Alhassanain(p) Network for Heritage and Islamic Thought

MAY, MIGHT, AND IF

[1]

Table of Contents

[Introduction] 3

1. Commands and Permissions 4

2. Epistemic modals 11

3. Indicative conditionals 18

References 27

Notes 29

[Introduction]

My main concern in this paper will be with the relation between semantic content and speech act force, with a focus on cases where a speech act aims at doing something other than communicating an item of information. I will try to bring out some connections and analogies between three controversies, each concerning a specific kind of modal construction. I will look first at David Lewis’s language game of command and permission, second at the problem of epistemic modals, and third at debates about whether indicative conditionals express propositions.[2]

The classic discussions of speech acts distinguished the propositional content of a speech act from the illocutionary force with which that content is expressed. On the account of assertion that I have proposed, assertive force is explained in terms of the way the speaker intends to change the context, where context is understood as the common ground. Specifically, in the simplified and idealized assertion game, an assertion is a proposal to change the common ground by adding the content of the assertion to it. The change takes effect unless the assertion is rejected. This account of assertive force is characteristic of a wider range of speech acts than those that are properly called assertion, but assertive force, even in the broad sense that covers this range of cases, still differs from the force of some other speech acts that we will consider.

While the assertion game that I sketched uses a very abstract notion of force, it retains the traditional force/content distinction. I want to empasize the difference between a dynamicpragmatics and a dynamicsemantic theory. The former says that content is determined as a function of context, and then a general force rule explains how the content changes the context. The latter streamlines the story, eliminating the middleman by building force into the semantic values of sentences. The projects I will discuss in this chapter all retain a distinction between content and force, in some form at least.

1. Commands and Permissions

I will start with what David Lewis called “a little language game” that he used to raise a problem about permission. Lewis’s game was not presented as an analysis of any natural language expressions, but was the construction of an artificial game designed to throw light on the content/force difference. Traditionally, there are two ways to think about the role of modal notions, including the deontic modality involved in commands and permissions. On the one hand, one may think of a modal operator as determining a distinctive kind of proposition as a function of the proposition on which it operates (which, following the linguists, who are following medieval theorists, I will call theprejacent ). But there is also a tradition of thinking of modality as determining themode with which a proposition is expressed, and not being a part of, or a determinant of, the proposition itself.  Lewis’s game defines both a distinctive kind of deontic content, and a distinctive kind of imperative force, or mode, with which that content is expressed. First, the compositional semantics for the deontic sentences of the language that Lewis specifies determines propositions stating what one is obliged and permitted to do. Second, pragmatic rules are given for the use of the sentences in the playing of the language game. The pragmatic rules say how the things that the players might say will affect the state of play.

Specifically,[3]the language is a standard deontic propositional modal language, with sentence letters and two interdefinable modal operators, ‘!’ and ‘¡’ (which Lewis called ‘fiat’ and ‘taif’) for saying, respectively, what is required and what is permitted. In the standard Kripke-style semantics for such a language, a model consists of a set of possible worlds and a binary accessibility relation: the relation holds between worlds x and y if and only if world y is compatible with what is permissible in world x. Lewis’s semantics is close to this familiar modal semantics, with world-time pairs playing the role of the possible worlds. Sentences of the form !fand ¡f, when used in possible worldw at timet ,  say what is required or permitted at that time in that world. Their truth values, atát,x ñ, are determined by whetherfis true at some or all world-time pairs within a set of world-times that is defined in terms ofát ,x ñLewis calls this set the ‘sphere of permissibility’ forát,x ñ. 

There is little novelty in the language or in the truth-conditional semantics for it. The distinctive feature of the game is in the pragmatic rules, which are as follows: There are three players with distinctive roles: the master, the slave, and the kibitzer. The master controls the sphere of permissibility. When she issues a statement of the form !f(at timet in worldx ), the sphere of permissibility adjusts to make the statement true at that time. More specifically, the master’s command (atát ,x ñ) makes it the case that the sphere of permissibility for timet in worldx is the intersection of the sphere as it was beforet with the proposition expressed byf.  The slave’s job is to act in a way that ensures that the actual world remains within the sphere of permissibility. The kibitzer has no special powers or responsibilities, but can comment on the situation, perhaps reminding the slave what he must do, or the master what she has commanded or permitted. The point of having a kibitzer in the game is to bring out the fact that the same sentence, with the same content, can be, in the mouth of one player, a command, and in the mouth of another an assertion. Both speech acts will have deontic content, but only one will have imperative force.[4]

The master can issue permissions as well as commands, and just as a command by the master makes it true that something is required, so a permission statement is supposed to make it true that something is permitted. In the case of a command, there is a straightforward answer to the question, what is the minimal adjustment to the prior sphere of permissibility necessary to make the content of the command true? So it is clear what the rule specifying the force of a command should be. But with a permission statement, there is no such answer. There is no unique way of “subtracting” a requirement in order to make a permission statement true. The task of finding a rule that says how the issuing of a permission statement by the master changes the context is the problem about permission that Lewis is referring to in the title of his paper. The paper does not offer a solution to the problem. It is argued that each of the proposed solutions that are considered either fails to be adequate, or is just a way of restating the problem.

I am not sure what Lewis would have counted as a solution to his problem (as contrasted with a restatement of it), since it is clear that any solution will require that new resources be added to the model, and any postulation of new resources sufficient to provide a determinate rule by which the spheres of permissibility evolve might be charged with being just a way of posing the problem. But a reformulation of the problem may still be helpful in sharpening it. Whether or not it counts as a solution, one can say something about the abstract structure of the resources that need to be added, and perhaps about the way the added resources might have application to other problems. Lewis’s own work on the logic and semantics of counterfactual conditionals points the way, since there are parallels between the problem about permission and the problem of counterfactuals. The problem about permission might be put this way: suppose something impermissible was made permissible. What else would then be permissible?  This looks a lot like the question: suppose a certain proposition that is in fact false were true. What else would then be true?  The rough idea of Lewis’s analysis of counterfactuals is that a counterfactual, (f£®y) is true in possible world x if and only ifyis true in all of the possible worlds in whichfis trueand which are otherwise minimally different from x .  A model for interpreting counterfactuals specifies a comparative “closeness” relation that determines what “minimal difference” comes to. One could add an analogous relation to the models for the commands and permissions game. There are alternative ways of making the structure precise, but one might suppose that the spheres of permissibility are nested in a succession of wider backup spheres, with some impermissible worlds “closer” to permissibility than others. When the master says ‘¡f’ at a given world-time, the prior sphere of permissibility expands to include those points at whichfis true, and which are in the “closest” sphere that includes some points at whichfis true. Nothing substantive could be said about the relevant notion of closeness at this level of abstraction, but it seems reasonable to think that a permission game of the kind Lewis defined will require a relation with this structure, and if our models contained such a relation, it would yield a determinate rule for the evolution of the spheres of permissibility in response to permission statements by the master.[5]

It is this problem about permission that gets most of Lewis’s attention, but there is also a small problem about commands (and permissions) that he does not consider, but that will be important for the analogy with epistemic modals that I will develop. The problem is this: The force rule for the master’s imperative utterances is clear enough for simple commands – simple sentences of the form !f. But Lewis’s game gives a complete compositional semantics for sentences of the deontic language, including truth-functions of sentences that mix deontic and descriptive content. We need to consider what should happen when the master utters a sentence with mixed deontic and factual content. Suppose the master (Scrooge, in this example) says to the slave (Bob Cratchit), after having reluctantly given him permission to take Christmas off: “If you do take Christmas off, you must work an extra hour the next day.” Or perhaps Scrooge uses a disjunctive sentence to perform his speech act: “Either you work on Christmas, or you must work an extra hour the day after.”  (If ‘C’ is ‘Cratchit works on Christmas’, and ‘W’ is ‘Cratchit works an extra hour the next day’ then Scrooge’s sentence is (CÚ!W)) ). What is the effect of the utterance of this disjunction? The general rule for the master’s speech acts was supposed to be this: the sphere of permissibility adjusts in the minimal way required to make the master’s sentence true, but it is not clear how to apply this rule to the disjunctive sentence with one imperative disjunct. If the sphere contracts to require that the Cratchit is (categorically) required to work the extra hour, this will ensure that Scrooge’s utterance is true, but this is too strong, since the statement might be true without this change. On the other hand, if the sphere contracts only enough to require that Cratchit is obliged to make the disjunction (CÚW) is true, this will not suffice to ensure that Scrooge’s sentence, interpreted in a straightforward way, is true. Suppose Cratchit fulfills his obligation by taking Christmas off, and then working the extra hour the next day. Scrooge’s statement will then be false since the first disjunct will be false, and because there is no categorical requirement, the second will be false as well. 

The literal-minded Cratchit might be tempted to reason this way: “Either the command disjunct is true, in which case I have to work the extra hour whether or not I take Christmas off, or it is false, in which case I have no extra obligations, no matter what I do. In the former case, I prefer to take Christmas off rather than work Christmas, and also the extra hour the next day. In the latter case, I also prefer to take Christmas off (since in this case, I still won’t have to work any extra hours). So in either case, that is what I should do. Of course I recognize that since I plan to take Christmas off, it must be thatif the Master’s command is true, it is the second disjunct that is true. but perhaps the master’s statement is false, since it is at leastpartly a prediction, and therefore not automatically true. Furthermore, since I know that the master has not issued any new categorical command, I have reason to think that the second disjunct is false, whatever I do, and so (given that I am planning to falsify the first disjunct) it seems that the master’s statement is just mistaken.” Has the clever Cratchit found a loophole that will allow him to have his Christmas off, with no extra hours the next day? Scrooge might protest, “What Imeant to say was that you must either work Christmas, or work an extra hour the next day.” “But,” Cratchit replies, “that is not what you said.”[6]

Of course Lewis’s game is just a made-up exercise, and we can adjust either the compositional semantics or the force rules in any way we like. One might simply stipulate that an utterance from the master counts as a command (or a permission) only if it is an unembedded deontic sentence. On this proposal, a sentence with an embedded deontic clause will always be treated as an assertion, even in the mouth of the master. On this stipulation, the reasoning that we put into the mouth of Cratchit is perfectly correct. To avoid this consequence, one might stay with this semantics, and this policy, for the official language, but allow commands to be made withsurface sentences with imperative parts so long as they can be reinterpreted and formalized as categorical imperatives (for example taking the real form of “either C or ought-W” to be ‘!(CÚW)’). But these moves would rob the game of much of its interest, which is the promise that it can combine the advantages of a compositional semantics with a general account of speech acts that are used to do something different from what straightforward assertions do, which is to state what the world is like. The hope is that a game with this feature will throw some light on the way deontic and other modal expressions work in natural language. For this reason, the way we adjust the rules of the artificial game to solve the problem should be guided by the related phenomena in natural language, and it seems intuitively that complex sentences with embedded deontic clauses can be used (by a speaker with the right status) to change what is required. The problem for the game, and the adjustment to solve it, should help to explain why the natural language constructions that are the analogues of the operators in our simple game have some of the features they have.

The solution I will suggest modifies, not the force rule, but the compositional semantics, and it will make use of the notion of a subordinate context that is independently motivated by its use in the explanation of phenomena concerning presupposition and anaphora. The simplest case of a subordinate or derived context is a temporary context created by a supposition. In the case of an indicative suppositions, the derived context is represented by the subset of the set of basic context set in which the proposition supposed is true. Subordinate contexts or this kind are wholly defined in terms of basic contexts, so in a sense they are features of the basic context – the common ground. One central role of subordinate contexts is to help to explain the dynamic process of presupposition accommodation, and to bring into focus the information provided by the basic context that is available for determining the propositions expressed or denoted by embedded clauses. But there is no reason why a language could not have modifiers or operators that are interpreted by semantic rules that appeal to relevant subordinate contexts, when the operators or modifiers occur in embedded clauses. If we interpret the deontic operators in Lewis’s language this way, we can explain why some complex sentences with imperative parts can have the structure that they appear to have (a disjunction with one imperative disjunct, or a conditional with an imperative consequent), and also be governed by the general force rule when they are used by the master. This is the rule that says that the sphere of permissibility adjusts in the minimal way required to ensure that the sentence as a whole is true. So suppose we add to the semantics for Lewis’s game an extra parameter of the interpretation, acontext , represented by a set of world-time pairs. The semantic rule for the imperative, in the unmodified theory, was this:

[!f]át,xñ= 1 iff [f]áy,tñ= 1 for all yÎSát,xñ

(where Sát,xñis the sphere of permissibility atát,xñ)

The modified rule will be this:

                   [!f]át,x, Cñ= 1 iff [f]áy,t, Cñ= 1 for all yÎSát,xñÇC.

(where C is the new parameter, a set of time-world pairs)

The default or initial context (for the interpretation of unembedded sentences) will be the set of all the relevant time-world pairs, “all of those such thatt is a time during the game, andw is accessible (at the actual world) at the time at which the game begins.”[7]So the modified rule will yield the same result as the original rule for unembedded commands. But the context parameter may be shifted by a compositional rule for another operator. With this modification to the semantics, the force rule can be general: the master’s utterance of the sentence with the embedded deontic clause will adjust the sphere of permissibility to ensure the truth of the complete sentence.

It is not that every sentence with an embedded deontic clause will be suitable for issuing commands. There is no way, for example, that a belief attribution to someone other than the master could be used, by the master, to change the sphere of permissibility. If the master said to the slave “The kibitzer believes that you must work an extra hour on the day after Christmas,” this will be interpreted as an ordinary assertion, since no change in sphere of permissibility would suffice to make it true.

Though the suggested modification of the semantics is motivated by the role that we want  imperative and permission statements to have in the overall game, the semantics remains independent of the force rule, and the modified semantics is still static in the sense that the semantic value of any sentence in a given context, and at a given time, is a function of the semantic values of the parts at that same context and time.

We haven’t said exactly how the parameter shifts in a disjunctive or conditional context – that will depend on the semantics and pragmatics of disjunction and the conditional. Conditionals I will discuss later. Disjunction is complicated, with the order of the disjuncts sometimes mattering, and sometimes not. (It seems to matter in this case). The parameter shift might in some cases be optional, allowing for scope distinctions, though some possible interpretations that make sense for the kibitzer’s assertions might not make sense for the master’s commands. If the shift is optional, then even with the modified rule, the disjunctive sentence, in the Scrooge example, might have the interpretation that Cratchit took it to have. The kibitzer, for example, might remember that either the master commanded the slave to work an extra hour, or else the slave decided to take Christmas off, but can’t remember which. But the master could not use the sentence, interpreted this way, to issue a command.

  There is more to say about the ways that Lewis’s game might be refined and extended, but I will leave that for another time. To conclude this section I will point to some features of the game that are relevant to our general concern with the relation between content and force.

To the question, “Should the distinctive character of a command or the issuing of permission be represented with a modal operator, affecting the content, or by a force operator, determining the way that a given content affects the context?”  Lewis answer was “both.” Deontic content is explained independently of force, so we can account for propositions about requirements and permissions that are embedded in complex statements, and explain how propositions about requirements and permissions can be the content of speech acts of different kinds. But the theory also gives a precise account of a distinctive kind of imperative force, and an explanation of the relation between the distinctive kind of content and the distinctive kind of force. The semantic account of the content isstatic in the following sense: The compositional rule for a deontic sentence, !for ¡f, specifies the proposition expressed at a given point (world-time pair) as a function of the proposition expressed by the prejacentfat that same point.

The pragmatic force rule is like the rule for assertion in that it explains force in term of the way that the speech act changes the context, as a function of the content of the speech act. But commands and permissions issued by the master contrast with assertions (including assertions of deontic propositions) in this way: they change the context by changing a parameter of interpretation (the sphere of permissibility) so as to make the proposition true. The result is that in these cases the determination of the content of the speech act isprospective in the following sense: the content of the deontic sentence is interpreted relative theposterior context – the context as it is after the force rule is applied.  Because of this feature of imperative force, it contrasts with assertive force, where the content of the assertion is determined relative to theprior context. The prior context is not the context as it was before the speech act took place, but the context as it is after the manifest fact that the speech event has occurred is recognized. But the context change, in the case of the imperative speech acts of Lewis’s game, is not a case of presupposition accommodation. In these cases, it is the application of the force rule itself that brings about the change in the parameter of the context relative to which the content of the speech act is determined.

The form of this dynamic rule (context is changed as a function of a proposition that is determined as a function of the context that results from the change) introduces an obvious threat of circularity. The strategy for avoiding circularity is to specify that the context is to be changed in the minimal way required to make the proposition true. In the case of commands, it is clear what the unique minimal change is, but in the case of permission, additional structure must be added to the models in order to get a determinate force rule that avoids circularity.

So let me sum up the lessons of Lewis’s little language game, lessons that will carry over to the other modal expressions I will consider: First, the semantics is static, and is explained independently of force. Second, the way imperative speech acts change the context is prospective. Third, the prospective character of the force rule requires (in the case of permission) that structure beyond that required for the static semantics be introduced in order to give a determinate account of the dynamics of the game.