Recent work in philosophical logic has taken interesting and unexpected turns. It has seen not only a proliferation of logical systems, but new applications of a wide range of different formal theories to philosophical questions. As a result, philosophers have been forced to revisit the nature and foundation of core logical concepts, chief amongst which is the concept of logical consequence. This essay sets the contributions of the volume in context and identifies how they advance important (...) debates within the philosophy of logic. (shrink)

One of the great successes in the study of language has been the application of formal methods, including those of formal logic. Even so, this chapter argues against one way of accounting for this success, by arguing that the study of natural language semantics and of logical consequence relations are not the same. There is indeed a lot we can glean about logic from looking at our languages, and at our inferential practices, but the semantic properties of natural (...) languages do not determine genuine logical consequence relations. We can get from natural language semantics to logical consequence, but only by a significant process of identification of logical constants, abstraction, and idealization. The chapter also discusses different approaches to the nature of logical consequence, and examines which allow logic and natural language to come closer together. (shrink)

Deflationists about truth seek to undermine debates about the nature of truth by arguing that the truth predicate is merely a device that allows us to express a certain kind of generality. I argue that a parallel approach is available in the case of logical consequence. Just as deflationism about truth offers an alternative to accounts of truth's nature in terms of correspondence or justification, deflationism about consequence promises an alternative to model-theoretic or proof-theoretic accounts of (...) class='Hi'>consequence's nature. I then argue, against considerations put forward by Field and Beall, that Curry's paradox no more rules out deflationism about consequence than the liar paradox rules out deflationism about truth. (shrink)

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the (...) rich will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)

There are two general conceptions on the relationship between probability and logic. In the first, these systems are viewed as complementary—having offsetting strengths and weaknesses—and there exists a fusion of the two that creates a reasoning system that improves upon each. In the second, probability is viewed as an instance of logic, given some sufficiently broad formulation of it, and it is this that should inform the development of more general reasoning systems. These two conceptions are in conflict with each (...) other, where the root issue of contention is the proper abstraction of the concept of logical consequence. In this work, we put forth a proposal on this abstraction based on an extension of the subset relation through the use of projections, which in turn, allows for the formalization of valid inferences to more general settings. Our proposal results in a formalism that encompasses probability and classical logic, and importantly, does so with minimal machinery. This formalism makes assertions about the relationship between these two systems that are explicit, and suggests a path forward in the development of alternatives to them. (shrink)

In his classic 1936 essay "On the Concept of Logical Consequence", Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. (...) Many of his criticisms are meant to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties: (1) (a) Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right. (b) Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible. (2) There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong. (3) Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account. (4) Tarski's account depends on there being a distinction between the "logical terms" and the "non-logical terms" of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties. (shrink)

Tarski's 1936 paper, “On the concept of logical consequence”, is a rather philosophical, non-technical paper that leaves room for conflicting interpretations. My purpose is to review some important issues that explicitly or implicitly constitute its themes. My discussion contains four sections: terminological and conceptual preliminaries, Tarski's definition of the concept of logical consequence, Tarski's discussion of omega-incomplete theories, and concluding remarks concerning the kind of conception that Tarski's definition was intended to explicate. The third section involves (...) subsidiary issues, such as Tarski's discussion concerning the distinction between material and formal consequence and the important question ofthe criterion for distinguishing between logical and non-logical terms.§1. Preliminaries. In this paper an argument is a two-part system composed of a set of propositions P and a single proposition c. The expression ‘c is a [logical] consequence of P’ is used with the same meaning as the expression ‘c is [logically] implied by P’. The expressions ‘is a logical consequence of’ and the converse ‘implies’ are relational. Often, I shall be talking in the same sense of validity of an argument. Validity is a property of arguments; an argument with premise-set P and conclusion c is valid if and only if P implies c; i.e., c is a logical consequence of P. Notice that this notion of argument is strictly ontic; it does not involve any agent that thinks, determines or establishes that a given proposition is or is not a consequence of a given set of propositions. (shrink)

In the paper, there is presented the theory of logical consequence operators indexed with taboo functions. It describes the mechanisms of logical inference in the environment of forbidden sentences. This kind of processes take place in ideological discourses within which their participants create various narrative worlds (mental worlds). A peculiar feature of ideological discourses is their association with taboo structures of deduction which penalize speech acts. The development of discourse involves, among others, transforming its deduction structure towards (...) the proliferation of consequence operators and modifying penalty functions. The presented theory enables to define various processes of these transformations in the precise way. It may be used in analyses of conflicts between competing elm experts acting within a discourse. (shrink)

Our pretheoretic sense of the relation of logical consequence arises from our experience of deductive inference. By ignoring the priority of inference and failing to provide an account of the ontological grounds of the conceptual experience and of the modal and truth elements in the statement of our pretheoretical sense, informal and technical accounts are at best partial. This paper proposes an ontological analysis of both elements which accounts for our conceptual experience and differentiates genuine from ersatz (...) class='Hi'>logical consequence. (shrink)

The main question addressed in this chapter is how to analyze the modal ingredient in the concept of logical consequence or logical validity of an inference, here expressed by saying that the truth of the conclusion of a logically valid inference should follow by necessity of thought from the truth of the premisses. It is claimed that this modal ingredient is not taken care of by Tarski’s requirement, later developed in model theory, that for all interpretations of (...) the non-logical terms of the sentences, the conclusion is true if the premisses are. Instead we must bring in reasoning or the notion of proof in the analysis, and it is shown how one may develop a notion of proof or validity of an argument based on the constructive meaning of the logical constants. It is proposed that from a constructive point of view, a sentence is a consequence of a set of premisses if and only if there is a proof in the sense explained of the sentence from the set of premisses. Knowledge of such a proof compels us to hold the conclusion true given that we hold the premisses true. (shrink)

I discuss the account of logical consequence advanced in Wittgenstein's Tractatus. I argue that the role that elementary propositions are meant to play in this account can be used to explain two remarkable features that Wittgenstein ascribes to them: that they are logically independent from one another and that their components refer to simple objects. I end with a proposal as to how to understand Wittgenstein's claim that all propositions can be analysed as truth functions of elementary propositions.

This paper develops a modal, Sentential logic having "not", "if...Then" and necessity as logical constants. The semantics (system of meanings) of the logic is the most obvious generalization of the usual truth-Functional semantics for sentential logic and its deductive system (system of demonstrations) is an obvious generalization of a suitable (jaskowski-Type) natural deductive system for sentential logic. Let a be a set of sentences and p a sentence. "p is a logical consequence of a" is defined relative (...) to the semantics and "p is demonstrable from a" is defined relative to the deductive system. Main meta-Theorem: p is demonstrable from a if and only if p is a logical consequence of a. Henkin-Type methods are used. The theorems of the logic are exactly those of s5. The deductive system is rigorously developed as a system of linear strings. (shrink)

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are (...) tightly related, and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)

It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.

It has been argued that alethic pluralists -- who hold that there are several distinct truth properties -- face a problem when it comes to defining validity. Via consideration of the classical concept of logical consequence, and of strategies for defining validity in many-valued logics, this paper proposes two new kinds of solution to the problem.

In "Logical consequence: A defense of Tarski" (Journal of Philosophical Logic, vol. 25, 1996, pp. 617-677), Greg Ray defends Tarski's account of logical consequence against the criticisms of John Etchemendy. While Ray's defense of Tarski is largely successful, his attempt to give a general proof that Tarskian consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of logical consequence (...) and should be replaced by a stronger absence-of-counterexamples criterion. It is argued that the latter criterion reflects the modal character of our intuitive concept of logical consequence, and it is shown that Tarskian consequence can be proved to satisfy this criterion for certain choices of logical constants. Finally, an apparent inconsistency in Ray's interpretation of Tarski's position on the modal status of the consequence relation is noted. (shrink)

To understand logic is, first and foremost, to understand logical consequence. This Element provides an in-depth, accessible, up-to-date account of and philosophical insight into the semantic, model-theoretic conception of logical consequence, its Tarskian roots, and its ideas, grounding, and challenges. The topics discussed include: the passage from Tarski's definition of truth to his definition of logical consequence, the need for a non-proof-theoretic definition, the idea of a semantic definition, the adequacy conditions of preservation of (...) truth, formality, and necessity, the nature, structure, and totality of models, the logicality problem that threatens the definition of logical consequence, a general solution to the logicality, formality, and necessity problems/challenges, based on the isomorphism-invariance criterion of logicality, philosophical background and justification of the isomorphism-invariance criterion, and major criticisms of the semantic definition and the isomorphism-invariance criterion. (shrink)

A substitutional account of logical validity for formal first‐order languages is developed and defended against competing accounts such as the model‐theoretic definition of validity. Roughly, a substitution instance of a sentence is defined as the result of uniformly substituting nonlogical expressions in the sentence with expressions of the same grammatical category and possibly relativizing quantifiers. In particular, predicate symbols can be replaced with formulae possibly containing additional free variables. A sentence is defined to be logically true iff all its (...) substitution instances are satisfied by all variable assignments. Logical consequence is defined analogously. Satisfaction is taken to be a primitive notion and axiomatized.For every set‐theoretic model in the sense of model theory there exists a corresponding substitutional interpretation in a sense to be specified. Conversely, however, there are substitutional interpretations – in particular the ‘intended’ interpretation – that lack a model‐theoretic counterpart. The substitutional definition of logical validity overcomes the weaknesses of more restrictive accounts of substitutional validity; unlike model‐theoretic logical consequence, the substitutional notion is trivially and provably truth preserving. In Kreisel's squeezing argument the formal notion of substitutional validity naturally slots into the place of intuitive validity. (shrink)

t is often suggested that truth-preservation is insufficient for logical consequence, and that consequence needs to satisfy a further condition of relevance. Premises and conclusion in a valid consequence must be relevant to one another, and truth-preservation is too coarse-grained a notion to guarantee that. Thus logical consequence is the intersection of truth-preservation and relevance. This situation has the absurd consequence that one might concede that the conclusion of an argument was true (since (...) the argument had true premises and was truth-preserving); yet should refuse to infer the conclusion from the premises, in the absence of demonstration of the relevance of the premises to the conclusion. The error lies in giving insufficient attention to the notion of truth-preservation. Relevance is no separable ingredient in the analysis of logical consequence, but a necessary condition of it. What we show is that if an argument really is truth-preserving, then that in itself is enough to show that the premises are (logically) relevant to the conclusion. (shrink)

The semantic analysis of logical consequence must obey a set of requisites which nowadays have acquired a dogmatic status. This situation prevents the development of other varieties of this fundamental relation. In this issue we try to define what we call a naive variety of logical consequence. The main feature of this relation is the way it depends on formulas in premises and conclusion: every sentence must contribute to the acceptability of an argument in a significative (...) way. This circumstance can be of some interest for research programs demanding a logical apparatus sensitive to application context. We think of the logic LP developed by G. Priest -- Priest [1979] -- in relation to Gödel incompleteness theorems as a test for our points of view. (shrink)

Logical consequence is a notion that every person who reasons must possess, at least implicitly. To give a precise and accurate characterization of this notion is the fundamental task of logic. In a similar way, the notion of effectivity is a concept that anyone with a basic training in mathematics possesses, and the most fundamental task of a theory of computability is to give a precise characterization of this notion. The problem concerning effectivity was solved in the 1930s, (...) almost as soon as it was raised, by the work of Turing, Church, and others. By contrast, the correct and precise characterization of logical consequence has been hotly contested through the two and a half thousand-year history of logic. (shrink)

In this paper I ask what logical consequence is, and give an answer that is somewhat different from the usual ones. It isn’t clear why anyone would need a new approach to logical consequence, so I begin by explaining the work that I need the answer to do and why the standard conceptions aren’t adequate. Then I articulate a replacement view which is.

This paper examines from a historical perspective Tarski's 1936 essay, "On the concept of logical consequence." I focus on two main aims. The primary aim is to show how Tarski's definition of logical consequence satisfies two desiderata he himself sets forth for it: (1) it must declare logically correct certain formalizations of the -rule and (2) it must allow for variation of the individual domain in the test for logical consequence. My arguments provide a (...) refutation of some interpreters of Tarski, and notably John Etchemendy, who have claimed that his definition does not satisfy those desiderata. A secondary aim of the paper is to offer some basic elements for an understanding of Tarski's definition in the historical logico-philosophical context in which it was proposed. Such historical understanding provides useful insights on Tarski's informal ideas on logical consequence and their internal cohesion. (shrink)

What is the philosophical significance of the soundness and completeness theorems for first-order logic? In the first section of this paper I raise this question, which is closely tied to current debate over the nature of logical consequence. Following many contemporary authors' dissatisfaction with the view that these theorems ground deductive validity in model-theoretic validity, I turn to measurement theory as a source for an alternative view. For this purpose I present in the second section several of the (...) key ideas of measurement theory, and in the third and central section of the paper I use these ideas in an account of the relation between model theory, formal deduction, and our logical intuitions. (shrink)

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to (...) the position itself. (shrink)

In the first section, I consider what several logicians say informally about the notion of logical consequence. There is significant variation among these accounts, they are sometimes poorly explained, and some of them are clearly at odds with the usual technical definition. In the second section, I first argue that a certain kind of informal account—one that includes elements of necessity, generality, and apriority—is approximately correct. Next I refine this account and consider several important questions about it, including (...) the appropriate characterization of necessity, the criterion for selecting logical constants, and the exact role of apriority. I argue, among other things, that there is no need to recognize a special logical sense of necessity and that the selection of terms to serve as logical constants is ultimately a pragmatic matter. In the third section, I consider whether the informal account I have presented and defended is adequately represented by the usual technical definition. I show that it is, and provably so, for certain limited ways of selecting logical constants. In the general case, however, there seems to be no way to be sure that the technical and informal accounts coincide. (shrink)

I argue that recent defenses of the view that in 1936 Tarski required all interpretations of a language to share one same domain of quantification are based on misinterpretations of Tarski’s texts. In particular, I rebut some criticisms of my earlier attack on the fixed-domain exegesis and I offer a more detailed report of the textual evidence on the issue than in my earlier work. I also offer new considerations on subsisting issues of interpretation concerning Tarski’s views on the (...) class='Hi'>logical correctness of certain omega-arguments, on the Tarskian proof that Etchemendy took to be modal and fallacious, and on Tarski’s appeals to the “common concept of consequence”. (shrink)

Introduction -- The concept of logical consequence -- Tarski's characterization of the common concept of logical consequence -- The logical consequence relation has a modal element -- The logical consequence relation is formal -- The logical consequence relation is A priori -- Logical and non-logical terminology -- The meanings of logical terms explained in terms of their semantic properties -- The meanings of logical terms explained in (...) terms of their inferential properties -- Model-theoretic and deductive-theoretic conceptions of logic -- Linguistic preliminaries : the language M -- Syntax of M -- The definition of a well formed formula of M -- Semantics for M -- The sentential connectives are defined -- The notion of satisfaction is introduced and the quantifiers are defined -- Model-theoretic consequence -- Truth in a structure -- Satisfaction revisited -- Formalized definition of truth -- Model-theoretic consequence defined -- The model-theoretic definition and the concept of logical consequence -- Does the model theoretic consequence relation reflect the salient features of the common concept of logical consequence? -- What is a logical constant? -- Deductive consequence -- Deductive system n -- The deductive theoretic definition and the concept of logical consequence -- Tarski's criticism of the deductive theoretic definition -- Is N a correct deductive system? (shrink)

Shapiro (Philos Q 61:320–342, 2011) argues that, if we are deflationists about truth, we should be deflationists about logical consequence. Like the truth predicate, he claims, the logical consequence predicate is merely a device of generalisation and more substantial characterisation, e.g. proof- or model-theoretic, is mistaken. I reject his analogy between truth and logical consequence and argue that, by appreciating how the logical consequence predicate is used as well as the goals of (...) proof theory and model theory, we can be deflationists about truth but not logical consequence. (shrink)

Of course we all know now that mathematics has proved that logic doesn't really make sense, but Etchemendy (philosophy, Stanford Univ.) goes further and challenges the received view of the conceptual underpinnings of modern logic by arguing that Tarski's model-theoretic analysis of logical consequences is wrong. He may have found the soft underbelly of the dead horse. Annotation copyrighted by Book News, Inc., Portland, OR.

An interesting question is whether deflationism about truth (and falsity) extends to related properties and relations on truthbearers. Lionel Shapiro (2011) answers affirmatively by arguing that a certain deflationism about truth is as plausible as an analogous version of deflationism about logical consequence. I argue that the argument fails on two counts. First, it trivializes to any relation between truthbearers, including substantive ones; in other words, his argument can be used to establish that deflationism about truth is as (...) plausible as deflationism about an arbitrary sentential relation. Second, the alleged analogy between the arguments for deflationism about truth and deflationism about consequence fails. Along the way I consider what implications the failure of the equiplausibility thesis has for deflationism about falsity. (shrink)

In this paper we investigate the relation between the axiomatization of a given logical consequence operation and axiom systems defining the class of algebras related to that consequence operation. We show examples which prove that, in general there are no natural relation between both ways of axiomatization.

This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logical consequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind of (...) definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence. (shrink)

In ‘Logical Consequence (Slight Return)’, Gillian Russell asks ‘What is logical consequence?’, a question which has vexed logicians since at least the twelfth century, when people first began to wonder what it meant for one sentence (or proposition) to follow from another sentence (or proposition, or set of sentences, or set of propositions), or whether it was possible to put down rules determining when the relation of ‘follows from’ (or ‘is antecedent to’) holds. Her aim is (...) threefold: (1) to explain what an answer to the question ‘What is logical consequence?’ would need to be able to do in order to be a satisfying answer; (2) to identify previous answers to the question; and (3) to demonstrate why these previous answers are inadequate to do what the answer needs to be able to do, and to offer a new answer. In the present paper, I respond to these aims in two ways. The first is to say something about where Russell’s central question even comes from, because this is not a topic that is often discussed by twentieth- and twenty-first-century logicians, and even historians of logic tend to not have had much to say about when—and why—this question even comes about in the first place. The second is to evaluate the accounts proposed and discussed by Russell, including her new proposal. In the end, I will argue that she has reached the right account of the nature of logical consequence, but not necessarily for the right reasons. (shrink)

The pretheoretical notions of logical consequence and of a logical expression are linked in vague and complex ways to modal and pragmatic intuitions. I offer an introduction to the difficulties that these intuitions create when one attempts to give precise characterizations of those notions. Special attention is given to Tarski’s theories of logical consequence and logical constancy. I note that the Tarskian theory of logical consequence has fared better in the face of (...) the difficulties than the Tarskian theory of logical constancy. Other theories of these notions are explained and criticized. (shrink)

An essay review of Gila Sher's *Logical Consequence*.

This paper deals with the adequacy of the model-theoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have (...) a crucial role in determining logical consequence. Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a model-theoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro's blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formal-structural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed. (shrink)

It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logical consequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness . This paper explores a third notion of logical consequence, and discusses (...) its adequacy for the supervaluationist theory. The paper proceeds in two steps. In the first step, the paper provides a deductive notion of consequence for global validity using the tableaux method. In the second step, the paper provides a notion of logical consequence which is an alternative to global validity, and discusses i) whether it is acceptable to the supervaluationist and ii) whether it plays a better role in a theory of vagueness in the face of the problems related to the global notion. (shrink)

The interrelated logical concepts of validity, entailment, and consequence are all standardly defined in terms of truth preservation. However, imperative sentences can stand in these relations, but they are not truth-apt. This puzzle can be understood as an inconsistent triad: T1 Imperatives can be the relata of the consequence relation. T2 Imperatives are not truth-apt. T3 The relata of the consequence relation must be truth-apt. These three claims cannot all be true. So, to solve the problem (...) of imperative consequence we must reject one of the three claims. Solutions can be categorised into three types: those that reject T1, those that reject T2, and those that reject T3. In this thesis, I first outline and motivate each of these three claims. I then consider, in turn, theories of imperative logic and semantics, all of which fall into one of the three types of solution. I consider and reject two versions of solution type 1, the type that rejects T1. These versions argue that it is impossible for imperatives to stand in logical relations, and attempt to provide alternative explanations for what's happening when it seems like they are doing so. I then consider and reject several versions of solution type 2, the type that rejects T2. These theories claim that, despite appearances based on surface grammar, imperatives are disguised declaratives and thus truth-apt. Each theory proposes a translation schema-- it outlines the truth-conditions for imperatives. Next, I outline several versions of solution type 3, the type that rejects T3. These theories aim to develop a formal account of imperative logic. I reject each of these theories in turn, and finally propose a solution that avoids the problems I raise with the other theories. (shrink)