Imperatives lie at the heart of both practical and moral reasoning, yet they have been overshadowed by propositions and relegated by many philosophers to the status of ejaculations. One reason for this assimilation is that a sentence's having literal meaning seems to require its having truth conditions, and 'Keep your promises!' appears to lack such conditions just as 'Ouch!' does. Yet in the hopes of explicating a kind of rationality distinctive of the practical and moral domains certain philosophers and logicians have sought in this century to codify the logical properties of imperatives.

Because inference has its home in the concept of truth-preservation, one reductionist attempt to develop such a logic translates imperative sentences into declaratives and construes inferential relations among the former in terms of inferential relations among the latter. Since no such reduction seems fully to capture the meaning of imperatives others have expanded our notion of inference to include not just truth- but also satisfaction-preservation, according to which an imperative is satisfied just in case what it enjoins is brought about.

A logic capturing what is distinctive of imperatives may shed light on the question whether an 'ought' is derivable from an 'is', and may elucidate the claim that morality is, or comprises, a system of hypothetical imperatives. Further, instructions, which are often formulated with imperatives, as in 'Take two tablets on an empty stomach', are crucial to the construction of plans of action. A proper understanding of imperatives and their inferential properties may thus also illuminate practical reasoning.

1. Jorgensen's Dilemma and Ross' "Paradox"
Any attempt to codify the logical properties of imperatives must grapple with the following dilemma, first formulated by Jorgensen. On the one hand there appear to be cogent inferences involving imperatives, as in:

On the other hand the only widely agreed upon conception of good inference is in terms of truth-preservation: A set of sentences G implies a sentence S just in case there is no possible situation in which all members of G are true while S is false. Yet evidently this conception of cogency in terms of truth-preservation cannot be used to assess the validity of arguments containing imperatives, for imperatives are not, at least on the face of it, either true or false. Hence either we deny, what seems to be the case, that there are good inferences involving imperatives; or we grant that some such inferences are good, and then face the question, to what conception of inference could we appeal in order to ground such a claim?

This challenge for attempts to explicate the logical properties of imperatives is to be distinguished from another, less urgent concern first formulated by Ross and echoed by Williams. According to the classical logic of truth functions any proposition P implies P or Q, for any Q. Similarly it would seem that even the most conservative imperative logic would countenance

One who demands that the auditor either post the letter or burn it may be implicitly granting her permission to do either. But then if one committed to the premise is thereby committed to the conclusion, it may seem that one who demands that the addressee post the letter is implicitly granting her permission to burn it. This reasoning vacillates on the concept of commitment. We may distinguish between commitment to the content of a sentence and commitment to performing the speech act of uttering that sentence with its characteristic illocutionary force. One who utters the premise of the above inference is not thereby committed to performing the speech act of demanding that the addressee either post the letter or burn it, just as one who asserts P is not thereby committed to asserting P or Q. (Asserting P merely commits one to the truth of P or Q). Yet it is only the performance of the speech act of uttering an imperative sentence that grants permission to the addressee to satisfy that sentence by satisfying any disjunct that it contains. Mere commitment to the content of that sentence does not suffice to grant permission of any kind.

To yet others a logic of imperatives may seem trivially simple. It is common to distinguish between two elements in each imperative sentence, one of which is shared with indicative sentences and the other not. From both 'Shut the door!' and 'The door is shut' we can abstract a reference to the state of affairs of the door's being shut. The former sentence enjoins that state of affairs while the latter asserts that that state of affairs obtains. Following Stenius let us say that what is common to the two sentences is the sentence-radical, while what distinguishes them is their modal element. One might urge that the validity of arguments involving imperatives should be understood just in terms of sentence-radicals, since these require no modification in our "truth-preservation" conception of validity. But this leaves us with no account of when and where modal elements can occur in valid arguments. It is unclear, for instance, how without ad hoc postulation we shall keep from countenancing the argument:

Imperative logic seems neither trivial nor impossible, and approaches to the logic of imperatives may be seen as grappling with one or the other horn of Jorgensen's dilemma.

Reductionist approaches attempt to show that there are no good inferences that crucially involve imperatives; at best any inference that seems to involve imperatives can be replaced with an equivalent one comprising only indicatives, to which the truth-preservation conception of validity applies. To the objection that only propositions appear to be truth bearers Reductionists might reply that the difference in grammatical mood between imperatives and declaratives is an idiosyncracy of idiom, a mere reflection of the fact that these two types of sentence are typically used to perform different kinds of speech act. The difference of mood need be of no more interest to the logician than is the difference of active and passive voice in declarative propositions. To the further question of just what propositions imperatives are to be identified with, there are five well known answers.

On one proposal 'Shut the door!' is equivalent to 'You will shut the door'. This equation is perhaps suggested by the fact that the latter sentence is often used to convey a command; if it is correct then imperative inference may be understood in terms of inferential relations among statements in the future tense (see TENSE AND TEMPORAL LOGIC). Yet this identification runs afoul of our ability to make predictions without formulating any kind of directive: A parole officer might say to a repeat offender, 'You will steal again', without enjoining him to crime. Others have contended that 'Shut the door' is equivalent to 'I want you to shut the door'; here imperative inference is to supervene upon the logical properties of attitude locutions. Unfortunately this theory cannot make sense of a scenario in which one initiates capital punishment with the words, 'Even though I despise the thought of the convict's death, pull the switch!' Further, recipes and instructions are often formulated with imperatives but appear not to be reports of anybody's desires.

It has also been proposed that 'Shut the door' is equivalent to 'Either you are going to shut the door, or X will happen', where X is something bad for the person being addressed. Yet a speaker might reasonably utter an imperative such as 'Keep your promises!' knowing full well that no harm will come the addressee if she fails to conform. Second, the theory implies that for any action Y, either 'Do Y!' or 'Don't do Y' is true. A distinct, "performative" analysis of the imperative has it that 'Shut the door' is equivalent to 'I order you to shut the door' (see PERFORMATIVES). This proposal requires an imperative to be as multiply ambiguous as there are distinct illocutionary acts that can be performed with that sentence; on a given occasion of utterance the same sentence might mean, 'I request that you open the door.' This theory is thus committed to a multiplication of senses for what seem to be univocal sentences.

The most popular reduction may be traced to Kant, and equates 'Shut the door' with the "deontic" proposition 'You should (or ought to) shut the door.' On this approach imperative inference is a matter of inferential relations among deontic locutions (see DEONTIC LOGIC). We may distinguish between two species of imperative, fiats and directives, only the latter of which are directed at a particular person or group of persons. Clearly directives are the much more common imperative, and for these it would seem that being directed at a particular individual is part of their content. This is perhaps why imperatives are so naturally issued with vocatives, as in 'Mary, make sure John does his homework.' In contrast to imperatives, the truth of a deontic proposition does not, as such, lay obligations upon any one person rather than another. 'It is obligatory that A' does not discriminate among the various people who might be obligated to make it the case that A. This even holds for 'John should see to it that A': An imperator might want to lay responsibility on Mary for making John see to it that A, but will not be able to do so with just "deontic" propositions. A deontic reduction lacks the resources to capture the directedness of imperatives.

Grappling with the other horn of Jorgensen's dilemma involves formulating a notion of inference to include other things than truth-bearers. Since validity as here characterized is a semantical notion, an account of valid reasoning with imperatives would require assigning semantic values to imperative sentences. One proposal stems from Lemmon, according to whom the basic semantical value of an imperative is to be that of its being in force (or not). Thus when a commanding officer says, 'Clean the latrine!' to a soldier the command is typically in force, whereas if the soldier were to say the same to the commanding officer this would typically not be the case. This suggests the following criterion of validity:

This definition of validity sheds no light on the question whether, for instance, the being in force of 'Take all the boxes!' implies the being in force of 'Take this box!' when the imperator is unaware that this thing is one of the boxes. Lemmon's proposal is thus a mere schema for a definition. A more explicit proposal flows from the work of Hofstadter and McKinsey, Rescher, and Sosa: Say that an imperative is satisfied just in case its sentence- radical is true. One might suggest that an argument is valid iff, if its imperative premises are satisfied and its indicative premises are true, then its conclusion is satisfied if imperative and true if indicative. This definition would explain the apparent validity of the inference with which this article began. On the other hand it countenances the inference from 'Shut the door!' to 'The door is shut.'

Sosa attempts a definition in terms of satisfaction-preservation for arguments containing only imperatives, some of which may be hypothetical in form. Let us say that imperatives such as 'If it rains, close the window' are satisfied if it rains and the window is closed; violated if it rains and the window is not closed, and neutral if it does not rain. (All imperatives can be construed as hypothetical if we imagine P or ªP as antecedent when none is otherwise specified.) We now say:

A cognate definition given by Rescher founders on its inability to treat the relation 'is validly inferable from' as being transitive.

There is today no accepted account of imperative inference. Instead research focuses upon the semantics of imperatives while stopping short of formulating a calculus. Yet if agreement on these semantic questions can be reached it may be hoped that new proposals for understanding imperative inference may grow in the light such answers shed. Until that time reductionist approaches will continue to be attractive.

Austin, J.L. (1962) How to do Things with Words Oxford: Clarendon. (A classic work in the theory of speech acts; defends a version of the I order you to.. species of reduction.)

*Beardsley, E. (1944) 'Imperative sentences in relation to indicatives', Philosophical Review 53: 175-185. (Early proponent of Non-reductionism.)

Belnap, N. (1989) 'Declaratives Are Not Enough', Philosophical Studies 59: 1- 30. (Attacks the sentence-radical/modal element distinction as failing to capture the content distinctive of imperatives.)

*Bohnert, H. (1945) 'On the semiotic status of commands', Philosophy of Science 12: 302-315. (Referred to in 2. Argues for the reduction of imperatives to sentences of the form, 'Either you conform or something bad will happen.)

Castaneda, H.N. (1975) Thinking and Doing: The Philosophical Foundations of Institutions Dordrecht: D. Reidel. (Wide-ranging study of imperatives, particularly their semantics and their role in practical reasoning.)

*Chellas, B. (1969) 'Imperatives', in Theoria 37: 114-29. (Mentioned in 3. Formulates a logic for imperatives, which are treated as reducible to deontic propositions.)

Frege, G. (1892) 'On sense and reference', in Geach and Black (eds.) Translations from the Philosophical Writings of Gottlob Frege Oxford: Blackwell. (Historically important formulation of a distinction between illocutionary force and semantic content.)

Hamblin, C.L. (1987) Imperatives New York: Blackwell. (Best full-length treatment to date of the grammar, semantics and pragmatics of imperatives. Contains extensive bibliography.)

*Hare, R.M. (1952) The Language of Morals Oxford: Clarendon. (Mentioned in 1. Propounds the centrality of imperatives in ethical discourse. Distinguishes between phrastic and neustic.)

*Hofstadter, A., and J.C.C. McKinsey, (1939) 'On the logic of imperatives', Philosophy of Science 6: 446-457. (Mentioned in 3. Early formulation of the notion of satisfaction as a distinctive semantical value for imperatives.)

Huntley, M. (1984) 'The Semantics of English Imperatives', Linguistics and Philosophy 7: 103-133. (Sophisticated defense of a semantical treatment of imperatives as differing from propositions in lacking an indexical element.)

*Jorgensen, J. (1938) 'Imperatives and logic', Erkenntnis 7: 288-98. (Mentioned in 1. Explains the central challenge facing attempts to formulate an imperative logic.)

*Kant, I.(1964) Groundwork of the Metaphysic of Morals New York: Harper and Row. (Mentioned in 2. Defends a reduction of imperatives to deontic propositions.)

*Lemmon, E.J. (1965) 'Deontic logic and the logic of imperatives', Logique et Analyse 8: 39-71. (Mentioned in 3. Sketches a conception of imperative inference in terms of the concept of an imperative's being in force.)

Lewis, D. (1970) 'General semantics', reprinted in Philosophical Papers, Vol. I Oxford, 1983. (A classic paper in the philosophy of language. Defends a version of the I order you to... species of reduction.)

*Rescher, N. (1966) The Logic of Commands London: Routledge and Kegan Paul. (Mentioned in 3. Highly readable general treatment of imperative logic as well as an excellent introduction to the topic. Defends a notion of imperative inference in terms of satisfaction-preservation.)

*Ross, A. (1944) 'Imperatives and logic', Philosophy of Science 11: 30-46. (Mentioned in 1. Argues for the impossibility of a non-trivial imperative logic.)

Searle, J. and D. Vanderveken (1985) Foundations of Illocutionary Logic Cambridge, U.K.: Cambridge University Press. (Develops some logical features of devices used to indicate illocutionary force and inferential relations among various types of speech act.)

*Sosa, E. (1967) 'The semantics of imperatives', American Philosophical Quarterly 4: 57-64. (Mentioned in 3. Defends a notion of imperative inference in terms of satisfaction-preservation.)

*Stenius, E. (1967) 'Mood and language-game', Synthese 17: 254-274. (Mentioned in 1. Defends a distinction between sentence-radical and modal element.)

*Williams, B.A.O. (1963) 'Imperative inference' Analysis Supplement, for volume 23, pp. 30-36. (Mentioned in 1. Following Ross, argues for the impossibility of an imperative logic.)