Wolfgang Schwarz

Cariani on the modal future

I've been reading Fabrizio Cariani's The Modal Future (Cariani (2021)). It's great. I have a few comments.

This book is about the function of expressions like 'will' or 'gonna' that are typically used to talk about the future, as in (1).

(1) I will write the report.

Intuitively, (1) states that a certain kind of writing event takes place – but not right here and now. 'Will' is a displacement operator, shifting the point of evaluation. Where exactly does the writing event have to take place in order for (1) to be true?

Worlds, histories, and points

Here's a natural first idea. (1) is true as long as a relevant writing event takes place at some point in the future. This yields the standard analysis of 'will' in tense logic:

(TL) 'Will p' is true at a point x in a world w iff p is true at some point later than x in w.

Here we assume that possible worlds contain "points" at which one can evaluate sentences like 'I write the report'. We also assume that there is a temporal "precedence" relation between point that classifies some as earlier than others.

We can't assume that the precedence relation will always be linear. There might be "branching" worlds in which some point x1 is followed by two points x2 and x3, neither of which precedes the other.

Let's define a history as a maximal set of points within a world that is linearly ordered by the precedence relation. The branching world with points x1, x2, and x3 has two histories: { x1, x2 } and { x1, x3 }.

(TL) assumes that 'will p' is true at point x1 in the branching world as long as p is true at one of x2 or x3. We have a double existential quantification, once over histories and once over future points within any history.

Some have though that these truth-conditions are too weak. Perhaps we should say that 'will p' is true at x1 only if both futures x2 and x3 verify p. This yields what Arthur Prior called a Peircean semantics of 'will':

(PS) 'Will p' is true at a point x in a world w iff p is true at some point later than x on every history in w that contains x.

Both of these interpretations assume that 'will' doesn't touch the world w of evaluation. The truth of 'will p' is assumed to depend only on what happens in the actual world. As Cariani points out, this assumption can be challenged. Consider (2)-(5).

(2) A wolf might come in. It will eat you.

(3) If a wolf comes in, it will eat you.

(4) The washing will be dry by now.

(5) She will have told him of her plans long ago.

(2) is a case of modal subordination. The second sentence ('It will eat you') is interpreted not relative to the actual world but relative to the worlds introduced by the prejacent of the previous sentence. This would be unproblematic if the prejacent introduced a single world. We could then apply (TL) or (PS) with the shifted world parameter. But it's hard to see how the first sentence in (2) could introduce a single world. More likely, the sentence directs our attention to a wide range of wolf worlds. Intuitively, 'will' in the second sentence says that the eating takes place in all of them. This suggests that 'will' can act as a universal quantifier over a certain domain of worlds. 'Will' would be a modal. The same could be said about (3).

(4) and (5) are different. The first thing to note here is that 'will' doesn't seem to trigger a temporal shift. When I say that the washing will be dry by now, I'm not talking about what happens in the future. 'Will' here seems to have an epistemic flavour, meaning roughly the same as 'must'.

As we will see, Cariani disagrees with these judgements about (2)-(5). But he agrees that 'will' is a modal. It can shift the world of evaluation. I'll get to this later.

At this point, we can distinguish three questions about where p has to be true in order for 'will p' to be true.

1. Does 'will' require evaluating its prejacent in the future? If so, how?
2. How does 'will' deal with nonlinear cases where there are multiple futures?
3. Can 'will' shift the world of evaluation? If so, how?

Let's see how Cariani answers these questions, starting with the first.

Displacing time

To isolate the purely temporal effect of 'will', let's assume that we live in a linear world, so that we don't have to deal with multiple histories. (TL) and (PS) then agree. They both assume that 'will' involves existential quantification over future points in time. In chapter 7 of The Modal Future, Cariani explains how this could come about even though 'will' doesn't have quantificational force.

The explanation he outlines seems to come from Condoravdi (2002). I hadn't heard of this, but it's really neat. Here's the basic idea.

To begin, we set up a compositional semantics with intervals rather than points. In particular, we say that an "eventive sentence radical" like 'I write the report' is true at an interval (in a world) iff an event of the relevant kind (a report writing) takes place somewhere within the interval (in the world).

A sentence radical is a sentence with the tense removed. The function of the present tense in 'I will write the report' is to bind the interval parameter, setting it to { now }. The function of 'will' is then to extend the interval parameter, changing it from the singleton { now } to the interval [now,…] that ranges from now until the end of the universe – unless context imposes a restriction.

This predicts that 'I will write the report' is true (now) iff a relevant writing event takes place somewhere in the future. That's what we wanted. The existential quantification over future points/intervals is triggered not by 'will', but by the evaluation of the radical 'I write the report' at the interval [now,…].

Cariani doesn't spend a lot of time motivating this account. Here is one puzzle that it seems to explain. Suppose you ask me what I'm going to do tomorrow. I say:

(6) I will go shopping and I will play football.

Let's assume that playing football is incompatible with going shopping: one can't do both at the same time. Any event of playing football is then also an event of not going shopping. One might expect that if 'will p' is true, and p entails q, then 'will q' is also true. So (6) should entail (7):

(7) # I will go shopping and I will not go shopping.

But (7) sounds terrible. In Condoravdi's framework, we can explain what's going on. We only need to assume (plausibly enough) that 'not(p)' is true at an interval iff p is not true at the interval. Since 'will(not(p))' is true iff 'not(p)' is true in the interval [now,…], it follows that 'will(not(p))' is true iff p is not true in [now,…], i.e., iff there is no p event within [now,…]. In (7), the future interval is restricted by 'tomorrow', so the second conjunct in (7) states that I won't go shopping at any point tomorrow.

A similar move with 'and' explains why I could shorten (6) to 'I will go shopping and play football', even though the conjunction of shopping and playing football is an impossible activity.

So we have a nice theory of how 'will p' appears to quantify over the future.

What about (4) and (5) from above, where 'will' does not appear to invoke any shift into the future?

(4) The washing will be dry by now.

(5) She will have told him of her plans long ago.

Apparently Condoravdi suggests that 'will' here functions as an epistemic modal. Cariani prefers to stick with the temporal interpretation. He suggests (on p.134) that 'by now' in (4) restricts the interval at which the radical 'the washing be dry' is evaluated to the point interval { now }. For "stative" radicals like 'the washing be dry', truth at an interval only requires overlap with the interval. (4) therefore simply says that the washing is (now) dry.

Cariani doesn't discuss past-directed cases like (5). He actually mentions them on p.49, but then seems to forget that they exist, referring to all non-future directed uses of 'will' as 'present-directed'. But I guess one could tell a story similar to Cariani's account of (4) that makes (5) equivalent to 'she told him of her plans long ago'.

It seems odd that 'will' has no function at all in (4) and (5). Perhaps it would be better to say that it adds an "evidential" element, indicating that the speaker has indirect evidence in support of the relevant statement.

Cariani has an argument (on p.92) against reading 'will' in (4) and (5) as an epistemic necessity modal, akin to 'must': this would predict that the relative scope of 'will' and 'not' should make a difference, but it does not. For example, 'nobody's washing will be dry' seems equivalent to 'everyone's washing will not be dry'.

We'll see more of this argument when we look at other potential dimensions of displacement.

I'll mention another potential argument against the epistemic reading of (4) and (5), an argument Cariani doesn't consider. Since there appear to be present-directed and past-directed epistemic uses of 'will', one would expect that there are also future-directed uses. This is perhaps easier to test in languages like German, where the simple present form is commonly used when talking about the future:

(5b) Sie wird es ihm morgen sagen. (She will tell him tomorrow.)

We should expect that (5b) has an epistemic and a non-epistemic reading. But it's hard to detect such an ambiguity.

Displacing history

We've looked at the purely temporal effect of 'will'. Next, let's study how 'will' deals with multiple histories. Does it quantify universally over all histories through the point of evaluation, as assumed in (PS), or existentially, as assumed in (TL)?

Cariani makes it difficult to focus on this question due to a terrible choice of terminology. He decides to refer to histories as 'worlds'. So a "world", in Cariani's sense, is a maximal set of points that are linearly ordered by the precedence relation of some world. I will not follow this usage. I will use 'history' for histories and 'world' for worlds.

How much we should care about the function of 'will' in nonlinear worlds depends on how seriously we take such worlds. If they are just a far-fetched conceptual possibility, we may not spend a lot of effort on the question. Some philosophers, however, think that the actual world may well have multiple histories. (I am one of these philosophers.) In this case, it would be good to clarify how 'will' deals with such worlds.

Early on in Cariani's book, one gets the impression that he agrees. Chapter 2 is entirely about branching-time models. A little later, in chapter 4, we get extensive arguments against the assumption that 'will' is an existential quantifier over histories, as assumed in (TL), and also against the assumption that it is a universal quantifier over histories, as assumed in (PS).

At this point, I expected to learn about Cariani's own account of how 'will' deals with multiple histories. But the question is completely ignored until chapter 11, near the end of the book. From chapter 5 until chapter 10, it is simply assumed that sentences are evaluated relative to a history (what Cariani calls a "world") that gives us a linear sequence of points.

Giving a history-relative semantics is a familiar strategy in tense logic, started in Thomason (1970). This is usually combined with a supervaluationist account of utterance truth to explain when an utterance in a nonlinear world is true. Cariani doesn't like this account because it violates bivalence and because it renders utterances of future contingents untrue. In chapter 11, he instead appeals to the idea of "metaphysical indeterminacy", as in Barnes and Cameron (2009). On this view, worlds with multiple histories should be described as worlds in which there is a unique history, but it is metaphysically indeterminate which it is. A sentence is true, and its assertion appropriate, if it is true relative to the unique history. Since it is indeterminate which history that is, it can be indeterminate whether a sentence is true and an assertion appropriate.

I have to admit that I don't really understand this view. I can repeat the words, but I don't understand how they could be true. I struggle to see how it is meant to answer the questions I have about the function of 'will' in a nonlinear world.

I care about nonlinear worlds because of physics. I believe that our intuitive model of the world is linear. We take for granted that there is a unique past and a unique future, and that any two points can be compared in terms of the precedence relation. But physics seems to disagree. Relativity Theory suggests that the precedence relation among points forms a strange mesh of constant branching and reconverging (both towards the past and towards the future). The main realist interpretation of standard quantum physics, the Everett interpretation, suggests that the points at which ordinary statements can be evaluated form a branching structure in which each point precedes many points in the future that are neither earlier nor later than each other.

I'd like to know how we should talk about the future, given that we're in a world of this kind. If we know that p will take place on one branch of the wavefunction and not on another, should we say 'will p'? I'm genuinely unsure. I'd like to know. Cariani's answer doesn't help me. He says that it's metaphysically indeterminate whether I should say 'will p'. What am I supposed to do with that? Besides, I don't think the picture we get from Relativity or the Everett interpretation involves any metaphysical indeterminacy.

It would have been better to supervaluate, or to use existential or universal quantification, as in (TL) and (PS).

Cariani has some arguments against (TL) and (PS). He complains that the Peircean interpretation (PS) is 'too demanding' (pp.60f.). I don't understand the problem. Cariani seems to assume that the quantification over histories would range over all possible histories. But the history quantification only ranges over actual histories that pass through the point of utterance. Also, who decides what is too demanding?

Cariani also complains that (PS) and (TL) have bad consequences for credence and betting (pp.63ff.). Let's assume, with (PS), that 'will p' is true iff p occurs on all histories. Now suppose we know that p occurs on some histories and not on others. (PS) predicts that we should be certain that 'will p' is false, and that we should bet heavily against 'will p'. Cariani thinks that this is wrong. Apparently he thinks that we should have a middling credence towards 'will p', and bet accordingly.

This is not at all obvious to me. If I know that the world contains a p event on some history and none on another, why should I be unsure about 'will p'? What is this uncertainty about? I know all relevant facts!

As it turns out, this issue does come up in the Everett interpretation. Any realist understanding of quantum physics must make sense of the Born rule, and the born rule seems to demand specific credences towards future observations – which, on the Everett interpretation, are bound to take place on some histories and not on others. There is an interesting literature on this puzzle (see, for example, Greaves and Myrvold (2010), Wallace (2012), Sebens and Carroll (2017)). The main problem here is to explain what it could even mean to give credence 0.5 (say) to something of which one knows that it happens in one branch of the universe and not in another. It isn't important whether this attitude can be expressed with 'I'm 50% sure that p will be the case', and I see no good reason to think that it must.

So while there really appears to be a puzzle about credence and betting in some cases with multiple histories, this puzzle arises independently of whether we adopt (PS) or (TL) or the doctrine of metaphysical indeterminacy. It's not a fault of (PS) or (TL).

Cariani's third argument against the quantificational analyses (PS) and (TL) is their implication that the relative scope of 'will' and 'not' should make a difference. Cariani insists that it does not. He thinks that 'no student will pass' is equivalent to 'every student will fail'. If 'will' involves a universal or existential quantifier, the two should come apart.

It's crucial that we test the prediction in the relevant scenarios. We have to focus on strange and counterintuitive situations in which p is true in one future and false in another. For a toy model of what this involves, imagine we're talking about a group of students who are about to undergo fission. Each student will have two fission products, one of which will pass the test while the other will fail. Now, is 'every student will pass' true? What about 'no student will pass'? 'Every student will fail'? It's really not clear! I can easily get myself to accept both 'every student will pass' and 'every student will fail'.

There's a more general methodological point here.

When Cariani discusses nonlinear worlds, he assumes that they are meant to represent our commonsense model of time. In chapter 10, for example, he considers the view that (i) the world is nonlinear, and (ii) 'will p' is neither true nor false at a point if the point has one future with p and another future (on a different history) without p. He argues that this has the absurd consequence that we may never assert future contingents, on the plausible assumption that one may only assert something if it is true. But why is this consequence absurd? Because, he says (on p.199), we regularly assert future contingents and see nothing wrong with that. So what? This is only relevant if we all know or believe that the world is nonlinear, and take its nonlinearity into account when we make assertions. In my view, most people don't really believe that the world is nonlinear, and even those who do usually hide this disturbing belief in a compartment of their belief system where it doesn't interfere with everyday life.

Perhaps what Cariani should have said about nonlinear worlds is that he doesn't care about them. His aim is to study our ordinary thought and talk about the future, and he seems to agree that our ordinary thought and talk assumes linearity. He shouldn't have tried to argue against the existential interpretation (TL) or the universal interpretation (PS), and he shouldn't have proposed his metaphysical indeterminacy alternative. Or perhaps he should have presented the downsides of the various alternatives as evidence that our commonsense conception is linear. A nonlinear world requires a strange and unfamiliar way of speaking and thinking and evaluating other people's assertions. My hunch is that our existing rules of thought and talk don't settle how we should deal with multiple histories. Any way of settling the matter will seem weird.

Displacing the world

We've looked at the purely temporal effect of 'will': it extends the interval of evaluation into the future. We've also looked at how 'will' deals with multiple histories within the world of evaluation. Here we haven't reached a clear verdict. Now let's look at what 'will' does to the world of evaluation. Is it a modal? Does it shift the world of evaluation?

Earlier, I listed (2)-(5) as cases that may seem to call for a modal account of 'will'.

(2) A wolf might come in. It will eat you.

(3) If a wolf comes in, it will eat you.

(4) The washing will be dry by now.

(5) She will have told him of her plans long ago.

We've seen that Cariani rejects a modal analysis of (4) and (5). What about (2) and (3)? Cariani thinks that these really do call for a modal interpretation of 'will'. In particular, he suggests that the if-clause in (3) restricts the modal domain of 'will'. This only makes sense if 'will' has a modal domain. He doesn't say much about subordination cases like (2), but suggests that they work in a similar way. Let's focus on conditionals.

Why should we think that the if-clause in 'if A, will B' restricts the domain of 'will'? Many alternative possibilities are on the table.

We could say, for example, that the if-clause restricts a tacit epistemic modal, rather than 'will'. (If we go with the restrictor view, we have to posit tacit epistemic modals all over the place, so why not here?) We could then let 'will' have a purely temporal function. We would not have a "modal future". Cariani doesn't explain what's wrong with this alternative.

Almost every existing alternative to the restrictor analysis of conditionals would also allow us to retain a purely temporal interpretation of 'will'. We could analyse 'if A, B' as a material conditional, or as a Stalnaker conditional, or as a Lewis conditional, or as a strict conditional, or as some informational dynamic test, or whatever. All of these accounts only require a pointwise evaluation of the consequent 'will B' at particular worlds, for which a purely temporal 'will' would suffice.

OK, we can't reasonably expect Cariani to prove that his analysis of conditionals is superior to every alternative. I just want to note that if the thesis of the "modal future" hangs on this particular analysis of conditionals, and thereby on the falsity of almost every theory of conditionals anyone has ever proposed, then I'm not ready to say that the thesis is true.

Let's have a closer look at Cariani's analysis. The idea is that 'will' operates on a certain domain of worlds that can be restricted by if-clauses, in a pattern familiar from Kratzer (2012).

Two things need to be clarified to spell this out. What's the original domain associated with 'will'? And, how does 'will' operate on this domain? I'll start with the second question.

It's clear that 'will' can't be an existential quantifier over its domain, unless all the worlds in the domain agree about the future. Otherwise 'will p' could be true even though p never happens.

Could 'will' be a universal quantifier over its domain? Cariani denies this, for a reason that should be familiar: it would predict scope distinctions with negation that we don't observe. If the domain contains some worlds at which all students pass and others at which all students fail, then 'no student will pass' should be true and 'every student will fail' should be false. But the two sentences seem to say the same thing.

I wouldn't be convinced by this argument if I wanted to defend a universal reading of 'will'. The phenomenon looks too much like a kind of "homogeneity presupposition". Cariani considers this response on pp.69-72 and raises three objections. First, he thinks the response would be ad hoc. Would it? Second, he says that it doesn't help with the credence problem in multiple histories cases. That's true, but (a) no semantics of 'will' can solve that problem, and (b) the problem is irrelevant to the present topic, where we can set aside worlds with multiple histories. Third, he says that the homogeneity data also arises in contexts where the homogeneity is explicitly denied, as in 'it is possible that Riya will study X and it is possible that she will study Y'. I'm not sure how this argument is meant to go. Among other things, it seems to assume that the domain of 'will' is the same as that of 'possible'.

Anyway, what is Cariani's positive proposal? How does 'will' operate on its domain, if it is neither a universal nor an existential quantifier?

Cariani suggests that 'will' is a selectional modal. Its function is to select a single element from its domain. 'Will p' says that p is true at the selected world.

More needs to be said to make this plausible. Suppose the domain contains some worlds where p is going to happen and others where it won't happen. If the actual world is of the latter kind, we want 'will p' to be false. Cariani therefore stipulates that when 'will p' is evaluated at a world w then the selected world is always w itself – unless the domain doesn't contain w. The upshot is that 'will' only changes the world of evaluation if the modal domain has been restricted or shifted so as to exclude the world of evaluation.

If we add in the temporal effect of 'will', Cariani's semantics for 'will' goes roughly like this.

(C) 'Will p' is true at a point x in a world w iff p is true in some interval after x in the world selected by w from the modal domain of w.

(Cariani's actual semantics differs from (C) mainly by swapping the worlds for histories.)

I say that the selected world is "selected by w" because the selection process depends on the world of evaluation, as I just explained: if w is in the domain then the selected world is w. We need the modal domain to vary with the world of evaluation to give sensible results for sentences like 'it is possible that I will write the report'.

I haven't yet said what kind of domain is associated with 'will'. Cariani says (on p.79) that the domain of 'will' relative to a world w consists of all worlds that perfectly match w up to the time of evaluation in terms of local matters of fact. So 'will' is treated as a special kind of circumstantial modal.

I don't understand this decision. I may have missed it, but I don't think Cariani gives any explanation or motivation. On pp.116f., he briefly considers giving 'will' an epistemic flavour instead, associating it with a (possibly world-relative) class of epistemically possible worlds. He says that 'there is little to choose between' the two options.

I think it would have been better to go with an epistemic interpretation. Here are two reasons.

First. Circumstantial modals and epistemic modals differ in whether they allow back-reference to the actual world, as illustrated in (8) and (9). Circumstantial modals allow for back-reference, epistemic modals don't.

(8) I could have been taller than I (actually) am.

(9) # I might be taller than I (actually) am.

Indicative conditionals don't allow for this kind of back-reference:

(10) # If I take the pill then I will be taller tomorrow than I will (actually) be.

This is a strong reason to think that any modal involved in the indicative conditional is epistemic.

Second. Imagine our evidence is divided between two possibilities: either Bob is currently in Paris and about to travel to Lyon, or he is in London and about to travel to Edinburgh. Any other possibility can be ruled out. Cariani's semantics correctly predicts that (11) and (12) are true:

(11) It is possible that Bob will travel to Lyon today.

(12) It is possible that Bob will travel to Edinburgh today.

But it also predicts that one of (13) and (14) is false:

(13) If Bob is in Paris then he will travel to Lyon today.

(14) If Bob is in London then he will travel to Edinburgh today.

For example, suppose Bob is actually in Paris. Then the historical domain consists of worlds in which Bob has travelled to Paris so far. In some of these worlds Bob has now quantum tunnelled to London. These are the worlds we find in the historical domain when it is restricted by the antecedent of (14). The actual world is not among them. Who knows what's going on in the selected world from this domain, but it is very unlikely that it's a world where Bob is going to Edinburgh.

[Edit: I've fixed the previous paragraph after posting. I initially thought the restricted modal domain would be empty. We can make really sure that it's not empty by changing the case so that the antecedents are also about the future ('If Bob is in Paris at lunchtime then…').]

I don't think it's important for Cariani's overall view whether 'will' is epistemic of circumstantial, as long as it's a modal. Let's pretend that he defends the more plausible epistemic hypothesis.

As I mentioned above, Cariani's case for a modal interpretation of 'will' rests almost entirely on his analysis of conditionals, and I'm not willing to sign up for that. I do see the motivation. In light of Lewis (1975) and Kratzer (2012), it is tempting to think that the if-clause in 'if A then will B' restricts 'will', in the same way in which the if-clause in 'if A then would B' restricts 'would'. It's also tempting to think that 'will' has the same semantic function in 'if A then will B' and in 'will B' alone. Finally, it's tempting to think that 'if A then will B' is not a material conditional. Putting these three tempting ideas together leads us to Cariani's semantics. We should infer that 'will' is a selectional (epistemic) modal.

The problem is that there are a lot of tempting ideas that turn out to be wrong, especially in the field of conditionals. Cariani argues (in chapter 8) that his analysis improves upon Stalnaker's in certain respects. I agree. But this doesn't do much for me, since I'm not a great fan of Stalnaker's semantics to begin with.

One thing I'd definitely like to know before I subscribe to any form of selection semantics is how the selection parameter is supposed to be understood. When we utter a conditional, the utterance situation does not provide a selection function. We need to connect the formal evaluation points, which include a selection function, with a concrete utterance situation. What does it take for an utterance to be true or false? Cariani discusses this issue for the history parameter, but not for the selection parameter. Given what he says about history, I fear that he would say that every utterance situation provides a unique selection function, although it is often metaphysically indeterminate which function that is. At this point, I would definitely have jumped ship. This is a theory I don't even understand.