Suppose that a sign at the entrance of a hotel reads: “Don’t enter these premises unless you are accompanied by a registered guest”. You see someone who is about to enter, and you tell her: “Don’t enter these premises if you are an unaccompanied registered guest”. She asks why, and you reply: “It follows from what the sign says”. It seems that you made a valid inference from an imperative premise to an imperative conclusion. But it also seems (...) that imperatives cannot be true or false, so what does it mean to say that your inference is valid? It cannot mean that the truth of its premise guarantees the truth of its conclusion. One is thus faced with what is known as “Jørgensen’s dilemma” (Ross 1941: 55-6): it seems that imperative logic cannot exist because logic deals only with entities that, unlike imperatives, can be true or false, but it also seems that imperative logic must exist. It must exist not only because inferences with imperatives can be valid, but also because imperatives (like “Enter” and “Don’t enter”) can be inconsistent with each other, and also because one can apply logical operations to imperatives: “Don’t enter” is the negation of “Enter”, and “Sing or dance” is the disjunction of “Sing” and “Dance”. A standard reaction to this dilemma consists in basing imperative logic on analogues of truth and falsity. For example, the imperative “Don’t enter” is satisfied if you don’t enter and is violated if you enter, and one might say that an inference from an imperative premise to an imperative conclusion is valid exactly if the satisfaction (rather than the truth) of the premise guarantees the satisfaction of the conclusion. But before getting into the details, more needs to be said on what exactly imperatives are. (shrink)

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? (...) Much more, I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three -valued imperatives which mixes declaratives with imperatives. I develop such a logic. (shrink)

It is claimed that 'Do x!' means 'Then you will do x'. Answering a "Why?" question concerning the former may take either of two forms, viz., 'Because --' or 'If you wish to --'. The second answer completes the truncated hypothetical. "Ought" sentences are treated as a species of imperatives involving universality in the "if" clause ('If anyone wished to --'). Moral "ought" sentences involve a double universality, viz., the one mentioned above and universality connecting the action with social harmony (...) (e.g., "If everyone were to do x, then there would be social harmony'). (shrink)

Besides pure declarative arguments, whose premises and conclusions are declaratives, and pure imperative arguments, whose premises and conclusions are imperatives, there are mixed-premise arguments, whose premises include both imperatives and declaratives, and cross-species arguments, whose premises are declaratives and whose conclusions are imperatives or vice versa. I propose a general definition of argument validity: an argument is valid exactly if, necessarily, every fact that sustains its premises also sustains its conclusion, where a fact sustains an imperative exactly if (...) it favors the satisfaction over the violation proposition of the imperative, and a fact sustains a declarative exactly if, necessarily, the declarative is true if the fact exists. I argue that this definition yields as special cases the standard definition of validity for pure declarative arguments and my previously defended definition of validity for pure imperative arguments, and that it yields intuitively acceptable results for mixed-premise and cross-species arguments. (shrink)

Imperatives cannot be true, but they can be obeyed or binding: `Surrender!' is obeyed if you surrender and is binding if you have a reason to surrender. A pure declarative argument — whose premisses and conclusion are declaratives — is valid exactly if, necessarily, its conclusion is true if the conjunction of its premisses is true; similarly, I suggest, a pure imperative argument — whose premisses and conclusion are imperatives — is obedience-valid (alternatively: bindingness-valid) exactly if, necessarily, its conclusion (...) is obeyed (alternatively: binding) if the conjunction of its premisses is. I argue that there are two kinds of bindingness, and that a vacillation between two corresponding variants of bindingness-validity largely explains conflicting intuitions concerning the validity of some pure imperative arguments. I prove that for each of those two variants of bindingness-validity there is an equivalent variant of obedience-validity. Finally, I address alternative accounts of pure imperative inference. (shrink)

The theory of imperatives is philosophically relevant since in building it — some of the long standing problems need to be addressed, and presumably some new ones are waiting to be discovered. The relevance of the theory of imperatives for philosophical research is remarkable, but usually recognized only within the field of practical philosophy. Nevertheless, the emphasis can be put on problems of theoretical philosophy. Proper understanding of imperatives is likely to raise doubts about some of our deeply entrenched and (...) tacit presumptions. In philosophy of language it is the presumption that declaratives provide the paradigm for sentence form; in philosophy of science it is the belief that theory construction is independent from the language practice, in logic it is the conviction that logical meaning relations are constituted out of logical terminology, in ontology it is the view that language use is free from ontological commitments. The list is not exhaustive; it includes only those presumptions that this paper concerns. (shrink)

Besides pure declarative arguments, whose premises and conclusions are declaratives (“you sinned shamelessly; so you sinned”), and pure imperative arguments, whose premises and conclusions are imperatives (“repent quickly; so repent”), there are mixed-premise arguments, whose premises include both imperatives and declaratives (“if you sinned, repent; you sinned; so repent”), and cross-species arguments, whose premises are declaratives and whose conclusions are imperatives (“you must repent; so repent”) or vice versa (“repent; so you can repent”). I propose a general definition of (...) argument validity: an argument is valid exactly if, necessarily, every fact that sustains its premises also sustains its conclusion, where a fact sustains an imperative exactly if it favors the satisfaction over the violation of the imperative, and a fact sustains a declarative exactly if, necessarily, the declarative is true if the fact exists. I argue that this definition yields as special cases the standard definition of validity for pure declarative arguments and my previously defended definition of validity for pure imperative arguments, and that it yields intuitively acceptable results for mixed-premise and cross-species arguments. (shrink)

In a series of articles, P. Vranas recently proposed a new imperative logic. The strong and weak inferences of this logic are motivated by an appeal to a strong and weak ‘support by reasons’ that transfers from the premisses of an argument to its conclusion. They also combine nonmonotonic and monotonic reasoning patterns. I show that for any moral agent, Vranas’s proposal can be simplified enormously.

In this paper I will develop a view about the semantics of imperatives, which I term Modal Noncognitivism, on which imperatives might be said to have truth conditions (dispositionally, anyway), but on which it does not make sense to see them as expressing propositions (hence does not make sense to ascribe to them truth or falsity). This view stands against “Cognitivist” accounts of the semantics of imperatives, on which imperatives are claimed to express propositions, which are then enlisted in explanations (...) of the relevant logico-semantic phenomena. It also stands against the major competitors to Cognitivist accounts—all of which are non-truth-conditional and, as a result, fail to provide satisfying explanations of the fundamental semantic characteristics of imperatives (or so I argue). The view of imperatives I defend here improves on various treatments of imperatives on the market in giving an empirically and theoretically adequate account of their semantics and logic. It yields explanations of a wide range of semantic and logical phenomena about imperatives—explanations that are, I argue, at least as satisfying as the sorts of explanations of semantic and logical phenomena familiar from truth-conditional semantics. But it accomplishes this while defending the notion—which is, I argue, substantially correct—that imperatives could not have propositions, or truth conditions, as their meanings. (shrink)

The author contends that moral utterances and imperatives have different logical features. He discusses r m hare's "language of morals" in terms of his distinction between plain imperatives and deontic utterances. (staff).

The existing literature treats of several investigations with a certain bearing on the question which is roughly indicated by the title “Imperatives and Logic.” Some of those investigations, however, are entirely outside the scope of the present work.Mally sets himself the task of developing a “Logik des Willens” constituting a parallel to the usual logic, the “Logik des Denkens". In order to emphasize its independence, the author also calls this “Logik des Willens” “Deontik”, and he conceives it as (...) being based on the “Wesensgesetze” of will in the same way as the usual logic is conceived as being based on the “Wesensgesetze” of thought. The author develops a formalistic deductive system on the basis of 5 axioms of demands, including the axiom that there is at least one fact which is unconditionally demanded, and through a lengthy series of theorems he arrives at the sentence that what is unconditionally demanded is identical with what is actually the case: “was sein soll, ist Tatsache”. Similarly, the author develops a system of axioms for “right” volition, including the axiom that right volition is non-contradictory. (shrink)

When a conflict of duties arises, a resolution is often sought by use of an ordering of priority or importance. This paper examines how such a conflict resolution works, compares mechanisms that have been proposed in the literature, and gives preference to one developed by Brewka and Nebel. I distinguish between two cases – that some conflicts may remain unresolved, and that a priority ordering can be determined that resolves all – and provide semantics and axiomatic systems for accordingly defined (...) dyadic deontic operators. (shrink)

This paper represents an attempt to indicate the idea of a logic slightly more general than sentential calculus, which is applicable to many philosophical issues. In particular, I shall use this generalized calculus to discuss a variation of the logic of imperatives. In part I, certain general considerations about indicative calculi provide the basis, as well as indicate the need, for the more formal construction of part II. Part III illustrates the analytical power of the tool constructed, and (...) tries to show its relevance for philosophy. (shrink)

This paper attempts to outline the logical structure of imperatives. It criticizes the prevailing view that this structure is isomorphic with that for indicatives. For "mixed" imperatives with constituents in both indicative and imperative moods (e.G., Conditional imperatives with indicative antecedents) there are features unique to imperatives. These features are specified, And consequences of them are traced. Finally, Formation rules for imperatives are stated.

This paper articulates an account of imperatives that sensibly supports the idea of a logic of imperative inferences. We rebuke common objections to the very possibility of such a logic, from a perspective based on recent linguistic work on the morphosyntax of imperatives. Specifically, we develop the notion that the content of an imperative sentence includes both a force operator alongside an imperational content to which the force applies. We further argue that this account of the (...) content of imperatives constitutes a plausible and flexible framework to develop a logic of imperative by examining a number of reconstructions of this idea using semantical analogs of widespread modal semantics. After studying the performance of those approaches, we conclude that progress in imperative logic has been hindered by the failure to adopt conflict-tolerant and resource-sensitive semantics, but suggest that such considerations can be incorporated in this flexible framework. Finally, we also propose a simple account of the difference between operators applying to the content of imperatives and imperative operators, in a way that sheds light on some of the issues underlying the usual antinomies. (shrink)

This short essay attempts to challenge some of widely held philosophical assumptions on the nature of the relationship between logic, language and reality. In Section 1 the hegemony of theoretical logic is being questioned; Section 2 proposes a hypothesis on socially mediated semantics; Section 3 addresses the problem of ontology of logical sentential moods.

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for (...) the studies of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

It is the purpose of this paper to carry out a partial syntactical analysis of imperatives. Imperatives form a large body of linguistic expressions, appearing, e.g. in mathematical proofs be a continuous function!”), laws, moral injunctions, instruction, etc. For analytical purposes we distinguish between two forms of imperatives, the fiat and the directive. By a directive we mean an imperative which includes an indication of the agent who is to carry it out. For example, “Henry, don't forget to stop (...) at the grocery!” is a directive. By a fiat we mean an imperative which includes no reference to an agent who is to carry it out. For example, “Let there be light!” is a fiat. This is a distinction made in terms of meaning. If, however, proper symbolic devices were introduced for the formalization of imperatives, it could be made in a syntactical manner. Thus we could distinguish between imperatives which possess a certain operator—the directive operator formed by putting a name within square brackets—as “[Henry]!”, and imperatives which do not possess this operator, e.g. “Let it be the case that Henry does not forget to stop at the grocery!” In the following we pay attention only to fiats. This, of course, involves a great limitation of subject matter and excludes topics of great interest. (shrink)

As the journal is effectively defunct, I am uploading a full-text copy, but only of my abstract and article, and some journal front matter. -/- Note that the pagination in the PDF version differs from the official pagination because A4 and 8.5" x 11" differ. -/- Traditionally, imperatives have been handled with deontic logics, not the logic of propositions which bear truth values. Yet, an imperative is issued by the speaker to cause (stay) actions which change the state (...) of affairs, which is, in turn, described by propositions that bear truth values. Thus, ultimately, imperatives affect truth values. In this paper, we put forward an idea that allows us to reason with imperatives using classical logic by constructing a one-to-one correspondence between imperatives and a particular class of declaratives. (shrink)

The ambition of the paper is to provide a solution to the problem posed by Von Wright (1999): how is it possible that the two actions, one of producing P and the other of preventing P can have different deontic status, the former being obligatory and the latter being forbidden. The solution for the problem is sought for by an investigation into connections between imperative and deontic logic. First, it is asked whether a solution could be found in (...) Lemmon's (1965) system of "change logic", using his idea on connection between logic of orders being in force and deontic logic. The answer is the negative one. Next, the connection between Lemmon's imperative logic and deontic logic given in Aqvist's paper - "Next" and "Ought" (1965) - is analyzed. Than, the Lemmon's treatment of imperatives is restricted to the natural language imperatives and Aqvist's way of connecting imperative and deontic logic is modified accordingly. Some principles for the natural language imperatives are established (the negation rule ; the law of contraposition for imperative conditionals) and a simple "global" semantics is developed. The notion of "opposite action" is introduced and it is given an important role in semantics. Finally, a solution for von Wright's problem is given. In the closing sections some further topics for investigation are hinted: one of them being the connection between Aqvist's epistemic- imperative conception of interrogatives and "epistemic obligations", the other being formalization of the idea that imperatives create and re-create obligation patterns that can be described in deontic terms. (shrink)

Some arguments include imperative clauses. For example: ‘Buy me a drink; you can’t buy me that drink unless you go to the bar; so, go to the bar!’ How should we build a logic that predicts which of these arguments are good? Because imperatives aren’t truth apt and so don’t stand in relations of truth preservation, this technical question gives rise to a foundational one: What would be the subject matter of this logic? I argue that declaratives (...) are used to produce beliefs, imperatives are used to produce intentions, and beliefs and intentions are subject to rational requirements. An argument will strike us as valid when anyone whose mental state satisfies the premises is rationally required to satisfy the conclusion. For example, the above argument reflects the principle that it is irrational not to intend what one takes to be the necessary means to one’s intended ends. I argue that all intuitively good patterns of imperative inference can be explained using off-the-shelf formulations of our rational requirements. I then develop a formal-semantic theory embodying this view that predicts a range of data, including free-choice effects and Ross’s paradox. The resulting theory shows one way that our aspirations to rational agency can be discerned in the patterns of our speech, and is a case study in how the philosophy of language and the philosophy of action can be mutually illuminating. (shrink)