Abstract
An argument is usually said to be valid iff it is truth-preserving—iff it cannot be that all its premises are true and its conclusion false. But imperatives (it is normally thought) are not truth-apt. They are not in the business of saying how the world is, and therefore cannot either succeed or fail in doing so. To solve this problem, we need to find a new criterion of validity, and I aim to propose such a criterion.
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Notes
One solution to the problem is to claim that imperatives are in fact truth-apt. For discussion of this view, see my (2012).
Note that by “conservative” here, I do not mean what is often meant by this word in discussions of the “conversativeness of logic” in the related literature on “ought” and “is”—for example (Pigden 1989).
The rough-and-ready test cannot be applied to arguments whose conclusions have (conventional or conversational) implicatures that the premises lack. A person might, without making a logical mistake, be willing to assert (H1) “She was poor and honest” but unwilling to also assert (H2) “She was poor but honest”, even though (H1) logically entails (H2). Fortunately none of the examples we will need to apply it to have that feature.
I use the term “command” here in a technical sense which is broader than the usual non-technical one. Imperative sentences can be used to make speech acts that are not military-style orders: requests, suggestions, and the like. For the purposes of this paper, these are all to count as “commands” in my technical sense. Austin introduced the term “exercitive” for a broad category of speech acts including commands (Austin 1978, p. 155); but exercitives are a much broader category than I intend command to be, including bequeathings, finings, and that Austinian standby, namings of ships after dictators.
This example (like others in this paper) brushes over a difficulty in determining the tense and aspect of clauses in the imperative mood. (2) speaks of an attack to take place in the future, so perhaps (1) should be “You will attack at dawn.” I have ignored this because to consistently get it right would involve distracting and controversial excursions into the syntax and semantics of tense in natural language. For example, in (A1), “the weather is fine” speaks of the future, in spite of being in the present tense; this could be regarded as an implicit anaphora, with (A1) abbreviating “Attack at dawn if the weather is fine at that time!” To sort this out for every example in the text would be well beyond the scope of this paper.
Or, to accommodate “de se” content, sets of centered worlds, where a centered world is a possible world together with a time, a speaker, and perhaps other parameters. For the purposes of this paper, I will be speaking of propositions as “sets of worlds”, leaving it open whether “world” means possible world or centered world.
I have more to say about the differences between assertions and commands in Sect. 3.5. To foreshadow: on my view assertions and commands differ in what mental states they express—assertions express beliefs, commands express intentions—and it is these mental states that differ in direction of fit.
Principally, from Hare (1952, sect. 2.5) and (1967). Hare's other works clarify his views about the relationship between moral statements and imperatives a great deal; as I understand him, his basic views about the logic of imperatives remain much as they are set out in the Language of Morals. Clause (c) was particularly important to Hare, as it is connected with his arguments for prescriptivism—clause (c) together with prescriptivism explains why it is (allegedly) impossible to derive an ought from an is.
Bergström (1970), for example, suggests a way in which Hare could accept that (H) is valid.
More generally, in an “if”-conditional, the subordinate clause is the antecedent and the main clause the consequent; in an “only if” conditional, the subordinate clause is the consequent and the main clause the antecedent. The subordinated clause is the one that appears immediately after the word “if”. In English (unlike propositional logic) the order of clauses in a conditional is irrelevant to which is the antecedent and which the consequent; also irrelevant is whether the word “then” appears. Thus:
“If p, then q” is formalised…
p→q
“p if q”
q→p
“p only if q”
p→q
Subordinated clauses cannot occur in the imperative mood, which fact is responsible for the widespread but mistaken view that conditionals cannot have an imperative antecedent. It is possible to put an imperative into the antecedent of a conditional by using “only if”, as I have done here.
There are alternative views of “only if”, which may allow the standard view to escape this argument. For example, it may be thought that an “only if” conditional is not the converse, but the converse contrapositive, of the corresponding “if” conditional. On that view “p only if q” would be formalised “¬q→¬p”. This would only differ from the treatment of “only if” that I am assuming if contraposition is invalid (i.e. if → is not the material conditional, as I assumed, but some non-contraposable conditional). So the standard view could potentially escape the evil twins problem by embracing some fancy account of the conditional. I have a few things to say about this: first, rumours of the death of the material conditional are greatly exaggerated; second, the evil twins problem might reoccur for certain kinds of non-contraposable conditional; third, this type of solution to the problem, even if possible, seems to me to be less elegant than the solution I offer myself in Sect. 3.2.
Treating the imperative as a sentential-like operator was first proposed by Hofstadter and McKinsey (1939). They however, do not allow this operator to take narrow scope with respect to a normal conditional. This is because their imperativising operator is not, strictly speaking, sentential—it does not produce a sentence, taking sentences as parameters (as the logical connectives of the propositional calculus do) but produces an “imperative” taking a “sentence” as a parameter. For Hofstader and McKinsey imperatives are not sentences, and formulae in which they are used as such are not well formed. To deal with cases like (A1), they introduce a new set of operators that produce imperatives taking imperatives as parameters. This represents the logical vocabulary of natural languages (“if” “or” “and” etc.) as ambiguous in a way that it is not. The first treatment of the imperative mood as a genuine sentential operator was given by Chellas. He treats the imperative mood analogously to the obligation operator of a deontic logic and gives a possible worlds semantics. The price Chellas pays for this is that imperatives, in his formal language, are truth-apt! Chellas does not claim that natural language imperatives are truth-apt, though—this is simply a logically irrelevant difference between natural language and his formal system, he says. (Chellas 1968, p. 3) I aim to do better: like Chellas, my imperativising operator is genuinely sentential; like Hofstadter and McKinsey, my semantics does not (except in weird corner cases) assign any imperative a truth-value.
This syntactic move, of treating the imperative mood as a sentence operator, does not solve the problem of imperative consequence by itself—a semantic treatment of this operator is also needed. As well as the philosophical problems mentioned in the text, below, there is the purely formal problem that some argument forms containing the imperative mood—!(p∧q) therefore !p, for example—are intuitively valid but are “up for grabs” in the same sense that the intuitively invalid (B) is—they are not instances of a classically valid argument form.
The semantic theory that follows owes a debt to Allan Gibbard's norm expressivism—see his (1990), especially chapter 5. Like me, Gibbard is concerned to combine non-cognitivism (in his case, about morality) with the thesis that sentences that are not truth-apt can entail one another; like me he does this by using a possible worlds semantics on which the points of evaluation are not possible worlds (as they would normally be), but pairs of a world with something else. The key formal difference between Gibbard's approach and mine (setting aside the philosophical difference that Gibbard is interested in moral statements and I am interested in imperatives) is in what that “something else” is: for Gibbard it is a “system of norms”; for me, a second world. That makes it possible for me to give a formal analysis of the imperative mood, by making it a logical operator that looks at the internal structure of the points of evaluation.
Matrices like these were introduced by Stalnaker (1999), as a way of representing “propositional concepts”. Though Stalnaker's propositional concepts are formally similar to my preposcriptions, they play a quite different role in his paper. Also, Stalnaker's propositional concepts are functions from pairs of worlds to truth values, and so he writes T and F, where I would put a tick or a blank, respectively. Though I have no objection to trading in sets of things for functions from those things to boolean values, it would be quite misleading to identify tick and blank with truth and falsity, as we will see below.
These matrices are consistent with there being more than four worlds—you can either make the idealising assumption that only these four worlds are possible, or think of each column and row as abbreviating an infinite number of columns or rows containing the same pattern of ticks and blanks. .
With two exceptions: the set of all pairs of worlds (the matrix with all cells ticked) and the empty set (the matrix with all cells blank). These preposcriptions are both imperatival and assertoric—as makes sense, because both can be expressed either by a simple indicative (“The weather or not fine.”/“The weather is fine and not fine.” respectively) and or by a simple command (“Attack or do not attack!”/“Attack and do not attack!”). So without exception, every preposcription that is imperatival but not assertoric is neither true nor false.
It may be objected that I am here confusing truth-aptness with bivalence—with being either-true-or-false (perhaps, for example, “This man is bald”, said of a borderline case of baldness, is truth-apt, but not bivalent). I agree that truth-aptness is different from bivalence. To say that a sentence is not truth-apt is to say more that than it is neither true nor false. I'm not quite sure how to describe the difference except by giving contentious examples like the borderline case one. The crucial point of reply to this objection, though, is that my semantics is supposed to be consistent with imperatives not being truth-apt. It doesn't have to entail that they are not truth-apt. Whatever else a sentence must do to avoid being truth-apt, it must at least be neither true nor false, and I deliver that.
A (seemingly) much simpler proposal than mine, for example, would hold that conditional commands are dyadic speech acts, each having two propositional contents: the compliance conditions of the command (e.g. that you attack at dawn), and the antecedent conditions under which the command is active (that the weather is fine). This, however, fails to generalise to more complicated cases, in which imperative conditionals are cojoined, disjoined, or used with “otherwise”, “only if” or “unless”.
In the terminology of two-dimensional modal logic, the imperative operator is the “Stalnaker dagger” (Stalnaker 1999, p. 82) applied to preposcriptions.
I am thinking here of intentions as propositional mental states analogous to beliefs, and not reducible to a combination of desire and belief. Such a view of intentions has been developed at length by Michael Bratman—see (Bratman 1999), especially Chaps. 2 and 3. Also, I am departing from the tradition that holds that commands express, not intentions, but desires, as held, for example, by Searle (1969, pp. 64–67). Two arguments for this: first, consider the pacifist general, who combines no desire that any warlike acts occur with the intention to follow his own orders and command an attack. It seems to me that the pacifist general combines a lack of desire that an attack occur with an intention that an attack occur. This shows both that the intention that φ can occur without the desire that φ, and that commands express intentions, not desires, for when the general commands his soldiers “Attack!”, he does not express a desire that they attack, for he has no such desire. Second, if I am right that the optative mood functions like the imperative, except that it serves to express desires where the imperative expresses intentions (see footnote 22), then the difference between the imperative and optative moods is evidence that imperatives do not express desires.
How do other speech acts fit into this picture? The indicative mood is used to make assertions; imperative to make commands. But these two are not the only moods in English. Can preposcription semantics be extended to include the interrogative, used to make questions? In short, no, though this is a topic I would like to think more about. Questions seem to me to be quite different from assertions and commands. On my view, assertions express beliefs (and communicate them to others) and commands express intentions (and communicate them). In contrast, there is no propositional mental state (of “querying whether”?) that questions serve to express. It does seem to me to me that the optative mood (arguable present in the English sentence “O, to be rich!”) could be construed as a third dimension of preposcription semantics, related to desire as the imperative is related to intention.
Here I again draw on Robert Stalnaker's excellent article (Stalnaker 1999); the account of imperassertion here advocated is intended to be a generalisation of his account of assertion. Note that I am using Stalnaker's work in two quite different ways in this paper: here, as a model for a theory of imperassertion; and throughout Sect. 3 as the source of the matrix technique for visualising preposcriptions.
I earlier glossed “entanglement” as the possibility of a change in doxastic possibility constituting a change in intentional possibility or vice versa. More precisely, a preposcription is disentangled iff, in its matrix, every non-blank row carries the same pattern of ticks, and every non-blank column carries the same pattern of ticks. A preposcription is entangled iff it is not disentangled. Blanking a row (or a column) of a disentangled preposcription cannot have the effect of blanking a column (or row, respectively) unless it blanks the entire matrix.
I hasten to add that my argument for imperassertion does not rest on this treatment of (G), as (G) is quite an unusual argument. My argument for imperassertion is that it offers the best solution of the problem of imperative consequence consistent with the view that imperatives are not truth-apt.
I am grateful to David Ripley to pointing out KDDc4 to me, and for the disjunction argument that I use in my second reply to the objection. The proof that KDDc4 is sound and complete with respect to preposcription semantics is of some formal interest, and I hope to describe it elsewhere. When I say “in place of box” in the text here I could instead say “in place of diamond”—a distinctive feature of KDDc4 is that box and diamond are interchangeable.
This objection might favour an “accessibility” semantics like that of Chellas (1968), which delivers KD4, and could easily be weakened further. Chellas, however, has to hold that imperatives are truth-apt.
This is similar to the second objection to Hare's view of imperatives discussed in his (1967, pp. 317–324). Hare accepts the validity of the (D) and (Dc) principles—as he puts it, “Do p” and “Do not do p” are “contradictories”. I am in broad agreement with his reply to the objection.
See particularly my “unwanted consistency” (2012, pp. 53–54) argument against cognitivism about imperatives.
As developed by, for example, Vranas (2008).
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Acknowledgments
Thanks for comments and discussion on this paper to Charles Pigden, Dorothy Grover, Annette Baier, Jonathan McKeown-Green, Denis Robinson, Patrick Girard, Hannah Clark-Younger, Hannah Burgess, Peter Vranas, Arif Ahmed, David Ripley, Frances Howard-Snyder, Matthew Smith and to participants at the Bellingham Summer Philosophy Conference 2012.
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Parsons, J. Command and consequence. Philos Stud 164, 61–92 (2013). https://doi.org/10.1007/s11098-013-0094-x
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DOI: https://doi.org/10.1007/s11098-013-0094-x