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)

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)

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)

"Surrender; therefore, surrender or fight" is apparently an argument corresponding to an inference from an imperative to an imperative. Several philosophers, however (Williams 1963; Wedeking 1970; Harrison 1991; Hansen 2008), have denied that imperative inferences exist, arguing that (1) no such inferences occur in everyday life, (2) imperatives cannot be premises or conclusions of inferences because it makes no sense to say, for example, "since surrender" or "it follows that surrender or fight", and (3) distinct imperatives have conflicting permissive presuppositions (...) ("surrender or fight" permits you to fight without surrendering, but "surrender" does not), so issuing distinct imperatives amounts to changing one's mind and thus cannot be construed as making an inference. In response I argue inter alia that, on a reasonable understanding of 'inference', some everyday-life inferences do have imperatives as premises and conclusions, and that issuing imperatives with conflicting permissive presuppositions does not amount to changing one's mind. (shrink)

What do we learn when we find out that an argument is logically incorrect? If logically incorrect means the same as not logically correct, which in turn means not having a valid logical form, it seems that we do not learn anything too useful—an argument which is logically incorrect can still be conclusive. Thus, it seems that it makes sense to fix a stronger interpretation of the term under which a logically incorrect argument is guaranteed to be wrong. In this (...) paper, we show that pinpointing this stronger sense is much trickier than one would expect; but eventually we reach an explication of the notion of logical incorrectness which we find non-trivial and viable. (shrink)

Philosophers like G.H. von Wright and D. Makinson have pointed to serious challenges regarding the foundations of deontic logic. In this paper, I suggest that to deal successfully with these challenges a reconsideration of the research program of the discipline is useful. Some problems that have troubled this particular field of logical study for decades may disappear or appear more tractable if we view them from the perspective of a language game introduced by D. Lewis involving three characters: the Master, (...) the Slave and the Kibitzer. The adoption of this perspective opens a natural approach to a new layout of the domain of deontic studies. I propose dividing deontic logic into six sub-areas which are distinguished by their focus on the different idioms typical of the individual players, by conceiving the language game as either being static or as dynamic and by the aims of the logical inquiry. What kind of insights the proposed perspective provides is illustrated by an analysis of the so-called Ross paradox—a problem that has troubled deontic logic since its origins and, though it was many times pronounced solved, still keeps coming back ‘alive and kicking’. (shrink)

The status of constructivism as a metaethical or metanormative theory is unclear partly due to the lack of a clear semantics for central normative terms such as ‘reason’ and ‘ought’. In a series of recent papers, Sharon Street has attempted to clarify the central commitments of constructivism by focusing on the idea of a practical point of view and what follows from it. We improve upon the informal understanding provided by Street and attempt to provide a semantics for ‘ought’. Our (...) semantics respects the core intuition of the constructivist that normative claims are made true because of our practical commitments as agents and also reflects the constructivist’s commitment to the centrality of practical deliberation to normative truth. On our view, a normative claim of the form ⌜S ought to ϕ⌝ is true if ϕ is entailed from S’s set of evaluative attitudes. We argue that a virtue of our definition is that it allows us to see precisely what is distinctive about constructivism as opposed to realism and expressivism. (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.

J.C. Beall and Greg Restall's Generalised Tarski Thesis is a generalisation of the seemingly diverse conceptions of logical consequence. However, even their apparently general account of consequence makes necessary truth-preservation a necessary condition. Sentences in the imperative mood pose a problem for any truth-preservationist account of consequence, because imperatives are not truth-apt but seem to be capable of standing in the relation of logical consequence. In this paper, I show that an imperative logic can be formulated that solves the problem (...) of imperative consequence by leading naturally to a further generalisation of the GTT. (shrink)

Blackburn has outlined a formal account for moral expressivism, and we argued that the moral Frege-Geach problem can be solved formally by appending two rules for the boo-operator which are missing from his account. We then extended Blackburn’s formal account to generate a similar solution to the problem in modal context and showed that the validity of the modal argument can be preserved too in modal expressivism. However, the higher-order element endorsed by Blackburn does not seem necessary for solving the (...) Frege-Geach problem. Nor is his extension from moral expressivism to modal expressivism tenable, since the latter violates its own ontological constraint. A general moral is drawn on the basis on three observations made in evaluating Blackburn’s expressivism. (shrink)

This article surveys a range of current views on the semantics of imperatives, presenting them as more or less conservative with respect to the Truth-Conditional Paradigm in semantics. It describes and critiques views at either extreme of this spectrum: accounts on which the meaning of an imperative is a modal truth-condition, as well as various accounts that attempt to explain imperative meaning without making use of truth-conditions. It briefly describes and encourages further work on a family of views lying somewhere (...) in the middle. On such views, an imperative will semantically determine, without having as its meaning, a modal truth-condition, which figures centrally in accounting for various aspects of its meaning. (shrink)

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)

1 Th. 5:17 tells us to pray without ceasing. Many have worried that praying without ceasing seems impossible. Most address the problem by giving an account of the true nature of prayer. Unexplored are strategies for dealing with the problem that are neutral on the nature of prayer, strategies consistent, for example, with the view that only petition is prayer. In this article, after clarifying the nature of the problem for praying without ceasing, I identify and explore the prospects of (...) five different strategies that are neutral in this sense. I also raise problems for each strategy. (shrink)

This paper provides a proof-theoretic account of imperative logical consequence by generalising Greg Restall’s multiple conclusion bilateralism for declarative logic. According to imperative bilateralism, a sequent Γ ⊢ Δ is valid iff jointly commanding all the imperatives Φ ∈ Γ and prohibiting all the imperatives Ψ ∈ Δ clashes. This account has three main virtues: (1) it provides a proof-theoretic account of imperatives; (2) it does not rely on the controversial notion of imperative inference; and (3) it is neutral regarding (...) cognitivism about imperatives. (shrink)

An imperative conditional is a conditional in the imperative mood (by analogy with “indicative conditional”, “subjunctive conditional”). What, in general, is the meaning and the illocutionary effect of an imperative conditional? I survey four answers: the answer that imperative conditionals are commands to the effect that an indicative conditional be true; two versions of the answer that imperative conditionals express irreducibly conditional commands; and finally, the answer that imperative conditionals express a kind of hybrid speech act between command and assertion.

O dilema de Jørgensen tem atormentado os imperativistas até aos nossos dias. Resumidamente, se há uma Lógica das Normas, então esta tem por elementos proposições (as proposições normativas) e, simultaneamente, tem por elementos imperativos, que não possuem conteúdo proposicional. Neste ensaio, defender-se-á que o imperativismo é totalmente compatível com a concebilidade de uma Lógica Deôntica de proposições, pelo que não é necessário afastá-lo para manter a referida concebilidade (ainda que haja outras razões para rejeitar o imperativismo). Todas as posições que (...) aceitam a incompatibilidade suscitada pelo dilema de Jørgensen incorrem num erro, o de confundir imperativismo e prescritivismo. -/- Jørgensen's dilemma has plagued imperativists to this day. Briefly, if there is a Logic of Norms, then propositions participate in it (normative propositions) and, simultaneously, imperatives participate in it, which do not have propositional content. In this essay, I will argue that imperativism is fully compatible with the conceivability of a Deontic Logic of propositions, so it is not necessary to push it aside to maintain that conceivability (although there are other reasons for rejecting imperativism). All positions that accept the incompatibility raised by Jørgensen's dilemma incur an error, that of confusing imperativism and prescriptivism. (shrink)

I defend the view that linguistic meaning is a relation borne by an expression to a type of speech act, and that this relation holds in virtue of our overlapping communicative dispositions, and not in virtue of linguistic conventions. I argue that this theory gives the right account of the semantics–pragmatics interface and the best-available semantics for non-declarative clauses, and show that it allows for the construction of a rigorous compositional semantic theory with greater explanatory power than both truth-conditional and (...) dynamic semantics. (shrink)

Imperative sentences like Dance! do not seem to represent the world. Recent modal analyses challenge this idea, but its intuitive and historical appeal remain strong. This paper presents three new challenges for a non-representational analysis, showing that the obstacles facing it are even steeper than previously appreciated. I will argue that the only way for the non-representationalist to meet these three challenges is to adopt a dynamic semantics. Such a dynamic semantics is proposed here: imperatives introduce preferences between alternatives. This (...) characterization of meaning focuses on what function a sentence serves in discourse, rather than what that sentence refers to (e.g., a state of the world). By representing the meaning of imperatives, connectives and declaratives in a common dynamic format, the challenges posed for non-representationalism are met. (shrink)

Letting is a common practice in mathematics. For example, we let x be the sum of the first n integers and, after a short proof, conclude that x = n(n+1)/2; we let J be the point where the bisectors of two of the angles of a triangle intersect and prove that this coincides with H, the point at which another pair of bisectors of the angles of that triangle intersect. Karl Weierstrass's colleagues, in an attempt to solve optimization problems, stipulated (...) that the minimum area for a triangle with a given perimeter be a straight line segment conceived as a triangle with zero altitude. (Weierstrass complained that this obscured the insight that some problems have no solutions.) In mathematics applied to physics, we let x be the temperature in Fahrenheit corresponding to 30° Centigrade; we let v be the velocity of the Earth through the luminiferous ether. Before the error was spotted, the official rules for Little League Baseball made an inconsistent stipulation about the dimensions of home plate (Bradley 1996). (shrink)