 classes. (9) shows that this correct.

(9)

  • a.

    Surely, if a, b, and c dominate x, then a dominates x, too.

  • b.

    Surely, if all members of A are divisible by x, then the smallest member of A is divisible by x, too.

Third, we can demonstrate that the distinctness requirement is susceptible to what seem to be rhetorical factors.

(10)

  • a.

    The Republicans all voted against the bill, and Senator Blank did, too.

    (cf. Kripke 2009:380)

  • b.

    The Republicans all voted against the bill, so Senator Blank did, too.

(11)

  • a.

    The Republicans all voted against the bill, and Senator Blank did.

  • b.

    The Republicans all voted against the bill, hence Senator Blank did.

Kripke observes that an example like (10a) implies that Senator Blank is not a Republican. Strikingly, the effect disappears when we replace and with so in (10b). This seems impossible to explain on the presupposition account.4 I suspect that the reason is that, while the first clause is used to substantiate the second, the second clause is not uninformative: it serves the purpose of signaling which entailment of the first clause the speaker intends to convey (like a QED). As predicted, the same contrast obtains in the absence of too, as in (11).

So far, I have argued that an anaphoric presupposition is not needed to explain the distinctness effect in (3) and (4), and that the anaphoric approach faces empirical problems in (9) and (10). I will now argue that existing implementations of Kripke’s proposal fail to explain the distinctness effect in (4) that it was designed to explain.

One way of making Kripke’s idea precise is along the lines of Heim 1992 (see also Heim 1990). Heim treats too as though it means ‘in addition to x’, where x is anaphoric; she states (12) as the general rule for the interpretation of too.5

(12)

This explains the distinctness of Herb and the boss in (3) (with Herb as the antecedent of x), but it fails to account for (4). If x is a normal anaphoric element, then nothing should prevent x from being anaphoric to just Herb, or just his wife, in which case the other spouse could be the boss. The same problem attends the implementation in Geurts and van der Sandt 2004 discussed in section 2.6

The problem arises in a slightly different form in Soames’s (2009) interpretation of Kripke’s proposal. Here, anaphoricity applies at the level of the proposition (as suggested earlier in Rooth 1999): the active context must contain at least one proposition that parallels the proposition expressed by the too-clause, except that, in effect, the value of the focused constituent that too associates with must differ from the value of the corresponding constituent(s) in the antecedent(s). More precisely, the clause modified with too must add information to the preceding parallel proposition by virtue of containing a focused associate of too that is distinct from its parallel counterpart.7 It appears that this will allow one to explain (4) by means of the following reasoning. The antecedent of the proposition that the boss will come cannot be the proposition that Herb will come, or the one that his wife will come, since these propositions are not in the active context, even though they are entailed by a proposition in the active context. The only structured proposition present in the active context, and therefore available as an antecedent, is that Herb and his wife will come to the party. Hence, too requires that the boss is disjoint from Herb and his wife. We will see later that this reasoning cannot be maintained (see (26)), but no matter: it is easily defeated by (13).

(13) If Herb comes to the party, and his wife comes to the party, then [the boss]F will come, too.

Like (4), (13) conveys that neither Herb nor his wife is the boss. But this is not predicted by Soames’s interpretation, since even if, say, Herb’s wife is the boss, the proposition that the boss will come has at least one salient parallel antecedent (to wit, the proposition that Herb will come), from which it differs only in the value of the focused constituent. If the requirement imposed by too were anything like normal anaphoricity, such as is found with pronominals, then the tooclause in (13) should ambiguously choose either the first or the second conjunct as its antecedent, and nothing should follow as to whether the subject of the other clause could be the boss.8

One might attempt to solve these problems for Heim’s and Soames’s treatments of (4) by arguing that the anaphoric element cannot pick out just Herb, or his wife, because an anaphoric element (perhaps a fortiori: a covert one) cannot select one conjunct in a coordinate DP. And it is indeed hard to interpret (14) in such a way.

(14) The boys and the girls announced that they would come to the party.

There are several reasons why this solution will not work. First, it would not extend to structures with CP-coordination such as (13): the covert pronominal element in anyone else in (15) can ambiguously take Brad Pitt, or his wife, or the couple as its antecedent, depending on how one understands the situation.9

(15) If Brad Pitt comes to the party, and his wife comes to the party, then no one will want to talk to anyone else.

Second, if some readings of (15) are still less than prominent, they can easily be brought out by adding some pragmatically disambiguating material. This will also work in structures with DPcoordination.

(16)

  • a.

    If my eight-year-old daughter and Bill Clinton go to the party together, then other politicians will surely be jealous.

  • b.

    If my eight-year-old daughter goes to the party, and Bill Clinton goes to the party, then other politicians will surely be jealous.

Rather than having to choose the coordinate DP as its antecedent, and thereby forcing us to accept that my eight-year-old daughter is a politician, the hidden pronominal in other happily selects just one conjunct in (16a); likewise for (16b). Clearly, choosing one member of a coordinate structure as antecedent is not impossible in principle, but merely difficult in examples such as (14) that lack disambiguating information, because both conjuncts are equally topical.10 But if this is the case, then Heim’s presupposition for too stated in (12) fails to account not just for (13), with coordinated propositions, but for (4), with coordinated DPs, as well. Let it be given in the common ground that Herb is the boss; then (12) fails to predict a presupposition failure for (4). Instead, it leads us to expect that the common ground will function as disambiguating information, and will direct us to pick his wife as antecedent for x so that a presupposition failure is avoided, just as in (16).

In this section, I have argued that the distinctness effect in (4) does not supply sufficient grounds for adopting Kripke’s anaphoric treatment of too. The effect is also found in the absence of too, which independently motivates a conversational implicature that explains the effect. This also explains why the effect is defeasible. Finally, existing implementations of anaphoric too fail to explain the distinctness effect convincingly.11 The next section addresses Kripke’s argument on the basis of (2).

2 The Argument from the Active Context Requirement

Recall (2).

(2) #[Peter]F had dinner in New York last night, too.

Kripke argues that the anaphoric treatment of too explains why (2) cannot be used out of the blue (since there will be no antecedent for the anaphor), whereas the mere existential presupposition that previous treatments attributed to too cannot explain this (the presupposition that someone other than Peter had dinner in New York last night would not even need to be accommodated, since it is generally known that many people have dinner in New York every night). In this section, I will argue that Kripke’s observation can be explained as resulting from the independently attested constraint that unfocused material must be Given.

This solution has its origins in yet a third implementation of Kripke’s proposal, which I will briefly outline first. Geurts and van der Sandt (G&vdS) (2004) adopt the Discourse Representation Theory (DRT) approach to presupposition (van der Sandt 1992), according to which presuppositions are anaphors that are preferably bound by accessible elements in the Discourse Representation Structure, and accommodated otherwise (see also Geurts 1999, van der Sandt and Geurts 2001, and references cited). They propose that the clause associated with too bears two separate presuppositions.

(17)

  • a.

    The focused expression is not identical to x, x pronominal (triggered by too):

    [φ . . . α + F . . . ] too presupposes: [x: x ≠ α]

  • b.

    Some x verifies the nonfocused part of the clause (triggered by absence of focus due to the Background Presupposition Rule, BPR):

    [φ−F . . . α+F . . . ] presupposes: [x: φ(x)]

This proposal accounts for Kripke’s two observations in the following manner. (2) cannot be used out of the blue because the first presupposition, (17a), is so attenuated that it cannot be accommodated. The distinctness effect is derived as shown in (18), the DRT analysis of (3). (18a) is the initial representation after resolution of Herb and the boss. By (17a), the consequent presupposes that the boss is distinct from x (double underlining). By (17b), it presupposes that x comes to the party (single underlining). We can resolve x to Herb in the main Discourse Representation Structure, and resolve the second presupposition in the antecedent of the conditional, resulting first in (18b) and finally in (18c) (G&vdS 2004:48, (58)–(60)).

(3) If Herb comes to the party, then [the boss]F will come to the party, too.

(18)

graphic

Technical difficulties apart, it should be immediately evident that this proposal fails on (4) and (13) in the same way as the proposals by Heim (1992) and Soames (2009) discussed above. The anaphor x could resolve to just Herb or just his wife, and then the other spouse could be the boss.

However, I feel there is an important insight to be gained from the manner in which, according to G&vdS, the presupposition stated in (17b) arises. It is not triggered by too. Instead, it is triggered by the focus structure of the sentence that too associates with. The insight that I will be building on is that, just because focus in the too-clause serves to identify the associate of too, this does not prevent absence of focus on the remainder of the clause from having its usual effect on interpretation as well. This point is nicely demonstrated in Schwarzschild’s (2004) review of G&vdS 2004. Consider (19), a variant of his (23) with an additive particle.

(19)

    A:
  • I heard that there are some theories that not only John misunderstood, but Mary as well. So tell me,

    which theory did [Mary]F misunderstand, too?

  • B:

    #[Mary]F misunderstood my theory, too.

In B’s utterance, my theory is not focused. This serves the purpose of allowing too to associate with Mary, which is. At the same time, however, absence of focus retains its usual function, in this case rendering the discourse incoherent because my theory is inappropriately flagged as old information.

For G&vdS, absence of focus on φ triggers a presupposition: namely, that something satisfies φ (their BPR in (17b)). For reasons explained below, I believe this is incorrect. I will take the more traditional view that unfocused material must be ‘‘old information,’’ and I do not take this requirement to be a presupposition (I will return to this issue in section 3). For concreteness, I adopt Schwarzschild’s (1999) constraint that any constituent that is not F-marked must be Given. For our purposes, the definition in (20) will suffice.

(20)

  • Givenness (after Schwarzschild 1999)

  • A constituent that is not F-marked must be Given.

  • A constituent C is Given iff it has an antecedent A that entails it (after replacing all F-marked constituents in C with variables, and raising both C and A to type t by filling any open argument positions with variables, followed by existential closure). Exception: referential expressions are Given iff they have coreferential antecedents.

This condition trivially explains Kripke’s (2). Given that had dinner in New York last night is not F-marked, it requires an antecedent that, after the necessary type-shifting operations, entails ∃x[x had dinner in New York last night]. Absent any previous discourse, (2) is blocked.12 In the well-formed case (1b), drinks is not F-marked, hence in need of an antecedent, which is provided by drinks in (1a): ∃x[x drinks] entails ∃y[y drinks].

If this is correct, then like (3) and (4), (2) is simply not an example that is suitable for examining the properties of too, because it is ruled out for independent reasons. This is confirmed by the fact that (2) remains unacceptable (with the indicated focus structure, and in the given context) when too is removed.13

(21) #[Peter]F had dinner in New York last night.

In light of the evidence in the literature for a constraint like (20),14 it is not clear how we could prevent it from explaining (2).

Several predictions follow. First, we expect that whenever too is allowed, and is not associated with a constituent C, C should be a proper target for processes that depend on Givenness/absence of focus: absence of a pitch accent, phonological reduction (Tancredi 1992), and even ellipsis (if the condition of lexical recoverability is satisfied; see Rooth 1992). This is confirmed by the simple example in (22) and the more subtle examples in (23)–(25).

(22)

  • a.

    Today, Mary passed the exam, and tomorrow, Susan will pass the exam, too.

  • b.

    Today, Mary passed the exam, and tomorrow, Susan will pass the exam.

  • c.

    Today, Mary passed the exam, and tomorrow, Susan will [VP e].

(23)

  • a.

    First Mary insulted my friends, and then she [praised]F my friends.

  • b.

    First Mary insulted my friends, and then she [praised]F my friends, too.

(24)

  • a.

    #First Mary insulted absolutely everyone, and then she [praised]F my friends.

  • b.

    #First Mary insulted absolutely everyone, and then she [praised]F my friends, too.

(25)

  • a.

    #I have ten marbles and you have one. Only nine of mine are transparent. Your marble is opaque, too.

    (Beaver 2001:93n12)

  • b.

    #I have ten marbles and you have one. Only nine of mine are transparent. [Your marble]F is opaque.

(23b) allows the additive particle to associate with the verb, which correctly predicts that (23a) allows absence of a pitch accent on friends (where the pitch accent would land if the object were not Given). Conversely, deaccenting my friends in (24a) is disallowed (it violates Givenness), so too cannot associate with the verb in (24b). Finally, the unacceptability of (25b) shows that Givenness will also explain why too is blocked in Beaver’s (2001:93) (25a), which he takes as a confirmation of Kripke’s anaphoric approach.

The second prediction is that, whenever phonological reduction demonstrates that absence of focus is allowed, too should also be allowed (modulo the other constraints on too: the Informativeness condition of section 1 and the existential presupposition to be discussed in section 3 must be satisfied). There are two cases of interest to consider. First, we know that phonological reduction can be licensed by implicational bridging, as in (26a). We correctly predict that this should license the additive particle in (26b) as well.

(26)

  • a.

    First Mary called me a Republican, and then [Susan]F insulted me.

  • b.

    First Mary called me a Republican, and then [Susan]F insulted me, too.

The same point can be demonstrated on the basis of Kripke’s (2009:380) (27), which is allowed provided that the common ground tells us that to checkmate is one way to defeat (at chess), that Karpov is the challenger, and that Kasparov is the champion.15

(27) If Karpov checkmates Kasparov in the next game, probably the challenger will defeat the champion [in the Berlin game]F, too.

Another special circumstance that allows phonological reduction is the presence in the context of a nonlinguistic antecedent. As Soames (2009) points out, such antecedents license too as well. This is illustrated in (28).

(28) (Context: We observe Mary insulting her husband.)

  • a.

    Yesterday, [Susan]F insulted her husband.

  • b.

    [Susan]F insults her husband, too.

The parallelism between licensing of too and phonological reduction observed in (22)–(28) is straightforwardly predicted by Givenness.

Summarizing so far, I have argued that Kripke’s anaphoric presupposition is not needed to explain the fact that (2) cannot be used out of the blue. This fact also follows from a well-known independently motivated constraint on absence of focus. Taking this as the relevant constraint immediately explains why licensing of too patterns with licensing of deaccenting. I now turn to some examples involving multiple foci that are potentially problematic for both theories of too.

Our discussion so far has not touched on the conditions under which an element can or cannot associate with the additive particle (see, e.g., Reis and Rosengren 1997, Krifka 1998, Rullmann 2003 for discussion), because for the most part these conditions do not bear on the choice between an existential and an anaphoric presupposition. They become relevant, however, when we consider a potential problem for my explanation of (2). I exclude (2) because the unfocused VP violates Givenness. This appears to predict that we could salvage (2) by adding pitch accents in appropriate positions in the VP, marking it as new information, as shown in (29) ( pitch accents indicated with uppercase, and association with superscripts).

(29) PETERi had DINNER in New YORK last NIGHT, tooi.

But (29) is still not allowed out of the blue. This is predicted, furthermore, by Kripke’s approach. Even if VP does not violate Givenness, the postulated anaphoricity of too requires a parallel proposition in the active context that differs from (29) only in the subject, and an out-of-the-blue context does not provide it. Thus, (29) seems to favor the anaphoric approach over the existential one; I will show that this is only apparent.

(29) is an instance of a more general pattern: too cannot associate with Peter because the additive particle, in selecting its associate, cannot ‘‘skip’’ the closest focused element and associate with a focused element further to the left. That is, the pattern in (30a) is blocked, but the pattern in (30b) is allowed.

(30)

  • a.

    *AFi R BF tooi

  • b.

    AF R BFi tooi

Some constraint like this must be adopted, also under the anaphoric theory of too. Consider (31) (note that the indicated judgment applies to the reading where too associates with Peter, while both Peter and firstborn bear a pitch accent; see footnote 16 for other options).

(31)

  • (John knows all my children)

  • #and PETERFi knows my FIRSTBORNF, tooi.

The example has been carefully constructed so that the direct object is not Given (it does not have a coreferential antecedent), but the context nonetheless satisfies whichever presupposition one attributes to too. The point of the example is that both the anaphoric and the existential theory of too incorrectly allow it, unless they are supplemented by (30a). My firstborn obeys Givenness by focusing. If too associates with Peter, then by the anaphoric theory the context must entail a parallel proposition differing only in the associate, and it does: John knows my firstborn (see footnote 15 for details on this calculation). There is a clear contrast between (31) and (32).

(32)

  • (All my children love sushi)

  • and my FIRSTBORNF loves PASTAFi, tooi.

(32) is considerably better than (31). It satisfies the anaphoric and existential theories in the same way, and differs from (31) only in not violating (30a). (30a) explains why (29) is blocked, which removes the potential problem for the existential theory.16

This is not the place to develop an explanation of (30a), but I suspect that the proposal in Büring 2008 comes close to explaining it. Büring proposes that a focus operator must associate with the most prominent focus in its domain; this includes the sentence-level CC (ContextConnect) operator responsible for Givenness. This constraint can only be obeyed in (30a) if CC associates with both A and B, and focus on A is the most prominent. But this seems to violate a further constraint: when CC associates with multiple foci, the rightmost one must be the most prominent.17 Whether this suggestion can be maintained must be left for further research.

The existential and anaphoric theories of too are equally capable of explaining the data discussed so far. But (30) suggests ways of constructing examples that disprove the anaphoric theory. If we can associate too with an adjacent element (as in (30b)) and focus the remainder of the clause so as to avoid a Givenness violation, then the existential theory predicts that it should be possible to use a too-clause out of the blue. One structure that allows us to test this prediction is illustrated in (33).

(33) THISFi, tooi, shall PASSF.

(33) can indeed be used without any previous mention or introduction into the active context of things passing; this cannot be explained on the anaphoric approach.18 Consider also (34).

(34)

  • (Background context: My mother once deciphered Linear A. Active context: empty (beginning of discourse))

  • Did you hear? My MOTHERF has just DECIPHEREDF Linear BFi, tooi.

(34) is allowed by (30), as too associates with an adjacent element.19 Kripke’s theory (in Soames’s formulation) predicts, incorrectly, that (34) is disallowed in the absence of a parallel proposition in the active context. Heim’s (12) incorrectly requires a salient counterpart to Linear B. We will return to examples like (33) and (34) in section 4.

In this section, I have argued that the unacceptability of (2) in out-of-the-blue contexts does not supply sufficient grounds for adopting an anaphoric treatment of too. The effect is also found in the absence of too. It is explained by an independently motivated constraint on absence of focus, Givenness (or some variant thereof ), which is successful in explaining when the additive particle is licensed (notably, by implicational bridging, and with nonlinguistic antecedents), and why its distribution mirrors that of deaccenting and ellipsis. In addition, I have presented some examples that cannot be explained by the anaphoric approach. Before returning to such examples, I will consider whether the constraints discussed so far exhaustively describe the semantics of the additive particle construction.20

3 Too Triggers a Presupposition

If, as I have argued, the semantic and pragmatic effects discussed so far do not arise from a presupposition triggered by too, but from constraints on informativeness and Givenness, then what, if anything, is left for too to contribute? If nothing were left, the interesting conclusion might be that too functions as a lexical realization of Rooth’s (1992) ~ operator. However, this is not the case: we must assume that too triggers a presupposition of its own. To see why, let us return first to G&vdS’s claim that absence of focus triggers an existential presupposition, which combines with the distinctness presupposition triggered by too. Schwarzschild (2004) has already pointed out that G&vdS’s rules for resolving presuppositions incorrectly predict that (35) should be allowed.

(35)

By G&vdS’s BPR (17b), unfocused is staying there triggers an existential presupposition that can be resolved to staying at the Ritz, even though this is embedded under negation. Their presupposition resolution rules must allow this, because phonological reduction and VP-ellipsis are allowed here.

(36) Fred is not staying at the Ritz, and Barney is [VP e].

The following data also show that the additive particle has a more restricted distriLING_a_00184.ex37bution than absence of focus does.21

(37)

  • a.

    If no one else eats a green apple, I will [VP e] (#too).

  • b.

    If no one else eats a green apple, I will eat a green apple (#too).

(38)

  • a.

    If John ate the green apple, he will lose the game.

    Fortunately, Peter did [VP e] (#too).

  • b.

    If John ate the green apple, he will lose the game.

    Fortunately, Peter ate the green apple (#too).

(39)

  • a.

    I don’t think a single woman ate a green apple, but I do think Peter did [VP e] (#too).

  • b.

    I don’t think a single woman ate a green apple, but I do think Peter ate a green apple (#too).

(40)

  • a.

    There is a woman who did not eat a green apple,and there is a man who did[VP e](#too).

  • b.

    There is a woman who did not eat a green apple,and there is a man who did eat a green apple(#too).

The explanation I propose for (35)–(40) is the obvious one. Each too-clause triggers an (existential) presupposition, which remains in need of accommodation. This presupposition is not filtered, even though it is entailed by the clause containing the ellipsis/reduction antecedent, because this antecedent clause is embedded (under negation, etc.), so that the too-clause is not interpreted in a context that has been updated with the antecedent clause.

Several minor conclusions can be drawn from the contrasts in (35)–(40). One conclusion is that there is more to too than the two components admitted by G&vdS: absence of focus on its nonassociate, and a distinctness presupposition. Otherwise, the additive particle should be allowed wherever ellipsis/reduction is allowed (distinctness is satisfied throughout). Another minor conclusion is that the admissibility condition for absence of focus is not in the nature of a presupposition, as advocated by G&vdS (their BPR in (17b)). If it were, it would be a presupposition with quite exceptional projection properties, as it could be filtered by clauses embedded under negation, and so on, unlike other presuppositions, such as the presupposition that, we have now determined, is triggered by too (a similar point is made in Rooth 1999).22

The main conclusion to be drawn from (35)–(40), however, is this: in addition to the Givenness and informativeness constraints identified in sections 1 and 2, we must assume that too triggers a presupposition. As far as the data in (35)–(40) are concerned, this could be either the traditional existential presupposition or Kripke’s anaphoric presupposition.23 While the previous sections have mainly argued that there is no evidence favoring the anaphoric approach, the next section argues that there is evidence favoring the existential approach.

4 Against the Anaphoricity of Too

To summarize, I have shown that independently motivated constraints can explain the observations regarding (2)–(4) that, in Kripke’s view, demonstrated the insufficiency of a weak, existential presupposition for too and the need for a stronger, anaphoric presupposition. It follows that the conclusions based in the literature on the supposed inadequacy of the existential approach, and of a theory of presupposition incapable of incorporating an anaphoric presupposition, can no longer be maintained. This summarizes my central argument.

At the same time, while my counteranalysis of (2)–(4) removes the existing evidence favoring the anaphoric approach, it does not yet logically prove it wrong. Instead, it merely serves to set out the minimum requirements an example must meet to decide between the two approaches. We should consider examples that obey constraints like Givenness and informativeness, and see whether they are allowed in contexts that entail the existential presupposition, but do not provide an antecedent for the anaphoric one. The first example that comes to mind is (41).

(41) ??Peter did not have dinner in New York last night, but John did, too.

I am not sure what makes (41) so awkward (see footnote 18 for a suggestion and discussion of similar examples), but I find the following examples unexceptional (for (43) and (44), see footnote 13):

(42) Dean of students: Do PhD students even have families to take care of ? Student rep.: Yes, PhD students have families, too.

(43) Hey, that kitten has feelings too, you know!

(44)

  • The Russians love their children, too.

  • (Sting, ‘‘Russians’’)

(33) This, too, shall pass.

(45)

  • Guard: I am sorry, small children are not allowed to enter the garden.

  • Child: That’s not fair! I deserve the right to enter the garden, too.

Since these examples can all be used in contexts that do not make a referent for a hidden anaphor available, either linguistically or nonlinguistically, I do not see how they could be accommodated by the anaphoric approach without rendering it vacuous. If one were to claim that some process does make a salient referent available here (perhaps evoked by the example itself ), there would be no explanation for why this referent cannot be accessed by an overt anaphor (#This, too, shall pass, just like that/those things), and why the same process does not render Kripke’s (2) acceptable out of the blue. In combination with examples showing that the distinctness effect is defeasible ((9), (10b), (i) of footnote 4) and that existing implementations of the anaphoric approach do not explain the distinctness effect, and with earlier examples showing that a salient antecedent is not required ((34), (ii) of footnote 18), this constitutes initial support for the additional, though less important, conclusion that the existential approach is superior to the anaphoric approach.24

Notes

I am grateful to Euge`ne Bu¨skens, Tania Ionin, Ora Matushansky, audiences at TiN (Taalkunde in Nederland) 2013 and the Frankfurt Semantics Colloquium, and two anonymous LI referees for insightful comments and useful suggestions. Naturally, all the remaining errors are my own.

1 It is important to bear in mind that Kripke’s argument from the distinctness effect in (3) and (4) bears directly on the difference between an anaphoric and an existential presupposition, not just on the presence or absence of a distinctness requirement in the presupposition. As an anonymous reviewer points out, one might conceivably propose an anaphoric or existential presupposition that does not contain a distinctness requirement, that is, one that merely attributes to a clause φ[αF]too the presupposition φ[x], without requiring that (anaphoric or existentially bound) x be distinct from α, the associate of too. No presupposition of this type (be it anaphoric or existential) would explain the distinctness effect in (3) and (4). However, adding a distinctness requirement does not necessarily explain the distinctness effect: Kripke’s argument is that an existential presupposition cannot explain the distinctness effect in (4) even if the presupposition does contain the distinctness requirement that x ≠ α. I accept this argument, and I will propose that the distinctness effect is explained by some other constraint, so that an existential presupposition is enough. See footnote 23 for examples that suggest that the existential presupposition of too nonetheless should contain a distinctness requirement.

2 In addition, examples like (i) apparently demonstrate that the distinctness requirement should be allowed to apply at the level of aspects of individuals (Landman 1989).

(i) Chomsky as a mathematician is interested in strong generative capacity, and Chomsky as a linguist is too, but Chomsky as a political activist is not.

3 (8c) can perhaps be salvaged by a scenario similar to the ones that allow (6) or (7), but in this case, adding too is also possible.

4 As an anonymous reviewer observes, the relevant reading for (10b) may be masked by the alternative interpretation that Blank is a Democrat who habitually votes with the Republicans. (i) suppresses this reading by replacing Blank with a known Republican, clearly bringing out the intended reading that violates the supposed anaphoric distinctness presupposition (in fact, my informants prefer the presence of too here).

(i) The Republicans all voted against the bill, so obviously Mitt Romney did, too.

5 I assume that the nonidentity clause in Heim’s (12) should be read as a distinctness or nonoverlap clause. Otherwise, it would immediately and trivially fail on (4) and other examples where the associate of too is singular and its counterpart plural; similarly for (17a) below.

6 A separate problem that attaches to this formulation, but not to Soames’s discussed below, is that it cannot allow the type of discourse in (i), since nothing guarantees the salience of a discourse referent consisting of all runners in the New York marathon except John.

(i)

  • A:

    I hear that over 10,000 people ran the New York marathon.

  • B:

    Yeah, I know, John was there, too.

7 A separate problem that attaches to this formulation, but not Heim’s, is that it does not explain the contrast in (i).

(i)

  • a.

    Several women came to the party, and John came to the party, too.

  • b.

    #Not a single woman came to the party, and John came to the party, too.

In both cases, the clause modified by too ‘‘adds information.’’

8 This is so, since either conjunct in the antecedent clause can satisfy the presuppositions of the consequent, as (i) demonstrates.

(i)

  • a.

    If Herb stays home and his wife comes to the party, then the boss comes, too.

  • b.

    If Herb comes to the party and his wife stays home, then the boss comes, too.

9 For readers who are not familiar with the characters in this example: Brad Pitt is a Hollywood celebrity, and so is his wife.

10 The same point can also be illustrated with the hidden pronominal in someone else in examples like (i).

(i) John and Mary came to the party together, but he went home with someone else.

11 The descriptively most successful interpretation of Kripke’s proposal is suggested by the definite plural I have italicized in this passage from Kripke 2009:373:

When the focused element is a singular term, it is presupposed to be noncoreferential with the other corresponding elements in the parallel clauses or other bits of information in the (active) context.

In order to deal with (13), we require that the focused constituent is distinct from the corresponding constituent in all accessible parallel propositions. In order to deal with (2), we require that there is at least one parallel proposition. This leaves us with an ‘‘anaphor’’ that takes each and at least one potential antecedent as its antecedent. This is so much unlike any other form of anaphora, except in the most general sense, that attempting to align too with pronominals, as per Kripke’s suggestion, is not likely to provide much insight. Rather, the ‘‘each and at least one’’ condition suggests that more than one constraint is at work. The ‘‘each potential antecedent’’ part is explained by the conversational implicature discussed in this section; the next section attributes the ‘‘at least one’’ part to Givenness.

12 This explanation is based on the fact that the antecedent for Givenness cannot be accommodated. We can demonstrate this independently with the contrast in (i). Whereas we can use (ia) out of the blue, and accommodate that John has keys, the same accommodation will not render John’s keys Given; witness (ib). This explains the observations that caused Kripke to conclude that too requires an antecedent in the active part of the context.

(i)

  • a.

    John has lost his KEYS.

  • b.

    #John has LOST his keys.

Incidentally, this fact is problematic for G&vdS’s BPR (17b), which attributes to Givenness the status of a presupposition: if absence of focus on his keys in (ib) triggers an existence presupposition, why is it more difficult to accommodate than in (ia)?

13 The similarity between the cases extends to the exceptions. If a topic is sufficiently important and often discussed, the speaker can sometimes get away with pretending that it has recently been mentioned. For instance, in the midst of an economic collapse, one could start a conversation with (i), both with and without too (see Geurts 1999:85 for a similar example). I imagine that a sufficiently contrived scenario could render (2) and (21) acceptable, too.

(i) Did you hear? Now [Deutsche Bank]F has filed for bankruptcy (too)!

It is not impossible that in some examples unlike (2), an element might be focused without associating with too, in violation of (30a) below, in which case I expect it would not require an antecedent. See (43) and (44) below for further examples.

14 See Spathas 2010 for an overview of the literature.

15 The fact that my approach makes the correct predictions here without additional assumptions speaks in its favor. Whether these data also constitute a counterexample to the anaphoric theory of too depends on its exact formulation: the prediction can be tweaked either way. While Kripke points out the identities and inclusion relations necessary for examples like (27), he does not present a theory about which relations are required, and under which conditions: ‘‘It remains a project to characterize syntactically when we have inclusions and when converse inclusions’’ (p. 384). One way of stating the anaphoric theory is to require that the too-clause be parallel, in a sense to be made precise, to a proposition that is actively focused on. In this case, in order to explain examples like (26b), and also (i), the definition of parallelism should invoke the notion of entailment, but only in one direction (see (ii)). If the relation is one of anaphora, this does not follow automatically.

(i)

  • (i) John is reading a book, and Peter has his eyes open, too.

  • (ii) #Peter has his eyes open, and John is reading a book, too.

Another option is to require a stricter form of parallelism, but not necessarily to a proposition that is actively focused on; it could be enough for the too-clause to be parallel to a proposition that is merely entailed by one that is actively focused on. This basically repeats the definition of Givenness in the statement of the presupposition supposedly triggered by too, and does not seem any closer to the anaphoricity favored by Kripke.

16 A full account of the association properties of too must consider further options for (31). It can be somewhat improved by not accenting firstborn, even though this leads to a mild violation of Givenness. This confirms that the problem lies in a violation of (30a). (31) also improves somewhat when too associates with both focused elements, which raises the question of why (29) and (31) are not fully acceptable on this reading (an issue that arises both for existential and for anaphoric theories, at least in (31)). This is also an instance of a general pattern: Krifka (1998) observes that too can associate with only one focus. Another option, marginally available, is that the entire proposition functions as the associate, as in (i).

(i) (What an awful day! First, my sister broke my laptop) and now, a BURGLAR has stolen the STEREO, too.

It is unclear how either the anaphoric or the existential theory could explain any restrictions on this usage.

17 This is not quite how Büring phrases the constraint: his IP-HEAD-RIGHT is violable and requires that the rightmost stress in IP is the most prominent. Independent evidence that my formulation is to be preferred comes from examples like (i) (from Büring 2008:21, (44)).

(i) (Philippe will buy only FRENCH cheese.—Same here:) I only buy GERman BEER.

CC associates with both German and beer; only associates with German. The observation is that an intonation break is required after German, so that the more prominent focus, beer, is removed from the domain of only. The original formulation does not explain why a structure without the intonation break and with the nuclear pitch accent on German is blocked (violating IP-HEAD-RIGHT). I must leave for future research the question of how (30a) and (i), and the proposal based on Büring 2008, can be reconciled with the data in Katz and Selkirk 2011 (which do not, however, include cases involving the additive particle).

18 An anonymous reviewer points out that not every example with the structure of (33) is acceptable out of the blue.

(i) #SAM, too, is having DINNER in NEW YORK.

I suspect that an additional factor is involved here. Since too does not affect the assertion, but only adds an existential presupposition, I presume that the function of too must be to highlight the fact that the context admits this presupposition. If so, too would tend to be unacceptable unless the hearer can figure out why the presupposition is being highlighted. I feel examples like (i) can be made acceptable by facilitating this process.

(ii) Sam used to be really poor, which made him feel ostracized and lonely. But now that Sam has struck it rich, he no longer feels alone. Now he too can drive a Mercedes, and have dinner in fancy restaurants in New York.

The same reasoning also explains (iii), offered by the same reviewer.

(iii) #Who had dinner in New York last night? PeterF had dinner in New York last night, too.

In any case, my approach correctly predicts that (33) is acceptable, and it allows room for an additional explanation of (i); it is unclear how the anaphoric approach could be modified to explain (33) or (ii). See section 4 for further examples.

19Deciphered can also remain unaccented and integrate with its direct object; then too associates with the VP. This option is also not explained by the anaphoric theory.

20 Given the discussion in this section, it is tempting to try to derive the distinctness effect discussed in section 1 from Givenness, as well. Perhaps the boss in (3) must be distinct from Herb, because the boss must not be Given, because it is F-marked? But this does not follow from (20), which is unidirectional, and rightly so. The boss can be Herb in (i).

(i) Herb came to the party. Peter had a drink, and [the boss]F did, too.

The idea also fails on (ii) and (iii).

(ii)

  • a.

    If Johni comes to the party, I will be so happy. And if Peter comes to the party, I’m pretty [sure]F hei will.

  • b.

    If John comes to the party, I will be so happy. And if Peter comes to the party, I will [kiss]F John.

(ii)

  • a.

    If John comes to the party, I will be so happy. And if Peter comes to the party, then John will come, too.

  • b.

    If John comes to the party, I will be so happy. And if Peter comes to the party, then the boss will come, too.

The second occurrence of John (he) in (ii) behaves as Given for F-marking, even though the antecedent is embedded in the protasis of the preceding conditional sentence. In the same context, too in (iii) does not impose distinctness between John/the boss in the second clause and John in the first clause (as correctly predicted by Kripke’s and Beaver’s approach). Hence, distinctness is not imposed by Givenness.

I do not exclude that the distinctness requirement could be derived from Krifka’s (1998) proposal that the associate of too is a contrastive topic (see also Rullmann 2003). I will not explore this possibility here.

21 Note that I am not using the # sign to denote unacceptability; rather, I use it to indicate a remaining (unfiltered) presupposition, requiring additional context.

22 G&vdS cite observations from Zeevat 1992 that appear to show that the presuppositions carried by a too-clause project in such a way that they can indeed be satisfied by embedded propositions.

(i) John believes that Mary was in Egypt. Sue was there, too.

However, (ii) suggests that (i) only works to the degree that undisputed belief reports tend to enter the reported belief into the common ground.

(ii) #John believes that Mary was in Egypt. She actually wasn’t, but Sue was there, too.

Likewise, (iii) only apparently supports G&vdS’s proposals: too is acceptable, but only on a modal subordination reading of the second sentence ((iii) does not entail that Peter’s coming to the party will make me ecstatic regardless of whether John comes).

(iii) If John comes to the party, I will be happy. And if Peter comes to the party, too, I will be ecstatic.

23 Following up on footnote 1, there is some evidence that the presupposition triggered by too contains a distinctness requirement. (i), provided by an anonymous reviewer, can only be blocked if this requirement is in place. Likewise for (ii).

  • (i) Who won the race? #Peter won the race, too.

  • (ii) John likes fish, and nobody else does. But because John likes fish (#too), we always have to pass by the fish shop.

Hence, I tentatively assume that φ[αF]too presupposes ∃x[x ≠ α & φ[x]].

24 I remain agnostic for now regarding the validity of existing arguments for the anaphoricity of other items touched on by Kripke (again, stop).

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