The paper suggests a definition of the idea of topic-neutrality, and indicates some of the consequences of identifying logicality with topic-neutrality so defined.

One of the oldest topics in foundational metaphysics is the issue how particulars are to be individuated. To individuate a particular, x, means to find criteria that are necessary and sufficient to ensure the assertibility of x ≠ y, for all and only y that are distinct from x. One can distinguish two separate issues that are run under the heading of individuation. One is the question: what is it about a particular that makes it distinct from all other particulars? (...) The other is the question: how do we single out a particular qua distinct from all other particulars? The distinction closely resembles the one put forward by Hector- Neri Castañeda (1975), except that Castañeda talks about the first question in terms of the issue of the ‘internal constitution’ of objects. This way of speaking is misleading, as it insinuates that it is only intrinsic facts about particulars that could serve as candidates for individuation. Instead, in this essay, I will put forward a theory of individuation in which both questions are treated on equal footing, with the implication that both intrinsic and extrinsic, as well as some special properties that I will introduce play a role in individuating particulars. I call the theory ‘derivational contextualism’. It is an elaboration of some ideas I have put forward in an earlier work (Author forthcoming), regarding some basic conditions for individuation, with a structuralist component. I will.. (shrink)

Leibniz notoriously insisted that no two individuals differ solo numero, that is, by being primitively distinct, without differing in some property. The details of Leibniz’s own way of understanding and defending the principle –known as the principle of identity of indiscernibles (henceforth ‘the Principle’)—is a matter of much debate. However, in contemporary metaphysics an equally notorious and discussed issue relates to a case put forward by Max Black (1952) as a counter-example to any necessary and non-trivial version of the principle. (...) Black asks us to imagine, via one of the fictional characters of his dialogue, a world consisting solely of two completely resembling spheres, in a relational space. The supporter of the principle is then forced to admit that although there are ex hypothesi two objects in that universe, there is no property (except trivial ones), not even relational ones, to distinguish them, and hence the necessary version of the principle is falsified. In this essay I will argue that Black’s possible world, together with the dialectic between the potential friends and foes of the Principle as expounded by Black himself.. (shrink)

I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of the (...) existential quantifier that in effect sets a given degree of connectedness among the putative parts of an object as a condition upon there being something (in the sense in question) with those parts. I then argue that such an implicit definition, taken together with an “auxiliary logic” (e.g., introduction and elimination rules), proves to function as a precisification in just the same way as paradigmatic precisifications of, e.g., “red”. I also argue that with a quantifier that is stipulated as maximally tolerant as to what mereological sums there are, precisifications can be given in the form of truth-conditions of quantified sentences, rather than by implicit definition. (shrink)

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.

Many philosophers claim that understanding a logical constant (e.g. ‘if, then’) fundamentally consists in having dispositions to infer according to the logical rules (e.g. Modus Ponens) that fix its meaning. This paper argues that such dispositionalist accounts give us the wrong picture of what understanding a logical constant consists in. The objection here is that they give an account of understanding a logical constant which is inconsistent with what seem to be adequate manifestations of such understanding. I then outline an (...) alternative account according to which understanding a logical constant is not to be understood dispositionally, but propositionally. I argue that this account is not inconsistent with intuitively correct manifestations of understanding the logical constants. (shrink)

Knowledge of the basic rules of logic is often thought to be distinctive, for it seems to be a case of non-inferential a priori knowledge. Many philosophers take its source to be different from those of other types of knowledge, such as knowledge of empirical facts. The most prominent account of knowledge of the basic rules of logic takes this source to be the understanding of logical expressions or concepts. On this account, what explains why such knowledge is distinctive is (...) that it is grounded in semantic or conceptual understanding. However, I show that this cannot be the correct account of knowledge of the basic rules of logic, because it is open to Gettier-style counter-examples. (shrink)

What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.

This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of `proof"; (2) Kreisel"s explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of can be easily and safely ameliorated; (4) the definition of in terms of `proofs from premises" results in a loss of the inductive character of the definitions (...) of and and (5) the same occurs with the definition of in terms of `proofs with free variables". (shrink)

The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in (...) particular of the vexed issue of demarcating the class of logical constants. I begin with a characterization of currently widespread views on form and matter in logic, which I refer to as ‘logical hylomorphism as we know it’—LHAWKI, for short—and argue that the hylomorphism underlying LHAWKI is mereological. Next, I sketch an overview of the historical developments leading from Aristotelian, non-mereological metaphysical hylomorphism to mereological logical hylomorphism (LHAWKI). I conclude with a reassessment of the prospects for the combination of hylomorphism and logic, arguing in particular that LHAWKI is not the only and certainly not the most suitable version of logical hylomorphism. In particular, this implies that the project of demarcating the class of logical constants as a means to define the scope and nature of logic rests on highly problematic assumptions. (shrink)

Donald Dvaidson has claimed that a theory of meaning identifies the logical constants of the object language by treating them in the phrasal axioms of the theory, and that the theory entails a relation of logical consequence among the sentences of the object language. Section 1 offers a preliminary investigation of these claims. In Section 2 the claims are rebutted by appealing to Evans's paradigm of a theory of meaning. Evans's theory is deliberately blind to any relation of logical consequence (...) among the sentences of the object language, and entails only what Evans takes to be a distinct and deeper relation of structural validity among the sentences of the object language. In Section 3 we turn to Evans's motivation in order to compare the two paradigms of a theory of meaning. Evans laid down criteria under which a theory of meaning gives what he called a ‘transcendent’ semantic classification of the lexicon of the object language, in contrast to a mere ‘immanent’ classification. However, when these criteria are applied we find that, pace Evans, they favour Davidson's paradigm over Evans's. In the final section we show that Evans's conception of structural consequence turns out to be a deeper formulation of logical consequence. (shrink)

I shall argue in this paper that it should. To begin with, I shall defend (CP) against several criticisms that have been launched against it. These criticisms are of two kinds, which I shall call internal and external respectively. Internal objections are that a theory that includes (CP) fails to give an account of what it is rational to believe that is satisfactory by its own standards. In particular, since almost everyone agrees that belief in a contradiction is not rational, (...) (CP) is criticized on the grounds that it would imply that beliefs in some contradictions are rational. External objections maintain that the degree of idealization in a theory including (CP) is so great as to make it irrelevant to various real-world phenomena to which a theory of rational belief should be relevant.2. (shrink)

There have been several different and even opposed conceptions of the problem of logical constants, i.e. of the requirements that a good theory of logical constants ought to satisfy. This paper is in the first place a survey of these conceptions and a critique of the theories they have given rise to. A second aim of the paper is to sketch some ideas about what a good theory would look like. A third aim is to draw from these ideas and (...) from the preceding survey the conclusion that most conceptions of the problem of logical constants involve requirements of a philosophically demanding nature which are probably not satisfiable by any minimally adequate theory. (shrink)

The model-theoretic analysis of the concept of logical consequence has come under heavy criticism in the last couple of decades. The present work looks at an alternative approach to logical consequence where the notion of inference takes center stage. Formally, the model-theoretic framework is exchanged for a proof-theoretic framework. It is argued that contrary to the traditional view, proof-theoretic semantics is not revisionary, and should rather be seen as a formal semantics that can supplement model-theory. Specifically, there are formal resources (...) to provide a proof-theoretic semantics for both intuitionistic and classical logic. We develop a new perspective on proof-theoretic harmony for logical constants which incorporates elements from the substructural era of proof-theory. We show that there is a semantic lacuna in the traditional accounts of harmony. A new theory of how inference rules determine the semantic content of logical constants is developed. The theory weds proof-theoretic and model-theoretic semantics by showing how proof-theoretic rules can induce truth-conditional clauses in Boolean and many-valued settings. It is argued that such a new approach to how rules determine meaning will ultimately assist our understanding of the apriori nature of logic. (shrink)

It may be that all that matters for the modalities, possibility and necessity, is the object named by the proper name, not which proper name names it. An influential defender of this view is Saul Kripke. Kripke’s defense is criticized in the paper.

Some bilateralists have suggested that some of our negative answers to yes-or-no questions are cases of rejection. Mark Textor (2011. Is ‘no’ a force-indicator? No! Analysis 71: 448–56) has recently argued that this suggestion falls prey to a version of the Frege-Geach problem. This note reviews Textor's objection and shows why it fails. We conclude with some brief remarks concerning where we think that future attacks on bilateralism should be directed.

Timothy Smiley's wonderful paper 'Rejection' (Analysis 1996) is still perhaps not as well known or well understood as it should be. This note first gives a quick presentation of themes from that paper, though done in our own way, and then considers a putative line of objection - recently advanced by Julien Murzi and Ole Hjortland (Analysis 2009) - to one of Smiley's key claims. Along the way, we consider the prospects for an intuitionistic approach to some of the issues (...) discussed in Smiley's paper. (shrink)

I present an argument that negation is a problem for proof-theoretic semantics: it's meaning cannot be defined by rules of inference, and that's particularly problematic for Dummett's and Prawitz' Justification of Deduction. I won the Jacobsen Essay Price of the University of London for this essay a few years ago.

The focus of this paper are the meaning-theoretical arguments against classical logic that Dummett bases on consideration about the meanings of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In (...) particular, I shall grant Dummett his general bias towards verificationism or justificationism, encapsulated in the slogan `meaning is use'. The second general assumption I see no need to question is Dummett's particular breed of molecularism. Some of Dummett's assumptions will have to be given up, if classical logic is to be vindicated in his meaning-theoretical framework. A major result of this paper will be that the meaning of negation cannot be defined by rules of inference in the Dummettian framework. (shrink)

In this paper, I'll present a general way of "reading off" introduction/elimination rules from elimination/introduction rules, and define notions of harmony and stability on the basis of it.

This is a lightly edited version of my comments on Brandom’s Lecture 2, as delivered in Prague at the “Prague Locke Lectures” in April, 2007. I try to say why Brandom’s proposed demarcation is significant, by placing it in a broader context of demarcation proposals from Kant to the twentieth century. I then raise some questions about the basic ingredients of Brandom’s demarcation—the notions of PP-sufficiency and VP-sufficiency—and question whether the vocabulary of conditionals, Brandom’s paradigm for logical vocabulary, can be (...) universal-LX. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they maintain, cannot be justified (...) from this proof-theoretic perspective. This paper argues that, while classical logic can be formulated so as to satisfy a number of harmony constraints, the meanings of the standard logical constants cannot all be given by their introduction and/or elimination rules; negation, in particular, comes under close scrutiny. (shrink)

It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is fully determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen (2008) argues that this view - call it logical inferentialism - is undermined by some "very little known" considerations by Carnap (1943) to the effect that "in a definite sense, it is not true that the standard (...) rules of inference" themselves suffice to "determine the meanings of [the] logical constants" (p. 2). In a nutshell, Carnap showed that the rules allow for non-normal interpretations of negation and disjunction. Raatikainen concludes that "no ordinary formalization of logic ... is sufficient to `fully formalize' all the essential properties of the logical constants" (ibid.). We suggest that this is a mistake. Pace Raatikainen, intuitionists like Dummett and Prawitz need not worry about Carnap's problem. And although bilateral solutions for classical inferentialists - as proposed by Timothy Smiley and Ian Rumfitt - seem inadequate, it is not excluded that classical inferentialists may be in a position to address the problem too. (shrink)

I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.

The nontechnical ability to identify or match argumentative structure seems to be an important reasoning skill. Instruments that have questions designed to measure this skill include major standardized tests for graduate school admission, for example, the United States-Canadian Law School Admission Test (LSAT), the Graduate Record Examinations (GRE), and the Graduate Management Admission Test (GMAT). Writers and reviewers of such tests need an appropriate foundation for developing such questions--they need a proper representation of phenomenological argumentative structure--for legitimacy, and because these (...) tests affect people's lives. This paper attempts to construct an adequate and appropriate representation of such structure, that is, the logical structure that an argument is perceived to have by mature reasoners, albeit ones who are untrained in logic. (shrink)

In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of Dummett and (...) his followers. In the theory of truth, a key distinction now is made between substantial theories and minimalist or deflationist views. According to the former, truth is a genuine substantial property of the truth-bearers, whereas according to the latter, truth does not have any deeper essence, but all that can be said about truth is contained in T-sentences (sentences having the form: ‘P’ is true if and only if P). There is no necessary analytic connection between the above theories of meaning and truth, but they have nevertheless some connections. Realists often favour some kind of truth-conditional theory of meaning and a substantial theory of truth (in particular, the correspondence theory). Minimalists and deflationists on truth characteristically advocate the use theory of meaning (e.g. Horwich). Semantical anti-realism (e.g. Dummett, Prawitz) forms an interesting middle case: its starting point is the use theory of meaning, but it usually accepts a substantial view on truth, namely that truth is to be equated with verifiability or warranted assertability. When truth is so understood, it is also possible to accept the idea that meaning is closely related to truth-conditions, and hence the conflict between use theories and truth-conditional theories in a sense disappears in this view. (shrink)

Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may (...) be said to exhibit “general-elimination” harmony. Ge-harmony ensures that the meaning of a logical expression is clearly visible in its I-rule, and that the I- and E-rules are coherent, in encapsulating the same meaning. However, it does not ensure that the resulting logical system is normalizable, nor that it satisfies the conservative extension property, nor that it is consistent. Thus harmony should not be identified with any of these notions. (shrink)

The paper argues that a philosophically informative and mathematically precise characterization is possible by (i) describing a particular proposal for such a characterization, (ii) showing that certain criticisms of this proposal are incorrect, and (iii) discussing the general issue of what a characterization of logical constants aims at achieving.

This paper argues that logical inferentialists should reject multiple-conclusion logics. Logical inferentialism is the position that the meanings of the logical constants are determined by the rules of inference they obey. As such, logical inferentialism requires a proof-theoretic framework within which to operate. However, in order to fulfil its semantic duties, a deductive system has to be suitably connected to our inferential practices. I argue that, contrary to an established tradition, multiple-conclusion systems are ill-suited for this purpose because they fail (...) to provide a 'natural' representation of our ordinary modes of inference. Moreover, the two most plausible attempts at bringing multiple conclusions into line with our ordinary forms of reasoning, the disjunctive reading and the bilateralist denial interpretation, are unacceptable by inferentialist standards. (shrink)

The notion of harmony has played a pivotal role in a number of debates in the philosophy of logic. Yet there is little agreement as to how the requirement of harmony should be spelled out in detail or even what purpose it is to serve. Most, if not all, conceptions of harmony can already be found in Michael Dummett's seminal discussion of the matter in The Logical Basis of Metaphysics. Hence, if we wish to gain a better understanding of the (...) notion of harmony, we do well to start here. Unfortunately, however, Dummett's discussion is not always easy to follow. The following is an attempt to disentangle the main strands of Dummett's treatment of harmony. The different variants of harmony as well as their interrelations are clarified and their individual shortcomings qua interpretations of harmony are demonstrated. Though no attempt is made to give a detailed alternative account of harmony here, it is hoped that our discussion will lay the ground for an adequate rigorous treatment of this central notion. (shrink)

In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.

This volume provides analyses of the logic-reality relationship from different approaches and perspectives. The point of convergence lies in the exploration of the connections between reality – social, natural or ideal – and logical structures employed in describing or discovering it. Moreover, the book connects logical theory with more concrete issues of rationality, normativity and understanding, thus pointing to a wide range of potential applications. -/- -/- The papers collected in this volume address cutting-edge topics in contemporary discussions amongst specialists. (...) Some essays focus on the role of indispensability considerations in the justification of logical competence, and the wide range of challenges within the philosophy of mathematics. Others present advances in dynamic logical analysis such as extension of game semantics to non-logical part of vocabulary and development of models of contractive speech act. -/- Table of Contents: Introduction: Majda Trobok, Nenad Miščević and Berislav Žarnić.- I. Logical and Mathematical Structures.- Life on the Ship of Neurath: Mathematics in the Philosophy of Mathematics: Stewart Shapiro.- Applied Mathemathics in the Sciences: Dale Jacquette.- The Philosophical Impact of the Löwenheim-Skolem Theorem: Miloš Arsenijević.- Debating (Neo)logicism: Frege and the neo-Fregeans: Majda Trobok.- II. Epistemology and Logic.- Informal Logic and Informal Consequence: Danilo Šuster.- Logical Consequence and Rationality: Nenad Smokrović.- Logic, Indispensability and Aposteriority: Nenad Miščević.- III . Dynamic Logical Models of Meaning.- Extended Game-Theoretical Semantics: Manuel Rebuschi.- Dynamic Logic of Propositional Commitments: Tomoyuki Yamada.- Is Unsaying Polite?: Berislav Žarnić.- IV Logical Methods in Ontological and Linguistic Analyses.- Towards a Formal Account of Identity Criteria: Massimiliano Carrara and Silvia Gaio.- A Mereology for the Change of Parts: Pierdaniele Giaretta and Giuseppe Spolaore.- Russell versus Frege: Imre Rusza.- Goodman’s OnlyWorld: Vladan Djordjević.-. (shrink)

This comment piece examines the distinction between negation of a statement and denial of its truth (assertion of its falsity), in the context of an early examination of Quine's related views. Where P is "Jones is ill," the author maintains, in contrast to Quine, that the negation of P is "Jones is ill" is false.

The core language can be extended by defining additional logical constants. E.g., we can add ‘→’ (implication), ‘∨’ (disjunction), and ‘∀x’ (universal quantifiers). The choice of logical primitives is not as optional in DPL as it is in standard predicate logic.

Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told about (...) the truth or falsity of atomic sentences, A always receives the top-element of a certain partial order on non-ontic semantic values as its value. The ordering in question is a told-true order. Analogously, a formula A is logically false just in case no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain told-false order as its value. Here, truth and falsity are pari passu , and it is the treatment of truth and falsity as independent of each other that leads to an informational interpretation of these notions in terms of a certain kind of higher-level information. (shrink)

There is as yet no settled consensus as to what makes a term a logical constant or even as to which terms should be recognized as having this status. This essay sets out and defends a rationale for identifying logical constants. I argue for a two-tiered approach to logical theory. First, a secure, core logical theory recognizes only a minimal set of constants needed for deductively systematizing scientific theories. Second, there are extended logical theories whose objectives are to systematize various (...) pre-theoretic, modal intuitions. The latter theories may recognize a variety of additional constants as needed in order to formalize a given set of intuitions. (shrink)

There is as yet no settled consensus as to what makes a term a logical constant or even as to which terms should be recognized as having this status. This essay sets out and defends a rationale for identifying logical constants. I argue for a two-tiered approach to logical theory. First, a secure, core logical theory recognizes only a minimal set of constants needed for deductively systematizing scientific theories. Second, there are extended logical theories whose objectives are to systematize various (...) pre-theoretic, modal intuitions. The latter theories may recognize a variety of additional constants as needed in order to formalize a given set of intuitions. (shrink)

Greece is Hellas and Greeks are Hellenes. Azure is cobalt and everything (coloured) azure is (coloured) cobalt. Pre-Fregeans would call all these statements of identity. <span class='Hi'>Frege</span> taught us to distinguish between Conaming [Name] [Name]. Ngh: Greece is Hellas g=h. Nac: Azure is cobalt a=c Copredicating [Predicate] [Predicate]. PGH: Greeks are Hellenes (x)(Gx[identical with]Hx). PAC: Everything azure is cobalt (x)(Ax[identical with]Cx) Singular Predication [Name] [Predicate]. PcA: Como is azure Ac. PaC: Azure is a colour Ca. PaL: Azure is like indigo (...) Lai. PgD: Greece defeated Persia Dgp. With <span class='Hi'>Frege</span> the contrasts became marked but misconceived. (shrink)

Extending the language of the intuitionistic propositional logic Int with additional logical constants, we construct a wide family of extensions of Int with the following properties: (a) every member of this family is a maximal conservative extension of Int; (b) additional constants are independent in each of them.

This paper is divided in five sections. Section 11.1 sketches the history of the distinction between speech act with negative content and negated speech act, and gives a general dynamic interpretation for negated speech act. “Downdate semantics” for AGM contraction is introduced in Section 11.2. Relying on semantically interpreted contraction, Section 11.3 develops the dynamic semantics for constative and directive speech acts, and their external negations. The expressive completeness for the formal variants of natural language utterances, none of which is (...) a retraction, has been proved in Section 11.4. The last section gives a laconic answer to the question posed in the title of the paper. (shrink)

We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and complete- ness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems.