Biased modality and epistemic weakness with the future and MUST: nonveridicality, partial knowledge Anastasia Giannakidou and Alda Mari University of Chicago and Institut Jean Nicod, CNRS/ENS/EHESS 1 Epistemic future and MUST: Dutch, Greek and Italian The question of whether the notional category 'future' in natural languages is a tense or modality has received a lot of attention in linguistic semantics, and it seems inescapable to conclude that the semantics of future involves a modal component (e.g. see Bertinetto, 1979; Enç 1996, Copley, 2002; Squartini, 2004; Kaufmann 2005; Mari, 2009,2010,to appear, Klecha 2014, Giannakidou 2012, Giannakidou and Mari 2012a,b, Broekhuis and Verkuyl 2014). Even a purely temporal analysis such as Kissine 2008 posits epistemic modality with the future. Future words, often and in many languages, exhibit purely modal readings. Consider as an initial example the English modal verb will. (1) a. The French will be on holiday this week. b. As far as I know, oil will float on the water. (Haegeman 1993) The sentences here make no reference to the future, but seem to convey epistemic modality, e.g., given what I know, the French are on holiday this week. Modal uses for will are common (see Palmer 1987, Tsangalidis 1980), and likewise for future expressions in other European languages- e.g. they have been observed in Dutch (Broekhuis and Verkuyl 2014), German, Greek and Italian. Broekhuis and Verkuyl treat the Dutch future verb zullen as an epistemic modal expressing that the prejacent proposition is the result of reasoning based on information that judged as 'reliable and well-founded'. They go on to say that when using zullen 'the speakers feel sufficiently confident to say p is true at n [now] or is to be made true at i [later than now]. This confidence relies on information judged as reliable and well-founded. It may take all sorts of form dependent on the situation: as a hypothesis, a confident expectation, a reassurance, etc. What these circumscriptions have in common is that the speaker has entrance to sufficiently many worlds to be able to pick out the ones that seem convincing.' (Broekhuis and Verkuyl ibid.: Conclusions). This passage renders Dutch zullen akin to a purely epistemic modal like must, as noted in Giannakidou 2014 and illustrated below: (2) Context: Hein I zal can't (wel) see in Hein. de/op see zijn. 'He must be at sea (swimming/on a boat).' (3) Context: I know for sure: #Hein zal in de/op see zijn. 1 #Hein must be at sea. #Hein ist wohl auf Zee. We see here that zullen is being used epistemically, as an equivalent to must. We also see that a modal particle can be used wel, wohl in German (Zimmernann 2011) to convey this meaning equivalent to must. Though the inference that Hein is at sea is drawn based on 'reliable and well-founded' information (as Broekhuis and Verkuyl put it), if the speaker actually knows that Hein is at sea, she cannot use zullen or must. Zullen, importantly, receives purely epistemic readings also with past tense, as shown below (example from Giannakidou 2014, attributed to J. Hoeksema): (4) A: He is so grumpy. Hij zal wel slecht geslapen hebben! 'He must have slept really bad!' (5) #He will have slept really bad. Epistemic zullen, like must, allows an epistemic reading with a past, but will with the past appears to force future shifting.1 We will call this must-equivalent use of the future 'epistemic future', and modal particles such as wel, wohl will be thought on a par (Giannakidou 2014). Here is the puzzle they all present: must, epistemic future, and wel, wohl are used to convey 'strong' statements, products of reasoning that the speaker does; at the same time, they are all incompatible with full knowledge of the proposition, thus making weaker statements than unmodalized assertions. In this paper, we study the Greek and Italian future morphemes in their epistemic readings. Data from these languages, though relatively well known in mostly descriptive and typological works (Rocci, 2001; Squartini, 2004; Pietrandrea, 2005, Mari, 2009,2010; Giannakidou and Mari, 2013a, Tsangalidis 1998, Chiou 2012), are not very well known or widely discussed in the formal semantics literature, in contrast to English. Unlike will, which is a modal verb, the future markers (which we call FUT in this paper) in Greek and Italian are a bound morpheme (Italian) and a particle (Greek). Their use as epistemic futures is quite widespread, and appears with both past and non-past. Epistemic future also associates with the imperfective aspect, as we see in Greek, and the progressive in Italian (6-b): (6) a. I the Ariadne Ariadne tha FUT troi eat.imperf.non-past3sg tora. now 'Ariadne must be eating now' b. Giacomo Giacomo ora now starà FUT.be.3sg mangiando. eating. 'Giacomo must be eating now' (7) a. I the Ariadne Ariadne tha FUT ine be.3sg.nonpast arrosti sick (ji'afto (for-this dhen not ine is edo). here) 'Giovanni must/#will be sick (that's why she's not here).' b. Giovanni Giovanni sarà FUT-be.3sg malato. sick. 1It must also be noted that there is considerable variability in judgements among native English speakers, and some accept purely epistemic readings of will, as in the Greek and Italian cases above. We have also encountered speakers that accept epistemic will with past adverbs. It remains true, however, that although the Greek and Italian epistemic futures are unexceptional and widely attested, purely epistemic will is harder to find, and its existence has been contested in the literature (see e.g. Copley 2002). Another relevant fact is that in English there is competition between will and must but in Greek and Italian, MUST equivalents can co-occur with FUT (Giannakidou 2012, Giannakidou and Mari 2013). 2 'Giovanni must/#will be sick (that's why he's not here).' (8) a. I the Ariadne Ariadne tha FUT itan be.past.3sg arrosti sick xthes yesterday (ji'afto (for-this dhen not irthe). came.3sg 'Ariadne must/#will have been sick yesterday (that's why she didn't come).' b. Giovanni Giovanni sarà FUT.be.3sg stato been malato sick ieri. yesterday. 'Giovanni must/#will have been sick yesterday (that why he didn't come).' (9) a. I the Ariadne Ariadne tha FUT milise talk.past.3sg xthes. yesterday. 'Ariadne must have spoken yesterday.' b. Gianni Gianni avrà have.fut.3sg parlato spoken ieri. yesterday. 'Gianni must have spoken yesterday.' The past sentences contain the adverb meaning yesterday which makes it clear that the reading is not about the future. The reading we get is, to all intends and purposes, equivalent to epistemic must, and it is, as we said, fully productive. The predictive future of FUT is illustrated below: (10) a. Gianni John arriverà arrive-FUT.3sg domani. tomcorrow. 'John will/#must arrive tomorrow.' b. O The Janis John tha FUT ftasi arrive.nonpast.perf.3sg avrio. tomorrow. 'John will/# arrive at 5pm/tomorrow.' Here we observe the expected reading of prediction, which involves metaphysical modality; we will not discuss it here, as it has been discussed elsewhere (Giannakidou and Mari, 2013, 2015). Regarding the epistemic reading, as with must, the speaker has a strong attitude that the proposition is most likely true, but at the same time, she does not know that p is actually true. This is why she chooses to add the FUT. This difference becomes particularly obvious if we compare the FUT/MUST sentence with unmodalized ones, in both Greek (a sentences) and Italian (b sentences): (11) a. I Ariadne ine/itan arosti, #ala dhen ime ke endelos sigouri. b. Giacomo è malato, #ma non sono sicura. 'Ariadne/Giacomo is/was sick, #but I am not entirely sure.' (12) a. I Ariadne tha ine arosti, ala dhen ime ke endelos sigouri. b. Giacomo sarà malato, ma non sono sicura. 'Ariadne must be sick, but I am not entirely sure.' In the unmodalized present and past sentences, the speaker is fully committed to the truth of the sentences by asserting them. By asserting that Ariadne and Giacomo were sick, the speaker knows that Ariadne and Giacomo were sick, hence a continuation that questions this knowledge is impossible because it would attribute to the speaker inconsistent knowledge. The epistemic future, on the other hand, is fine with I am not entirely sure. The sentences indicate an epistemic state where the speaker considers a proposition very plausibly to be true while not being fully certain about it. This is in contrast to the positive unmodalized assertion where the speaker has 3 no doubt that p is true in the actual world, and we thus get a Moore effect. We can impressionistically describe this difference, following Kartunnen 1972, by saying that the future/must sentences are 'weaker' than the unmodalized assertion. Below, we give examples in Greek and Italian with the equivalents of must illustrating the same thing (in Greek prepi takes a subjunctive na-complement, like all modal verbs; Giannakidou 2009): (13) a. I the Ariadne Ariadne prepi must na subj troi eat.non-past3sg tora, now alla but den not ime am ke and endelos totally sigouri. certain b. Giacomo Giacomo deve must star be mangiando eat-gerund #ma but non not sono am sicura. certain . 'Giacomo/Ariadne must/will be eating now, but I am not entirely sure.' (14) I the Ariadne Ariadne prepi must na subj milise talk.past.3sg xthes, yesterday, alla but den not ime am ke and endelos totally sigouri. certain 'Ariadne must have spoken yesterday, but I am not entirely sure.' (15) a. Giovanni Giovanni sarà FUT-be.3sg stato been. malato, PERF. ma sick, non but sono not totalmente am sicura. totally certain. b. Giovanni Giovanni deve must.3sg essere be stato bee, malato, sick, ma bit non not sono am totalmente totally sicura. certain. 'John must have been sick, but I am not entirely sure.' The sentences with MUST, and the sentences with epistemic FUT are equivalent in speaker's intuitions. (We will be using MUST for the equivalents of must crosslinguistically, including, of course, must itself). They seem to be strong, but at the same time they are weaker than unmodalized assertions in that they are compatible with "I am not entirely sure". FUT and MUST can actually combine (Giannakidou 2012). The reading remains the same: (16) I the Ariadne Ariadne tha FUT prepi must na subj milise talk.past.3sg xthes. yesterday. 'Ariadne must have spoken yesterday.' (17) Giacomo Giacomo dovrà must-FUT.3sg aver have parlato spoken ieri. yesterday. 'Giacomo must have spoken yesterday'. Giannakidou 2012, and Giannakidou and Mari 2013, 2015 characterize this co-occurence as modal concord (Huitink 2014 for a recent overview and references). Given the epistemic FUT and the parallel with MUST, it becomes very appealing to argue that the epistemic future is an epistemic modal akin to must, and this what we pursue here, following our earlier works.2 The current debate in the literature recruits the terms 'weak' and 'strong' (see von Fintel and Gillies 2010), but we find these labels unsatisfactory. In our work here, we will argue that universal modals appear 'weak' because, like all modals, they are nonveridical (Giannakidou 1998, 1999; Beaver and Frazee 2011). We will define two kinds of (non)veridicality- objective and subjective (relying on epistemic commitment; for a first approach see Giannakidou 1994, 1997). All modals are nonveridical objectively because they do not entail actual truth; and they are nonveridical subjectively because they do not entail knowledge of p by the speaker. At the same time, universal modals are biased modals: they entail p in the Best worlds, and this is what makes them appear strong. Our discussion, finally, implies that the category 'modal' is 2In previous works we argued that the epistemic interpretation holds with both statives and eventives (and more precisely with perfective non-past in Greek), an issue that we do not discuss here. 4 primarily a semantic category, not specifically tied to the morphosyntatic category 'modal verb'. This is an important conclusion when we consider the larger cross-linguistic picture. The discussion proceeds as follows. In section 2, we present the notions of veridicality, nonveridicality, epistemic weakening and biased modal that we will use for the analysis of FUT and MUST. In section 3, we discuss evidentiality and partial knowledge, and in section 4 we deal with implications of our analysis when it comes to apparent Moore paradoxical effects. 2 FUT and MUST: non-veridicality, bias In this section, we present the notions of veridicality and nonveridicality that serve as the foundation for our analysis of modality. After we clarify the core notions, we define epistemic weakening as commitment weakening of the speaker, i.e. the creation of a nonveridical epistemic space (Giannakidou 2014). Commitment weakening is decisive also for the analysis of subjunctive mood, as illustrated in Giannakidou this volume, and we refer to that paper for more on that topic. 2.1 Veridicality and Nonveridicality Montague 1969 uses 'veridicality' to characterize sentences with direct perception verbs such as see (see Giannakidou 2013a for a formal connection between truth and existence in relative clauses and with progressives). Authors have also used other labels, e.g. factivity, factuality to refer to veridicality (Kartunnen 1971, Kartunnen and Zaenen 2005, Kiparksy and Kiparsky 1970), as well as actuality (Bhatt 2006, Hacquard 2010). Veridicality in this second use is understood objectively as truth in the actual world: a sentence is veridical if the proposition it denotes is true in the actual world (Egré 2008). Zwarts 1995 and Giannakidou 1994, 1997 define veridicality in terms of entailment as a property of expressions F such F entails the truth of its complement p: (18) Def 1. Objective veridicality. (based on Zwarts 1995, Giannakidou 1997, 1998, 1999). A F be a monadic sentential operator. The following statements hold: F is veridical just in case Fp→ p is logically valid; otherwise F is nonveridical. Functions that have veridicality and nonveridicality are propositional functions (but see Bernardi 2001 for type-flexible definitions). F is veridical iff Fp entails p, i.e. if whenever Fp is true, p is true too. F is nonveridical if Fp does not entail p, i.e. if when Fp is true, p may or may not be true. Note that nonveridical operators do not entail the falsity of p; this is a property of anti-veridical operators such as negation (Giannakidou 1998, 1999, 2013). We call nonveridicality under this definition objective, because it does not make reference to parameters other than the propositions and the functions. There are no subjective parameters such as what individuals think or believe, though these will be needed for the treatment of modality and mood (see below). For now, consider that if a verb such as know is our function F, know p, if true, entails p, know is therefore veridical. But if want is the F, want p, even if it is true, does not entail p, therefore want is non-veridical. Negation, is also nonveridical, because not p does not entail p. Objectively, veridicality appears close to factivity and actuality, and characterizes operators such as know which imply truth in the actual world. The sentences under the veridical or nonveridical operator can be called veridical and nonveridical too. Consider now temporal operators, such as past and present. Veridicality now has to be relativized with respect to the utterance time, as suggested in Giannakidou 2002, and can be 5 defined as follows (Giannakidou 2002 (23)): (19) Def. 2. Veridicality of temporal operators. Let F be temporal function, t an instant or an interval. F is veridical iff , if Fp is true at a time t, it entails that p is true at a (contextually given) time t′ ≤ t; otherwise F is temporally nonveridical. (20) If a sentence of the form PAST(p) is true at tu, then it entails that p was true at a time prior to tu. (21) If a sentence of the form PRES(p) is true at tu, then it entails that p is true at tu. Temporal veridicality is objective veridicality because the time of evaluation is an objective parameter and not a subjective one. Present and past, as we see are temporally veridical. The future is clearly not, by the definition above, since FUT p does not entail that p is true at a time prior or equal to tu. Moving now to modals, Giannakidou, and Beaver and Frazee 2011 present nonveridicality as a defining property of the category modality. Consider: (22) Nicholas might/must bring dessert. (23) Nicholas might/must have brought dessert. Nicholas bringing dessert is not, and cannot, be an actual fact under a modal. Logically, possibly p does not entail p. And must is also non veridical, since must p does not entail that p either. MUST does not validate the veridicality principle T that holds knowledge and aleithic modality (see Giannakidou 1998, 1999). As de Marneffe et al. 2012 put it: declaratives like Ariadne left convey firm speaker commitment, whereas qualified variants with modal verbs or embedded sentences imbue the sentence with uncertainty (deMarneffe 2012: 102). Similarly, Trnavac and Taboada 2012 use modals as nonveridical markers of uncertainty. Objective veridicality appears equivalent to actuality, but veridicality is often also discussed in the context of commitment. The speaker is said to be "fully committed" to the truth of an unmodalized sentence in the present or simple past, but is not fully committed in the case she uses a modal. Therefore, when we talk about the truth of a sentence, we talk about it in two ways: objectively, by appealing to what is the case in the actual world at a time, and subjectively by appealing to speaker's commitment to the truth of the sentence. Giannakidou tries to capture the connection between veridicality and speaker commitment, by making the veridicality judgement relative to individual anchors. The truth of a sentence is now anchored to the individual asserting it. In main clauses the anchor is by default the speaker.3 Giannakidou defined models of evaluation to describe the information states of anchors. These models are sets of worlds, relative to i, corresponding to what i believes or knows.4 We call these models epistemic states in our definition below: (24) Def. 3. Epistemic state of an individual anchor i (Giannakidou 1999: (45)) 3Individual anchoring of truth should be seen on a par with other kinds of anchoring of propositional content, i.e. temporal anchoring, or event anchoring (e.g. Hacquard 2010). The individual anchor is a parameter of evaluation similar to Lasersohn's (2005) judge. In embedded sentences, the main clause subject is also a potential anchor and this has repercussions for mood, as shown in Giannakidou's work. 4The difference between knowledge and belief is not so important for our purposes here, and in many other cases, e.g. for mood choice, it doesn't matter either-as verbs of knowledge and belief both select the indicative in many languages. Belief makes a difference for an agent typically when it is contrasted with knowledge, i.e. when the agent is aware that she doesn't have enough information to support a proposition. In this case, we can say that we have semantic narrowing (Geurts and van Tiel 2013). 6 An epistemic state M(i) is a set of worlds associated with an individual i representing worlds compatible with what i knows or believes. Given the epistemic state, we can now identify (non)veridicality subjectively. Truth is defined with respect to knowledge (and belief): (25) Def. 4 Subjective veridicality A function F that takes a proposition p as its argument is subjectively veridical with respect to an individual anchor i iff Fp entails that i knows or believes that p is true. This means that i's epistemic state M(i) is such that: M(i) ⊆ p. It follows that ∀w[w ∈ M(i) → w ∈ {w′|p(w′)}]. i knows/believes p, i is fully committed to p. Consider the following unembedded case: (26) O The Giannis John kerdise won.3sg to the agona. race. 'John won the race.' (27) a. John won the race. b. [[ John won the race ]]M(speaker) = 1 iff ∀w[w ∈M(speaker)→ w ∈ {w′| John won the race in w′}] If the speaker asserts John won the race, she must believe or know that John won the race, hence all worlds in M(speaker) are John-won-the race worlds: M(speaker) ⊆ p. The unmodalized sentence is therefore equivalent to the speaker knowing p. The indicative is therefore the mood that conveys homogeneity of a modal space M(i) as being a p space. This is useful also when we think of the direct evidential where it is simply an unmarked past or present. The simple past or present draws on "direct" evidence in the sense that it gives the more reliable, undisputed knowledge. In the absence of indirect evidential, all worlds in M(speaker) are p worlds. Subjective nonveridicality, on the other hand, is epistemic uncertainty (or non-commitment): it indicates that the speaker does not know for sure that p is true. In this case, the epistemic state only intersects with p, and therefore contains worlds where p is not true: (28) Def. 5. Subjective nonveridicality A function F that takes a proposition p as its argument is subjectively nonveridical with respect to an individual anchor i iff Fp does not entail that i knows or believes that p is true. This means that i's epistemic state M(i) is such that:M(i)−p 6= ∅. From Def. 5, it follows that ∃w′ ∈M(i) : ¬p(w′). Hence, a subjectively nonveridical function imposes non-homogeneity on the epistemic state, since there is at least one non-p world. Modals are objectively nonveridical, as mentioned earlier, but also subjectively. A speaker asserting MUST/MAY p has, in her epistemic state, non-p worlds. Modals and the FUT are objectively nonveridical, as mentioned earlier, but also subjectively: the modal bases (which are subsets of M(speaker) have a p and a not p space, and M(speaker) likewise is partitioned into p and not p worlds. Like us, Condoravdi 2002 also acknowledges the nonveridicality of modals in her diversity condition that requires that there be one not p world in the modal base. Subjective veridicality can thus be extended to characterize the epistemic states themselves. A veridical epistemic state is a non-partitioned, homogenous epistemic state. A nonveridical epistemic state, on the other hand, is a space partitioned into p and ¬p worlds. (29) Def. 7 Veridical, nonveridical epistemic states and commitment 7 a. An epistemic state (a set of worlds) M(i) relative to an individual anchor i is veridical with respect to a proposition p iff all worlds in M(i) are p-worlds. (full commitment). b. If there is at least one world in M(i) that is a ¬p world, then M(i) is nonveridical (weakened commitment, uncertainty). c. If all worlds in M(i) are¬pworlds, then M(i) is antiveridical (counter-commitment). A veridical epistemic state is a non-partitioned, homogenous epistemic state, a state of full commitment. A knowledge state is veridical; as we said, umodalized sentences in the past reveal veridical states. A nonveridical state M(i), on the other hand, is defined as one that contains at least one ¬p world. It is a non-homogenous, partitioned state; it allows uncertainty, and in this case we talk about weakened commitment. All epistemic modals convey weakened commitment, and states of indirect evidentials are also nonveridical (as discussed in Giannakidou and Mari 2015). Importantly, with modals, weakened commitment and nonveridicality arise because the modal base is ordered, and p is true only in the Best worlds conforming to the ordering source (Portner 2009). Modal ordering creates nonveridical spaces generally. When all the worlds are ¬p, the state is antiveridical, as with negative and counterfactual assertions, which express counter-commitment of the anchor. Antiveridicality characterizes generally non-assertion, i.e. optative and imperative sentences, since at the issuing of optative and imperative p clearly doesn't hold, and some may be invitations to bring about p (e.g. the imperative). Counter-commitment and weakened commitment are non-commitment to p, though only weakened commitment operators carry uncertainty. From the epistemic domain, we can move to generalize veridicality and nonveridicality to all kinds of modal spaces (sets of worlds), including various kinds of modal bases. Veridicality and nonveridicality are now properties of modal spaces: (30) Def. 8. Veridical, nonveridical modal spaces a. A set of worlds M is veridical with respect to a proposition p iff all worlds in M are p-worlds. (Homogeneity). b. A set of worlds M is non veridical with respect to a proposition p iff there is at least one world in M that is a ¬p world. (Non homogeneity). c. A set of worlds M is antiveridical with respect to a proposition p iff M and p are disjoint. Veridical spaces are homogenous whereas non veridical spaces are non-homogenous. All modal bases are non veridical spaces in this sense, since they are partitioned by their ordering in the Kratzerian semantics (see also Portner 2009, and Condoravdi's 2002 diversity condition that we mentioned earlier). Likewise, bouletic and deontic domains are nonveridical since they are also ordered. Ordering (Kratzer, 1981/1991) creates a partition, therefore necessarily a nonveridical modal space. (Anti-veridical states, on the other hand, are homogenous. A typical such example is the model of the speaker when interpreting a negative sentence.). Given nonveridical spaces, we must distinguish the cases in which we have ordering sources (Kratzer, 1981,1991; Portner, 2009) from those in which we do not. Ordering sources characterize stronger modals such as must. With Portner we define ordering sources and Best worlds. (31) Def. 9 Ordering of worlds Portner, 2009, p.65. For any set of propositions X and any worlds w, v : w 6X v iff for all p ∈ X , if v ∈ p, then w ∈ p. (32) Def. 10. Best worlds as per X . BestX : {w′ : ∀q ∈ X(w′ ∈ q)} 8 Now we define Support Set: (33) Def. 11. Support Set of a proposition p. In a nonveridical modal space M , the support set W ⊂M of a proposition p is the non-singleton set of worlds that rank as Best, and is such that all worlds w' in W are p-worlds. Given the notion of support set, we can now define projected truth with respect to that set. (34) Def. 12. Actual truth. p is actually true iff p is true in the actual world. (35) Def. 13. Projected truth. p is projectively true iff p is true in all the worlds of the support set W : W ⊆ p. In other words, a nonveridical modal spaceM supports a proposition if the there is a support set W for the proposition inM . Since the support set is the set of Best worlds, this structure reveals a bias towards Best worlds. Modals that come with support sets, such as MUST and FUT are nonveridical, like all modals, but are biased. We thus define the new category of biased modals: (36) Def. 14. Biased modals. A modal operator F is biased if its modal base M contains a support set W ⊂M : W ⊆ p. We can think of the support set as the inner domain of the modal F, and the modal base as its outer domain. In this structure, it becomes clear that strength does not mean that the modal entails actual truth (veridicality). Rather, the biased modal entails p in the inner domain, i.e. in the support set, while p remains unsettled in the modal base which is nonveridical and allows non-p worlds. There are two kinds of nonveridical epistemic modal spaces: those that contain a support set for a proposition (the biased modals), and the possibility modals that convey nonveridical equilibrium between p and ¬p (Giannakidou 2013b): (37) Def 15. Nonveridical equilibrium (Giannakidou 2013b). An epistemic state M is in nonveridical equilibrium iff M is partitioned into p and ¬p, and there are no Best worlds. A nonveridical state with equilibrium reveals no preference because there is no ordering. Take for example It might rain tomorrow. This is a mere possibility statement, and there is no ordering that could create a support set for the proposition 'it rains tomorrow'. Ordering sources add information restricting sets of possibilities and creating support sets, thus privileging one subset of the modal base over its complement (¬p). In terms of commitment, we propose the following scale of commitment strength, from strongest to weakest: (38) Commitment strength More committed < unmodalized p, MUST p, POSSIBLY p> less committed The modal space M of an unmodalized sentence contains only p worlds. When all worlds in M are p worlds, we have veridicality, and this conveys the strongest commitment. With a biased modal like MUST, we have a nonveridical space with a set of best worlds where p is true (Giannakidou 2013b, Giannakidou and Mari 2013). In this case, the pworlds are the support set of p, but the modal base and M(speaker) still allow non − p worlds. The possibility sentence, on the other hand, conveys equilibrium between p and non-p (Giannakidou 2013, Giannakidou and Mari 2015), i.e. there is no preference towards the p or non-p worlds, no best worlds, no support of p. This is so because there is no ordering with the possibility modal. Whenever 9 there is ordering there are best worlds, the universal modal will therefore give rise to stronger commitment. In other words, the universal modal is strong in the sense of partially supporting p in the Best worlds, but it is still weak because it is nonveridical objectively and subjectively. We define here commitment weakening (following Giannakidou 2014): (39) Commitment weakening of epistemic modals (i) All epistemic modals are subjectively nonveridical and convey weaker speaker commitment. (ii) Weaker speaker commitment means that the speaker's epistemic state is nonveridical. All modals have the function of commitment weakening, and in the class of modals, we include verbs, as well as particles (including the subjunctive; see Giannakidou this volume). Let us see now how this framework of modality applies to the analysis of epistemic future. 2.2 Epistemic future and MUST As noted at the beginning, FUT has extensive epistemic use in Greek and Italian. We repeat the basic data. The epistemic use arises with non-past and with past, statives and eventives: (40) a. I the Ariadne Ariadne tha FUT milise talk.past.3sg xthes. yesterday. 'Ariadne must have spoken yesterday.' b. Gianni Gianni avrà have.fut.3sg parlato spoken ieri. yesterday. 'Gianni must have spoken yesterday.' (41) a. I the Ariadne Ariadne tha FUT ine be.3sg arrosti. sick. 'Ariadne must be sick.' b. Giovanni Giovanni sarà FUT-be malato. sick 'Giovanni must be sick.' (42) a. I the Ariadne Ariadne tha FUT itan was.3sg arrosti. sick. 'Giovanni/Ariadne must have been sick.' b. Giovanni Giovanni sarà must stato been malato. sick. 'Giovanni must have been sick.' In all cases, the speaker is considering information she has and draws an inference based on that information. In accordance with what we said so far, the epistemic FUT/MUST modal base is nonveridical, as evidenced by the possibility of negative continuations illustrated below: (43) a. I the Ariadne Ariadne ine is arosti, sick, #ala but dhen not ime be.1sg ke and endelos absolutely sigouri. sure b. Giacomo Giacomo è is malato, sick, #ma but non not sono am sicura. certain. 'Ariadne/Giacomo is sick, #but I am not entirely sure.' 10 (44) a. I the Ariadne Ariadne tha FUT ine is arosti, sick, ala but dhen not ime be.1sg ke and endelos absolutely sigouri. sure b. Giacomo Giacomo sarà be.3sg.fut, malato, but ma not non am sono sure. sicura. 'Ariadne must be sick, but I am not entirely sure.' In contrast to an unmodalized sentence, the FUT/MUST sentence is compatible with a continuation revealing weakened certainty. This indicates that not all worlds in the modal base are p worlds. With unmodalized past sentences, on the other hand, the not entirely sure continuation is not possible, as we see, because they convey un-partitioned, veridical, epistemic states. We come back to these sentences in section 4. Below, we give examples, in Greek and Italian with the verb equivalents of MUST, and note that they pattern with FUT, and contrast with unmodalized assertions: (45) a. I the Ariadne Ariadne prepi must na subj troi eat.non-past3sg tora now ala but dhen not ime be.1sg ke and endelos absolutely sigouri. sure b. Giacomo Giacomo deve must star be mangiando, eat-gerund, ma but non not sono am totalmente totally sicura. certain. 'Giacomo/Ariadne must/will be eating now, but I am not entirely sure.' (46) a. I the Ariadne Ariadne prepi must na subj milise talk.past.3sg xthes, yesterday, ala but dhen not ime be.1sg ke and endelos absolutely sigouri. sure 'Ariadne must have spoken yesterday, but I am not entirely sure.' b. Gianni Gianni deve must aver have parlato spoken ieri. yesterday, ma non sono totalmente sicura. 'Gianni must have spoken yesterday, but I am not entirely sure.' Sentences with MUST and those with epistemic FUT are equivalent in the speaker's intuitions. FUT and MUST can combine- an instance of modal concord: (47) I the Ariadne Ariadne tha fut prepi must na subj milise talk.past.3sg xthes, yesterday, ala but dhen not ime be.1sg ke and endelos absolutely sigouri. sure. 'Ariadne must have spoken yesterday but I am not entirely sure .' (48) Giacomo Giacomo dovrà must-FUT.3sg aver have parlato spoken ieri. yesterday. 'Giacomo must have spoken yesterday, but I am not entirely sure'. Given the epistemic FUT and the parallel with MUST, we will pursue the same semantics for both. In Giannakidou and Mari (2015) we show that the predictive reading differs from the epistemic only in the modal base (which in the predictive reading is metaphysical). In the present paper, we focus strictly on the epistemic reading. Epistemic FUT associates with an epistemic modal base. Specifically, the modal base is the set of propositions known by the speaker (w0 is the actual world): ∩fepistemic(w0) = λw′.w′ is compatible with what is known by i (the speaker) in w0. Note that ∩fepistemic(w0) ⊂ 11 M(speaker). (Our epistemic modality is thus subjective, see the objective vs. subjective distinction of Papafragou 2006. In fact, given that we relativize with respect to individual anchors, there can be no objective modality, strictly speaking, in our system). Given what the speaker knows, the modal base contains p worlds, but also ¬p worlds; it is nonveridical, nonhomogenous. Let us define the ordering and then Best worlds given the ordering. (49) For any set of propositions S and any world w,w′: w 6S w′ iff for all q ∈ S, if w′ ∈ q, then w ∈ q. (50) Best worlds given the ordering S. BestS : {w′ ∈ ( ∩fepistemic(w0) ) : ∀q ∈ S(w′ ∈ q)}. BestS are a subset of worlds in the epistemic modal base, in which strange things do not happen (see Portner, 1998; Mari 2014a). For instance, if I have red cheeks and sneezing nose, then, under normal circumstances, I have the flu. However, circumstances are not necessarily normal. In such extraordinary circumstances these symptoms are secondary and indeed indicative of a potentially much worse disease. The modal base is thus partitioned and the modal space is subjectively nonveridical. One of the subsets of the modal base is ranked as the set of Best worlds given the ordering S. FUT universally quantifies over the set BestS (which is a subset of the modal base, as we see). Hence: (51) At the utterance time tu, [[FUTepistemic(NON-PAST(p))]]S will be defined only if the modal base M is nonveridical; if defined, [[FUTepistemic(NON-PAST(p))]]S = 1 iff ∀w′ ∈BestS : ∃t′ ∈ [tu,∞) ∧ p(w′t′) (52) At the utterance time tu, [[FUTepistemic(PAST(p))]]S will be defined only if the modal base M is nonveridical; if defined, [[FUTepistemic(PAST(p))]]S = 1 iff ∀w′ ∈BestS : ∃t′ ≺ tu ∧ p(w′t′) This truth-conditional content of FUT is identical to MUST, to which we assign exactly the same truth conditions: (53) At the utterance time tu, [[MUSTepistemic(NON-PAST(p))]]S will be defined only if the modal base M is nonveridical; If defined, [[MUSTepistemic(NON-PAST(p))]]S = 1 iff ∀w′ ∈BestS : ∃t′ ∈ [tu,∞) ∧ p(w′t′) (54) At the utterance time tu, [[MUSTepistemic(PAST(p))]]S will be defined only if the modal base M is nonveridical; if defined, [[MUSTepistemic(PAST(p))]]S = 1 iff ∀w′ ∈BestS : ∃t′ ≺ tu ∧ p(w′t′) Following Giannakidou 2009, we take it that the temporal information comes from the lower tense, which can be past or nonpast (see also Staraki 2013 for an analysis of Greek modals as purely modal operators and not mixed modal/temporal as in Condoravdi 2002). How about the actual world? Best worlds are those in which strange things do not happen. Typically the actual world tends to be non-extraordinary (Portner, 2009), but we also know that strange things happen. As a consequence, we do not claim that the epistemic agent actually knows that the actual world belongs to the set of best worlds. Given that the accessibility 12 relation is epistemic and therefore reflexive, it is ensured that the actual world is in the modal base (see Matthewson et al. 2007; Portner, 2009), but it is not guaranteed that the actual world belongs to the p worlds. With universal quantification over the set of Best worlds, however, truth is projected within the support set and this is responsible for the sense of strength that comes with FUT and MUST; but it must not be confused with veridicality, which expresses full commitment to p and therefore does not allow for the possibility of not p within the modal base.5 This account treats MUST as both strong (because of quantification within the set of Best worlds) and weak (because of the nonveridical modal base). p is entailed by the propositions over which MUST quantifies, although is it is not entailed by the propositions in the modal base. Our account is thus close to von Fintel and Gillies proposal that MUST is strong, that is to say p is entailed by the modal base determined in virtue of a Kernel (i.e. the set of propositions known by the speaker). Specifically, von Fintel and Gillies 2010 posit the existence of a kernel K which is a set of worlds representing the privileged information. They then pose a presupposition of 'direct unsettledeness' in the kernel: (55) Definition 5 (String must + evidentiality) Fix a c-relevant kernel K a. [[ mustφ]]c,w is defined only if K does not directly settle [[φ]]c b. If defined, [[ mustφ ]]c,w = 1 iff BK ⊆ [[φ]]c Von Fintel and Gillies say that K can fail to directly settle whether P even though K entails whether P (von Fintel and Gillies 2010: 372). The modal base, in their account is a homogeneous space of p worlds, in our it is not. However, because of the ordering source, we are able to carve out a set of worlds in which p is also true, and it is on this set that MUST quantifies. 3 The evidential component: partial knowledge In his seminal work, Kartunnen (1972) held that the weakness of MUST is intimately related to the weakness of the source of information. The view that we hold here is that epistemic weakening makes the biased modal statement compatible only with a partitioned, non-veridical epistemic state consisting of a subspace of best worlds that supports p (the inner domain), and a subspace that doesn't (the outer domain, the modal base). An important difference between our view and Kartunnen's is that the epistemic weakening is not due to the fact that knowledge is indirect, but to the fact that knowledge is partial. Kartunnen ties 'weakness' to indirect evidence: when the speaker has indirect evidence that the prejacent is true, she uses the modal to signal that she is uncertain about the truth of the prejacent. Von Fintel and Gillies (2010:361) challenge this position: 'Our point is simple: weakness and indirectness are not two sides of a single coin at all. They are just different'. Their claim is that the epistemic modal must presupposes indirect evidence, but it is 'strong'. In our view of epistemic weakening, the indirectness is reduced to a mere side-effect, not a real phenomenon. The key is partial knowledge: epistemic weakness arises because the speaker is 5In a recent work, Mari (2014b) argues that some other modals are veridical with respect a restricted domain that contains the actual world, and nonveridical with respect to an outer domain. This, she argues, is what happens with past modals with present orientation, triggering the veridicality (a.k.a. actuality entailments). What is common to MUST/FUT and these modals, is that the modal domain is articulated into two subdomains, with the inner one being veridical and the outer one, being nonveridical. 13 reasoning with partial knowledge, and she knows that she does not have all the facts (see also Mari, 2010). Recall the partition that lies at the heart of the truth condition of universal, biased modals: the partition between best and non-best worlds. When the speaker reasons with a universal modal, she is aware that she does not have all the knowledge she needs to draw a valid conclusion in all worlds in the modal base. When she has complete knowledge, she cannot use universal modal, as evidenced in direct visual perception contexts: (56) Context: Direct visual perception of rain a. #It must be raining. b. #Tha FUT vrexi. rain. c. #Piovera. rain-FUT.3sg. d. #Tha FUT prepi must na subjunctive vrexi. rain. e. #Dovrà Must-FUT.3sg piovere. rain. Recall that in this, biased modals are similar to devices such as the German and Dutch modal particles, as we me mentioned in the introduction. If I see the rain, I know that it is raining, and knowledge is veridical: if I know p, then all worlds compatible with my knowledge are p worlds. My epistemic space is not partitioned, but the opposite: it is homogeneously supporting p. Epistemic weakeners are incompatible with the state of complete, homogenous knowledge that comes with direct perception. Why we need partiality rather than indirectness of knowledge is nicely illustrated in the contrast between the context above where I see the rain, and the following case (57), where I only see a wet umbrella. (57) I see a wet umbrella a. It must be raining. b. Tha/Prepi FUT/Must na subjunctive vrexi. rain. c. Deve Must star be piovendo. raining. d. Pioverà. FUT-rain.3sg. e. Deve star piovendo, ma non sono sicura. 'It must be raining, but I am not sure.' f. Deve probabilmente star piovendo. 'It must probably be raining.' In this context, I see a wet umbrella, but I don't see the rain, therefore I do not know that it is raining. The wet umbrella is an indication of rain, and can support 'It is raining', by licensing the missing premise that the umbrella got wet because of the rain. The biased epistemic and FUT modals are fine in this case, in contrast to the direct perception of rain that we just saw, where they are bad. Continuation with 'I am not sure' is allowed here, as we see. Likewise, auditory perception is compatible with MUST and FUT because this too gives incomplete knowledge. 14 (58) Context: I am in a room with no windows, but I hear sounds of rain on the roof a. It must be raining. b. Tha FUT vrexi. rain. c. Pioverà. rain-FUT.3sg. d. Tha FUT prepi must na subjunctive vrexi. rain. I do not see the rain, so I do not know that 'it is raining', I only have the sound of rain. The sound might be caused by something else than the rain (hence, I am also missing the premise: if sound therefore rain). Only in the best worlds is the sound of raining due to rain. Auditory perception therefore provides only incomplete knowledge, and the modal is allowed. In other words, the apparent evidential effect of universal epistemic modals is due to the fact that they are indicators of reasoning with non veridicality and incomplete knowledge. We summarize this in the following: (59) Evidential component of Universal Epistemic Modals: partial knowledge a. Universal epistemic modals can only effectively weaken a proposition p, if the speaker's knowledge that supports p is not complete. b. Complete knowledge is knowledge of all the relevant facts for p. More technically, it is a set of propositions that entails p. c. All other knowledge is partial. The generalizations that we establish here for universal modals are very relevant for the discussion of evidentiality, especially in languages that have indirect evidential morphemes but do not mark direct perception (e.g. Native American languages such as Cheyenne, Murray to appear, and Turkish, Bulgarian, Smirnova 2013a). The 'direct' evidential is typically an unmarked past or present, and the marked form is the so-called indirect evidential, which indicates that the source of information is not first hand knowledge of the speaker. The indirect evidential- like the universal in English, Greek and Italian- can thus be understood as expressing reduced speaker commitment to p. Direct perception, on the other hand, as we discussed in the case of rain, entails full knowledge. If I see the rain, I know it is raining, hence direct perception gives that kind of veridical, complete, knowledge.6 Given partial knowledge, p is entailed only in the support set (the best worlds). Otherwise, in the modal base p remains unsettled just like in von Fintel and Gillie's kernel K. In fact, unsettledness in K is a presupposition for von Fintel and Gilles, just like nonveridicality is for us (recall in our definitions that nonveridicality characterizes the modal base M). Consider their definition given below: (60) Definition 5 (String must + evidentiality) Fix a c-relevant kernel K a. [[ mustφ]]c,w is defined only if K does not directly settle [[φ]]c 6Note, at the same time, that direct access in the sense of Willett (1988) does not count per se as a case of complete knowledge. There is a difference between 'seeing some facts that are compatible with p being true' and 'knowing that p is true in virtue of visual evidence'. As Lee 2012 explains, witnessing p is not equivalent to have visual evidence for p. Likewise, visual evidence can be incomplete evidence for assessing the truth of p (in (57), I see the umbrella, but I do not see the rain). Similarly, inferential knowledge can be complete or incomplete: it is complete if all the premises allowing to conclude that p is true are given and incomplete if there are some missing premises for concluding that p is true. 15 b. If defined, [[ mustφ ]]c,w = 1 iff BK ⊆ [[φ]]c The basic intuition, as von Fintel and Gillies say, is that K can fail to directly settle whether P even though K entails whether P (von Fintel and Gillies 2010: 372). In this respect, our analysis and theirs are similar. However, we differ in that we do not acknowledge a separate evidential component, but rely on the link between nonveridicality and partial knowledge. Current classification of sources of evidence focus on the distinction between direct and indirect knowledge, with visual evidence counting as direct evidence entailing full knowledge, and reprobative and other internal evidence counting as indirect, thus implying incomplete knowledge. Our claim is that every type of source of information comes as either complete or partial. Complete knowledge is a set of propositions that entail p and partial knowledge is a set of proposition that is only compatible with p (see also Mari, 2010). Greek and Italian do have a reportative evidential form (lei, ipan, si dice, dicono, pare): FUT can co-occur with it: (61) O the Janis John tha FUT (prepi (must na) SUBJ) gini become.3sg kala well, eipan. say.3pl. (62) Gianni Gianni guarirà, recover-FUT.3sg, pare. it seems. 'John must recover, it seems. However, the reportative context by itself is not sufficient to trigger universal biased modals. We reproduce here an example from Smirnova 2013b, to show the contrast between the Greek/Italian FUT and the Bulgarian evidential which is fine in this context. (63) Reportative context: you and your sister were out of touch for a couple of years. Today she calls you on the phone to catch up. She tells you that her daughter Maria plays the piano. Later, you tell your husband: a. Maria Maria svirela play.EV na on piano. piano Bulgarian evidential OK (Smirnova 2013b: (2)) b. #I Maria tha/prepi na pezi piano. #Maria must play the piano. c. #Maria suonerà il piano. #Maria must-FUT.3sg play the piano. The reason why the universal modal is blocked in this context is that here the speaker has knowledge that p provided by her sister's utterance. The assertion "Maria plays the piano' is part of the common ground due to the report, so the speaker's epistemic state is veridical, and it contains no worlds that negate this information. FUT is incompatible with this state, and so is MUST. This example clearly shows that it is not indirectness that matters but whether the speaker knows or not. If one has full knowledge of p, even if this knowledge is due to something that someone else said, one cannot use an epistemic weakening device, not even a biased one (MUST, future, modal particles). The inferential context, on the other hand, is compatible with the universal modals because it presents partial knowledge. We will use again an example modeled after Smirnova 2013b. You and your sister were out of touch for a couple of years. Today you visit her for the first time. As she shows you around her apartment, you see that there is a piano. Later, you tell your husband: 16 (64) a. Maria Maria svirela play na on piano. piano. (Bulgarian evidential) b. Maria Maria tha FUT pezi/prepi play/must na subjunctive pezi play piano. piano. c. Maria Maria suonerà/deve play.FUT.3sg/must suonare play il the piano. piano. d. Maria must play the piano. Here we have a piano, but we don't actually see Maria playing it, hence the knowledge is partial. An inferential context with missing premises is therefore an excellent environment for FUT, MUST and the other weakening devices. Again, it is not a matter of indirectness, as we see the piano directly: it is simply reasoning with incomplete knowledge so that we can effectively partition the modal base into worlds that support the proposition and those that do not, as is required by epistemic weakening. Now finally, consider FUT/MUST in a mirative use. Such uses have been reported for evidentials, e.g. in Gitiksan. If the speaker sees John standing in the doorway, as in (65), he has complete evidence. Both Greek and Italian futures are banned. (65) Gitkasan, Peterson (2010:143, ex. (30) =hiwitxw=t John EVID=CND arrive=PND (66) #Tha irthe o Janis! #Sarà Gianni! Again, FUT cannot be used in this context of veridical direct perception because it gives complete veridical knowledge. We are saying that inferential knowledge cannot be used with the biased modal if complete, and in support of this, Mari (2009,to appear; see also previous discussion in Pietrandrea, 2005) notes that the italian future cannot be used in the following context of complete premises: (67) a. La palla è in A, B, o C. 'The ball is in A, B or C.' b. Non è nè in A, nè in B. 'It is neither in A nor in B.' c. #Sarà in C. 'It will be in C.' Here we have full knowledge of the situation, and c follows as a logical conclusion from the other two premises. Italian FUT is banned from this use, as expected under our analysis. However, Mari (ibid.) also notes that the epistemic modal dovere (must) is indeed acceptable, and so is must: (68) a. La palla sarà in A, B, o C. b. Non è nè in A, nè in B. c. Deve essere in C 'It must be in C.' In Greek, both FUT and MUST are licensed in this complete knowledge context. (69) a. The ball is in A, B, or C. 17 b. The ball is neither in A nor B. c. I the bala ball prepei must na SUBJ ine be.3s / / tha FUT ine be.3s sto in.the C. C 'The ball must be/ FUT be in C.' Do these data challenge our idea of incomplete knowledge? We think not, because these do not seem to involve pure epistemic reasoning. They present an 'impure' (a term from Knobe and Szabo 2013) use of the universal modal, where epistemic reasoning is mixed with aleithic modality; or they are simply just aleithic because a conclusion is drawn based on the mathematical/logical disjunctive schema: p or q or r, ¬p and ¬q, therefore r. Hence, the occurrence of universal modals in these contexts is indeed evidence for strength (as von Fintel and Gillies suggest) but not of strength of the epistemic MUST; rather, they signal aleithic use of MUST, whose strength is indisputable anyway. In support of this being a different use, we want to add that often, this aleithic use of MUST/FUT is signaled by focus on the modal- in contrast to the regular epistemic weakening case where MUST is typically unstressed and disallows focus: The ball MUST be in C! as opposed to # John MUST be a doctor, but I am not entirely sure, which is quite odd with the emphatic stress on MUST. In other words, there is indeed evidence, at the suprasegmental level at least, that this use of MUST is distinct from the epistemic one. To conclude, we have proposed a theory of FUT and MUST as biased universal modals. As modals, they are nonveridical (hence weak), both objectively (they do not entail p) and subjectively (they do not entail that the speaker knows that p). Reasoning with universal modals relies on partial knowledge, and they appear to be strong because in the worlds compatible with that knowledge p is true. It turned out that no recourse to a separate evidential component was necessary. 4 Moore effects with biased modals and informational flow In this last section, we want to fine tune our analysis by examining some effects that appear to be Moore-paradoxical. The literature on the Moore paradox is vast, and we will not attempt a general analysis of it here, since our topic is not the paradox itself. Our new observations are that we find Moore-effect with biased modals, but different variants of Moore's paradox affect the modals in different ways. To explain the variation, we propose that Moore-effects do not necessarily reveal a veridicality conflict, but manifest also sensitivity to informational flow that previously has escaped attention. The classical Moore paradox itself arises with sentences like below: (70) #It is raining and I don't know that it is raining. (71) #It is raining and I don't believe it. The usual reaction is that the sentences above are odd, contradictory-sounding, and unassertable. In the literature, the sentences are treated as defective in that they involve the speaker in some kind of epistemic conflict. In our terms: as we said in section 2.1, a positive unmodalized assertion is subjectively veridical, i.e. the speaker is typically understood as knowing that p is true. If this is so, then in the sentences above the speaker's epistemic state M(speaker) is presented as both being included in p and allowing ¬p worlds. This is a contradictory epistemic state, and the sentences are defective because of this veridicality conflict imposed by the two conjuncts. Yalcin in a more recent discussion (Yalcin 2007) coins the term epistemic contradictions for 18 Moore variants with logical forms such as φ and it is not possible that φ, e.g: (72) #It is raining and it might not be raining. (73) #It is raining and it is possible that it is not raining. Yalcin calls these epistemic contradictions. Again, the conflict appears to be between a veridical epistemic state established by the unmodalized first conjunct (where all worlds are raining worlds), and a non-veridical state, allowing raining and non-raining worlds in the second conjunct. So, both Yalcin's examples and the classic Moore paradox examples involve an epistemic conflict which reveals a subjective veridicality conflict. Interestingly from our perspective, future and MUST sentences give rise to what appears to be a Moore paradoxical effect. We observe it below. (We replace and with but to make the sentences more natural sounding, but as can be seen, the effect is observed): (74) #It must be raining, but it might not be raining. (75) #Tha FUT vrehi, rain.imperf.non-past.3sg ala ala ine is pithano possible na subj min not vrehi. rain.imperf.non-past.3sg '#It must be raining, but it is possible that it it might not be raining. (epistemic)' (76) Gianni John sarà be.3sg.fut arrivato, arrived, #ma but è is possibile possible che that non not sia be.subj.3sg arrivato. arrived. 'John must have arrived, but it is possible that he has not arrived' (epistemic). (77) #Prepi must na SUBJ vrehi, rain.imperf.non-past.3sg ala ala ine is pithano possible na subj min not vrehi. rain.imperf.non-past.3sg '#It must be raining, but it is possible that it it might not be raining. (epistemic)' If biased modals are non veridical, as we argue, and convey a partitioned state, how can the data above be explained? If the nonveridical spaces associated with FUT and epistemic MUST are nonveridical (thus allowing ¬p worlds), as we are arguing, why aren't they compatible with a continuation that raises that possibility? As we proceed to show how the Moore effect can be explained in our account, we want to recall first the new set of data, of similar structure, that we mentioned earlier and which in fact support the nonveridical analysis. Recall that we used them as evidence for it. Here is a sample of the sentences with but I am not entirely sure. (78) a. I the Ariadne Ariadne tha FUT ine is arosti, sick, ala but dhen not ime am ke and endelos completely sigouri. sure b. Giacomo Giacomo sarà be.3sg.fut malato, sick, ma but non not sono be.1sg completamente entirely sicura. certain. 'Ariadne/Giacomo must be sick, but I am not entirely sure.' (79) a. I the Ariadne Ariadne prepi must na subj troi eat.non-past3sg tora, now, alla but den not ime be.1sg ke and endelos completely sigouri. sure. b. Giacomo Giacomo deve must star be mangiando, eat-gerund, ma but non not sono be.1sg completamene completely sicura. sure 'Giacomo/Ariadne must/will be eating now, but I am not entirely sure.' 19 With continuations like but I am not entirely sure, the Moore effect seems to be removed. Crucially, the effect remains with an unmodalized veridical sentence: (80) I the Ariadne Ariadne ine/itan is/was arosti, sick, #ala but dhen not ime be.1sg ke and endelos completely sigouri. sure Ariadne is/was sick, but I am not entirely sure. (81) Giacomo Giacomo è/era is/was malato, sick, #ma but non not sono be.1sg completamente completely sicura. certain. 'Giacomo is/was sick, #but I am not entirely sure.' The present and past sentences are subjectively and objectively veridical. When the speaker utters them, as far as she knows, Ariadne and Giacomo were sick, and knowledge of that cannot be cancelled by a continuation that questions it. All worlds in M (speaker) are worlds in which Ariadne and Giacomo are sick, so the second conjunct induces epistemic contradiction that comes from this veridicality conflict (all worlds inM (speaker) are pworlds in the first conjunct, while not all worlds in the same space are p worlds in the second conjunct). The epistemic future and MUST, on the other hand, are fine with but I am not entirely sure. Why? Because both conjuncts are not veridical, and they there're both of equal informational strength, so there is no conflict between them. The first conjunct establishes a nonveridical modal base which allows ¬p worlds, i.e. the worlds that are not Best. In the second conjunct, we move from the modal base, to the larger space, i.e. the speaker's epistemic state. The speaker is in a nonveridical epistemic state: I am not entirely sure that p is equivalent to I am committed to p but not fully, which means that my epistemic state is also biased toward p but allows ¬p worlds. The presence of entirely is crucial in the sentence as it reveals the bias (as opposed to I am not sure which is a neutral sentence with no bias towards p. Hence, the two conjuncts make reference to nonveridical modal spaces which are in agreement and not in conflict, since they are both nonveridical and biased. We will call this situation informational harmony. We do not get a Moore-paradox with informational harmony, unlike with the positive unmodalized assertion where I am not entirely sure that p creates exactly the kind of contradiction the classical Moore continuation gives (a contradictory epistemic state). Hence, I am not entirely sure fully supports our nonveridical treatment of epistemic FUT and MUST. What we just said relied on the notion of informational strength. The two sentences were of equal informational weight, we said. What goes wrong in the classical Moore cases and in our FUT/MUST variants of them is that the sentences do not have the same informational weight. This creates informational conflict that manifests itself in two ways: (a) as breakdown of information flow, which normally proceeds from weaker to stronger (as we define it below), and (b) as an "informational contradiction". The Moore effects with FUT and MUST are due to these. Consider first how the classical case illustrates breakdown of information flow: (82) #It is raining and/but it might not be raining. The first conjunct It is raining presents the rain as an actual fact (objective veridicality), or knowledge of the speaker of this fact (subjectively veridical), i.e. in all worlds compatible with the speaker's knowledge it is raining. The second conjunct conveys a weaker information, i.e. that the speaker considers it possible that it is not raining. This discourse makes the hearer conclude that the speaker is not being co-operative. She said something false either in the first or in the second conjunct, in both cases violating quality, thus being misleading. We end up with a conflict, as well as a breakdown of what can be thought of as normal information flow. 20 Proceeding from weaker to stronger is the normal course of information flow, expected by Gricean pragmatics: (83) Normalcy conditions on information flow Information flow is considered normal iff: (i) Information goes from weaker information A to stronger information B. Or, (ii) A and B do not informationally contradict each other. These conditions are nothing extraordinary, but mere summary of run-of-the-mill versions of Gricean views of how information normally proceeds. Weaker and stronger are the informational alternatives compared, i.e. the propositions denoted by the sentences. The problem, crucially, in the second conjunct, comes from the fact that a stronger information was established first: a veridical sentence is informationally stronger than a non-veridical sentence. And within non-veridical sentences, S with bias is stronger that S with equilibrium. Recall that the ordering source reveals bias. With equilibrium, there is no ordering source. With ordering sources the domain of quantification is more restricted and is thus informationally richer (à la Stalnaker). Below we give the relevant scale: (84) Informational strength ordering relevant for Moore's contrasts weaker 〈 might ¬p, MUSTp, p〉 stronger Let us represent Moore's sentences S as a pair of alternatives 〈S1, S2〉: (85) Moore's variant: p and might ¬p Alternatives: 〈S1 :p, S2 :might¬p〉 S1 is a stronger alternative than S2 because the veridical epistemic state is not partitioned: all worlds are p-worlds. S2 says something that is both informationally weaker and in veridicality conflict with S1. The reverse order, from weaker to stronger, is predicted to be fine, and this prediction is borne out: (86) It might not be raining, but in fact it is raining. Here, conversation proceeds normally, because the weaker S2 precedes S1 (and we added in fact to help the sentences connect; notice that in fact has no effect on the other order: It is raining but in fact it might not be raining remains odd). In the order above, the second sentence seems to correct the first one, to strengthen it; and, because information proceeds normally, the difference in veridicality is in harmony with the strengthening. There seems to always be a discourse function that strengthening serves, but it will lead us to far astray to develop this in more detail (see Geurts 2010 for a recent neo-Gricean pragmatic theory that addresses in detail informational strengthening, while also arguing that it doesn't always serve the same function.) For now, suffice it to raise awareness that the ill-formedness of the classic Moore sequence reveals both a veridicality conflict, and a violation of informational normalcy. If the latter gets fixed, the difference in veridicality becomes innocuous.7 7We think it is worth mentioning that the normalcy conditions we posited above are not specific to modality, but are general. Consider e.g. quantifiers: (87) a. #Every linguistics student came to the Halloween party, and some linguistics students came to the party. b. Some linguistics students came to the Halloween party; in fact, every linguistics student came to the party. 21 To go now to our FUT/MUST sentences, consider first the case of a negated possibility modal in the second conjunct: (88) a. #Tha FUT vrehi, rain.imperf.non-past.3sg ala but ine is pithano possible na subj min not vrehi. rain.imperf.non-past.3sg b. #Starà Stay.3sg.fut piovendo, rain.gerund, ma but è is possibile possible che that non not piova. rain.3sg.subj. '#It must be raining, but it might not be raining.' (89) #Prepi must na SUBJ vrehi, rain.imperf.non-past.3sg ala ala ine is pithano possible na subj min not vrehi. rain.imperf.non-past.3sg '#It must be raining, but it is possible that it it might not be raining.' In the cases where a universal modal is followed by the negation of a possibility modal, we have utterances of modalized sentences in both conjuncts. But we don't have the same informational weight in both conjuncts. Must p conveys bias towards p worlds, while the possibility utterance conveys equilibrium; hence S1 is the stronger alternative, while S2 is informationally weaker: we go from a stronger S1 (with ordering sources revealing bias) to a weaker S2 (with no ordering sources and equilibrium): (90) Moore's variant: MUST p and might ¬p Alternatives: 〈S1 :MUST p, S2 : might ¬p〉 According to the normalcy condition, information flow requires the stronger statement to be second. The information flow in the Moore sentence is thus not normal, and the sentence is defective for this reason. Notice, crucially, that if we reverse the order as we do below, the sequence is improved, and shows no Moore effect : (91) a. Ine is pithano possible na subj min not vrexi, rain.imperf.non-past.3sg, alla but malon probably tha FUT vrexi. rain.imperf.non-past.3sg. 'It is possible that is not raining, but most likely it must be raining.' b. È Is possibile possible che that non stay.3sg.subj stia not piovendo, rain.gerund, ma but starà stay.3sg.fut piovendo, rain.gerund, vedrai. see.2sg. 'It might not be raining, but I am pretty certain it is raining, you'll see.' These discourses are normal because the stronger sentence follows the weaker one. This fact illustrates that the problem with the Moore sentences with strong modals in the first conjunct followed by negations of weaker modals, are due to breakdown of normal information flow. The two alternatives are not epistemically inconsistent but informationally not-normal. Consider, finally, the continuations with I don't believe it: (92) Gianni John sarà be.3sg.fut arrivato, arrived, #ma but non not lo that credo. believe.1sg. The odd sequence is not normal because it proceeds from strong (with universal quantification) to weak (with existential quantification). Here violation of normalcy leads to redundancy. 22 '#John must have arrived, but I do not believe it.' Here, the alternatives are: (93) Moore's variant: MUST p and I do not believe that p Alternatives: 〈S1 :MUST p, S2 : I do not believe that p 〉 The speaker establishes bias towards pwith the use of a universal modal in the first conjunct. She continues then by saying that she does not believe that John arrived. Importantly, believe is a neg-raising verb, so not believe that p typically strengthens to believe that not p; (see Horn 1979 for a classical piece on neg-raising with belief verbs). In the strengthened reading, both conjuncts appear to be informationally equally strong, but, crucially, conflicting with each other: the first conjunct conveys bias towards the p set (John arrived) and the second alternative strengthens to the belief that John didn't arrive (there are no p worlds in the speakers epistemic state, counter commitment to p). This creates a conflict in the join utterance because the speaker is required to both have bias towards p and counter commitment to it. This is an informational "contradiction", a conflict that cannot be repaired. As we see, change of order has no effect: (94) a. Den not pistevo believe.1sg oti that irthe FUT.came.3sg o the Janis, John, #alla but tha FUT irthe. came.3sg. b. Non Not credo believe.1sg.pres che that John John sia be.3sg.subj arrivato, arrived, #ma but sarà be.3sg.fut arrivato. arrived. '#I do not believe it that John arrived, but he must have arrived.' Here the speaker remains in an informationally contradicting state where she is required to both have bias towards p, and believe p to be false. This is an impossible informational state. Notice that in the sentence below, without negation in the second conjunct, we have again informational harmony (though perhaps also a bit of redundancy: (95) It must be raining and I believe that it is raining. We will close our discussion here, by summarizing the three cases of Moore-continuations for FUT/MUSTp that we found: (a) A continuation that creates no effect, revealed with I am not entirely sure; this continuation illustrates informational harmony. (b) A continuation that violates informational normality from weaker to stronger information (with might not p); this effect can be fixed with reversing the order of conjuncts. (c) A continuation that creates informational contradiction (with I do not believe p). Order has no effect on this one. Certainly further study is required to understand better the interactions between modals in Moore sentences, and to refine how the notion of informational strength we proposed interacts with the semantics. Here, we offered but a few initial, and we hope helpful, observations about the behavior of FUT/must in Moore like sentences. 5 Conclusions In this article, we identified three new categories. The first one is the category of epistemic future. Epistemic future is equivalent to the epistemic modal verb MUST, and this fact is evidence 23 that the grammatical category 'future' cannot be a purely temporal one, in agreement with a substantial amount of recent work on Dutch, Greek, and Italian futures. We offered an analysis of epistemic future as a universal epistemic modal identical to MUST, and showed that in Greek and Italian the two can even co-occur. Our second contribution is the category biased modal. The epistemic future and MUST are biased modals, we argued, and biased modals are both strong and weak. They are strong because they entail p in the set of best worlds (the support set), but they are weak because their modal base is nonveridical and therefore contains non-p worlds too. Biased modals express weaker epistemic commitment of the speaker towards the propositional content, and function generally as epistemic weakeners. The category of biased modals includes, besides FUT and MUST, also modal particles such as wohl, wel in German and Dutch. Though we didn't offer an explicit analysis, we want to suggest that certain indirect evidentials, in languages exhibiting a binary opposition between evidential vs. unmarked, are also epistemic weakeners. The function os epistemic weakening is to create a nonveridical epistemic space, i.e. a partitioned space with at least one non-p world. The third category, then, is the category of (non)veridicality. Veridicality is a property of natural language expressions entailing the truth of their complement (objective veridicality), or knowledge of an individual of the truth of a proposition (epistemic, or subjective veridicality). Veridicality and nonveridicality are fundamental in characterizing the truth conditions of modal expressions (modal verbs and particles), but also propositional attitudes and mood choice (as is further discussed in Giannakidou's paper in this volume and in earlier work). The licensing of negative polarity items also seems to be sensitive to nonveridicality. We developed a framework for (non)veridicality of modal expressions that is flexible enough to allow analysis of new phenomena within a number of limited and well understood premises. Concerning, finally, the evidential component of MUST, we suggested that contrary to what has been claimed in the literature about indirectness, the key is partial knowledge. Partial knowledge represents a partitioned, non-homogenous, therefore non-veridical epistemic state, and explains nicely why the use of universal epistemic modals is constrained to such states. We also showed that visual perception of an event is privileged because it leads to complete knowledge, and therefore FUT and MUST, being non-veridical, cannot be used with direct visual perception. In other words, what much literature characterized as evidential component of MUST is simply an epiphenomenon, reflecting the nonveridical nature of MUST, and its incompatibility with full knowledge. Ackowledgements We presented this material at the workshop on Categories in Wroclaw, at the International Congress of Linguists in Geneva, and in colloquia at the University of Brussels, Groningen, and Chicago. We thank the audiences for their insightful feedback, and the organizers of the workshop for giving us the opportunity to first develop these ideas. We are also very grateful for comments and helpful discussion to Kai von Fintel, Itamar Francez, Jack Hoeksema, Chris Kennedy, Mikhail Kissine, Jason Merchant, and Malte Willer– as well as the anonymous reviewers of this volume for their help and suggestions. As for Alda Mari, this research has been founded by the ANR-10-LABX-0087 IEC and ANR-10-IDEX-0001-02 PSL. She also gratefully thanks the CNRS-SMI 2015. 24 References Bertinetto, P.M. 1979. Alcune ipotesi sul nostro futuro (con alcune osservazioni su potere e dovere), Rivista di grammatica generativa 4: 77-138. Broekhuis, H. and Verkuyl, H. (to appear). Binary Tense and Modality. Natural Language and Linguistic Theory. Ciardelli, I, Groenendijk, J and Roelofsen, F. 2013. Inquistitive semantics: a new notion of meaning. Language and Linguistic Compass, 7: 459-476. Chiou, Michael. 2012. The interpretation of Greek future: a pragmatic approach. Ms. Condoravdi, C. 2002. Temporal interpretation of modals: modals for the present and for the past. In The Construction of Meaning, eds D. Beaver, Luis D. Cassillas Maritinez, Brady Z. Clark, S. Kaufmann. Condoravdi, C. 2003. Moods and Modalities for Will and Would, Invited communication at Amsterdam Colloquium. Copley, B. 2002. The semantics of the future, PhD MIT. von Fintel, K. and Gillies, A. 2010. Must...stay... strong ! Nat. Language Semantics 18: 351-383. von Fintel, K. and Heim, I. 2007. Intensionality. Ms. MIT. von Fintel, K. and Iatridou, S. 2006. How to Say Ought in Foreign: The Composition of Weak Necessity Modals. Ms. MIT. Giannakidou, A. 1997. The Landscape of Polarity Items . PhD thesis, University of Groningen. Amsterdam. Giannakidou, A. 1998. Polarity Sensitivity as (Non)veridical Dependency. John Benjamins. Amsterdam. Giannakidou, A. 1999. Affective dependencies. Linguistics and Philosophy 22: 367421. Giannakidou, A. 2002. Licensing and sensitivity in polarity items: from downward entailment to nonveridicality. In Maria Andronis, Anne Pycha and Keiko Yoshimura (eds), CLS 38: Papers from the 38th Annual Meeting of the Chicago Linguistic Society, Parasession on Polarity and Negation. Giannakidou, A. 2009. The dependency of the subjunctive revisited: temporal semantics and polarity. Lingua 120: 1883-1908. Giannakidou, A. 2012. The Greek future as an epistemic modal. In the Proceedings of ICGL 10. Giannakidou, A. 2013a. (Non)veridicality, epistemic weakening, and event actualization: evaluative subjunctive in relative clauses, In Trnavac and Taboada, eds. Nonveridicality and Evaluation: theoretical, computational, and corpus approaches. Emerald, Studies in Pragmatics. Giannakidou, A. 2013b. Inquisitive assertions and nonveridicality. In The dynamic, inquisitive, and visionary life of φ, ?φ and possibly φ, A feestschrift for Jeroen Groenendijk, Martin Stokhof and Frank Veltman, ed. by Maria Aloni, Michael Franke, F. Roelofsen: 115-126. Giannakidou, A. 2014. The futurity of the present and the modality of the future: a commentary on Broekhuis and Verkuyl. Natural Language and Linguistic Theory. Giannakidou, A. this volume. The subjunctive as evaluation and nonveridiclaity. Giannakidou, A. and Mari, A. 2012a. Italian and Greek futures as evidential operators. To appear in Proceedings CLS 48. Giannakidou, A. and Mari, A. 2012b. The future of Greek and Italian: An epistemic analysis. Proceedings of Sinn und Bedeutung 17: 255-270. http://semanticsarchive. net/Archive/Dk3NGEwY/GiannakidouMari.pdf 25 Giannakidou, A. and Mari, A. 2013. A two dimensional analysis of the future: modal adverbs and speaker's bias. Proceedings of the Amsterdam Colloquium 2013, pp. 115-122. Giannakidou, A. and Mari, A. 2015. The future in Greek and Italian: objective and subjective dimensions. Ms University of Chicago and Institut Jean Nicod. Geurts, B. 2010. Quantity implicatures. Cambridge University Press Geurts, B. and Tiel, B. 2013. Embedded scalars. In Semantics and Pragmatics 6, 9: 1-37. Hacquard, V. 2006. Aspects of Modality. PhD MIT. Hacquard, V. 2011. Modality. In C. Maienborn, K. von Heusinger, and P. Portner (eds.) Semantics: An International Handbook of Natural Language Meaning. HSK 33.2 Berlin: Mouton de Gruyter, pp. 1484-1515. Huitink, J. 2012. Modal concord. A case study in Dutch. Journal of Semantics 29(3): 403-437. Huitink, J. 2014. Modal concord. Submitted to The Blackwell Companion to Semantics, edited by Lisa Matthewson, CŽcile Meier, Hotze Rullman and Thomas Ede Zimmermann. Karttunen, L. 1972. Possible and must. Syntax and Semantics: volume 1. J. Kimball. New York, Academic Press: 1-20. Karttunen, L. 1971. Some observations on factivity. Papers in Linguistics 4:1, 55-69. Karttunen, Lauri and Annie Zaenen. 2005. Veridicity. In Graham Katz, James Pustejovsky, and Frank Schilder, editors, Annotating, Extracting and Reasoning about Time and Events, number 05151 in Dagstuhl Seminar Proceedings, Dagstuhl, Germany. Kaufmann, S. 2005. Conditional Thruth and Future Reference. Journal of Semantics. doi: 10.1093/jos/ffh025 Kaufmann, S., Condoravdi, C. & Harizanov, V. 2006. Formal approaches to modality. In W. Frawley (ed.), The Expression of Modality, Mouton de Gruyter., 71-106. Kiparksy, P. and C. Kiparsky, 1970. Fact. In M. Bierwich and K. Heilolph (eds), Progress in Linguistics. Mouton. Kissine, M. 2008. From predictions to promises. Pragmatics and Cognition 16:169-189. Kratzer, Angelika. 1981. The Notional Category of Modality. In Words, Worlds, and Contexts. New Approaches in Word Semantics, ed. By H. J. Eikmeyer & H. Rieser, 38? 74. Berlin: de Gruyter. Kratzer, A. 1991. Modality. In Semantics: An International Handbook of Contemporary Research, ed. By A. von Stechow & D. Wunderlich, 639-650. Berlin: de Gruyter. Lassiter, D. 2011. Measurement and Modality: the Scalar Basis for Modal Semantics. PhD thesis, NYU. Lassiter, D. 2013. The weakness of must: In defense of a mantra. CSLI Workshop Perspectives on Modality. Montague, R. 1969. On the nature of certain philosophical entities. The Monist 53, 159-194. de Marneffe, M., C. Manning, and C. Potts. 2012. Did it happen? The pragmatic complexity of the veridicality judgement. Computational Linguistics 38: 300-333. Matthweson, L. 2010. Crosslinguistic variation in modality systems: the role of mood. Semantics and Pragmatics 3: 1-74. Matthewson, L. Rullmann, H., and Davis, H. 2007. Evidentials as Epistemic Modals: Evidence from St'at'imcets. The linguistic Variation Yearbook 7. Mari, A. 2009. Disambiguating the Italian Future. In Proceedings of Generative Lexicon, 209-216. Mari, A. 2010. On the evidential nature of the Italian future. Ms. IJN http://jeannicod. ccsd.cnrs.fr/docs/00/67/85/49/PDF/Evidential_Future_Italian.pdf 26 Mari, A. 2014a. Each Other, asymmetry and reasonable futures. Journal of Semantics, 31(2): 209-261. Mari, A. 2014b. Actuality Entailments: broadening the space of the possibilities. Ms. Institut Jean Nicod and Talk at Linguistics Colloquium University of Chicago, Dec. 2014. Mari, A. to appear. Modalités et Temps. Peter Lang AG. McCready, E. and N. Ogata. 2007. Evidentiality, modality, and probability. Linguistics and Philosophy 30:147-206. Murray, S. to appear. Evidentials and Illocutionary Mood in Cheyenne. To appear in International Journal of American Linguistics. Palmer, F.R. 1987. Mood and Modality. Cambridge UP. Pietrandrea, P. (2005). Epistemic modality : functional properties and the Italian system. Amsterdam : John Benjamin. Portner, Paul 1998. The Progressive in Modal Semantics. Language 74(4): 760-87 Portner, P. 2009. Modality. Oxford University Press. Prior, A. 1957. Time and Modality. Oxford: Oxford University Press. Smirnova, A. 2013a. The meaning of the Bulgarian and Turkish evidentials. Contrastive Linguistics 2013, 2/3: 205-223. Smirnova, A. 2013b. Evidentiality in Bulgarian: Temporality, epistemic modality, and information source. Journal of Semantics 2013, 30(4): 479-532. Squartini, M. 2004. Disentangling evidentiality and epistemic modality in Romance. Lingua, 114: 873-895. Squartini, M. 2012. Evidentiality in interaction: The concessive use of the Italian Future between grammar and discourse. Journal of Pragamtics. doi.org/10.1016/j.pragma.2012.09.008 Thomason, R. 1984. Combination of Tense and Modality, in D. Gabbay; F. Guenthner (eds.), Handbook of Philosophical Logic: Extensions of Classical Logic, Dordrecht: Reidel, 135-165. Trnavac , R. and Taboada, M. 2012. The contribution of nonveridical rhetorical relations to evaluation in discourse. In Language Sciences 34: 301-318. Tsangalidis, A. 1998. Will and tha: a Comparative Study of the Category Future. Thessaloniki: University Studio Press. Willett, T. 1988. A cross-linguistic survey of the grammaticization of evidentiality. Studies in Language 12: 51-97. Yalcin, S. 2007. Epistemic Modals. Mind 116, 464: 983-1026. Zimmermann, M. 2011. Discourse particles. von Heusinger, Maienborn and Portner (eds.) 2011, Handbook of Semantics (HSK 33.2), de Gruyter, 2011-2038. Zwarts, Frans. 1995. Nonveridical contexts. Linguistic Analysis.