PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make it more widely available beyond university libraries to individual readers, the non-profit publisher and the author have agreed to issue the printed edition at cost. ●●●●● The printed edition was released on September 1, 2021 and is now available through (...) all booksellers, including Barnes & Noble, Amazon, and brick-and-mortar bookstores under ISBN 978-0-578-88646-6. ●●●●● In light of the length of this book, readers who would like to have a more detailed description of the book's objectives and method may find it helpful to read the detailed and clearly written Wikipedia entry about this work: From the Wikipedia search page, use the search phrase "Critique of Impure Reason". At least at the time of this writing (11/29/2021), the Wikipedia entry is well-researched and accurate. ●●●●● In addition, a "Primer on Bartlett's CRITIQUE OF IMPURE REASON" has been made available by the author. It is available under its title through PhilPapers and other philosophy online archives. ●●●●● COMMENDATIONS OF THIS WORK, from the back cover of the published edition: ●●●●● “I admire its range of philosophical vision.” – Nicholas Rescher, Distinguished University Professor of Philosophy, University of Pittsburgh, author of more than 100 books. ●●●●● “Bartlett’s _Critique of Impure Reason_ is an impressive, bold, and ambitious work. Careful scholarship is balanced by original analyses that lead the reader to recognize the limits of meaning, knowledge, and conceptual possibility. The work addresses a host of traditional philosophical problems, among them the nature of space, time, causality, consciousness, the self, other minds, ontology, free will and determinism, and others. The book culminates in a fascinating and profound new understanding of relativity physics and quantum theory.” – Gerhard Preyer, Professor of Philosophy, Goethe-University, Frankfurt am Main, Germany, author of many books including _Concepts of Meaning_, _Beyond Semantics and Pragmatics_, _Intention and Practical Thought_, and _Contextualism in Philosophy_. ●●●●● “[This work’s] goal is of a unique and difficult species: Dr. Bartlett seeks to develop a formal logical calculus on the basis of transcendental philosophical arguments; in fact, he hopes that this calculus will be the formal expression of the transcendental foundation of knowledge.... I consider Dr. Bartlett’s work soundly conceived and executed with great skill.” – C. F. von Weizsäcker, philosopher and physicist, former Director, Max-Planck-Institute, Starnberg, Germany. ●●●●● “Bartlett has written an American “Prolegomena to All Future Metaphysics.” He aims rigorously to eliminate meaningless assertions, reach bedrock, and place philosophy on a firm foundation that will enable it, like science and mathematics, to produce lasting results that generations to come can build on. This is a great book, the fruit of a lifetime of research and reflection, and it deserves serious attention.” — Martin X. Moleski, former Professor, Canisius College, Buffalo, NY, studies of scientific method, the presuppositions of thought, and the self-referential nature of epistemology. ●●●●● “Bartlett has written a book on what might be called the underpinnings of philosophy. It has fascinating depth and breadth, and is all the more striking due to its unifying perspective based on the concepts of reference and self-reference.” – Don Perlis, Professor of Computer Science, University of Maryland, author of numerous publications on self-adjusting autonomous systems and philosophical issues concerning self-reference, mind, and consciousness. ●●●●● ●●●●● The _Critique of Impure Reason: Horizons of Possibility and Meaning_ comprises a major and important contribution to philosophy. Thanks to the generosity of its publisher, this massive 885-page volume has been published as a free open access eBook (3.75MB) as well as an open access printed edition. It inaugurates a revolutionary paradigm shift in philosophical thought by providing compelling and long-sought-for solutions to a wide range of philosophical problems. In the process, the work fundamentally transforms the way in which the concepts of reference, meaning, and possibility are understood. The book includes a Foreword by the celebrated German philosopher and physicist Carl Friedrich von Weizsäcker. ●●●●● In Kant’s _Critique of Pure Reason_ we find an analysis of the preconditions of experience and of knowledge. In contrast, but yet in parallel, the new _Critique_ focuses upon the ways—unfortunately very widespread and often unselfconsciously habitual—in which many of the concepts that we employ _conflict_ with the very preconditions of meaning and of knowledge. ●●●●● This is a book about the boundaries of frameworks and about the unrecognized conceptual confusions in which we become entangled when we attempt to transgress beyond the limits of the possible and meaningful. We tend either not to recognize or not to accept that we all-too-often attempt to trespass beyond the boundaries of the frameworks that make knowledge possible and the world meaningful. ●●●●● The _Critique of Impure Reason_ proposes a bold, ground-breaking, and startling thesis: that a great many of the major philosophical problems of the past can be solved through the recognition of a viciously deceptive form of thinking to which philosophers as well as non-philosophers commonly fall victim. For the first time, the book advances and justifies the criticism that a substantial number of the questions that have occupied philosophers fall into the category of “impure reason,” violating the very conditions of their possible meaningfulness. ●●●●● The purpose of the study is twofold: first, to enable us to recognize the boundaries of what is referentially forbidden—the limits beyond which reference becomes meaningless—and second, to avoid falling victims to a certain broad class of conceptual confusions that lie at the heart of many major philosophical problems. As a consequence, the boundaries of _possible meaning_ are determined. ●●●●● Bartlett, the author or editor of more than 20 books, is responsible for identifying this widespread and delusion-inducing variety of error, _metalogical projection_. It is a previously unrecognized and insidious form of erroneous thinking that undermines its own possibility of meaning. It comes about as a result of the pervasive human compulsion to seek to transcend the limits of possible reference and meaning. ●●●●● Based on original research and rigorous analysis combined with extensive scholarship, the _Critique of Impure Reason_ develops a self-validating method that makes it possible to recognize, correct, and eliminate this major and pervasive form of fallacious thinking. In so doing, the book provides at last provable and constructive solutions to a wide range of major philosophical problems. ●●●●● CONTENTS AT A GLANCE ▪▪▪▪▪ Preface ▪▪▪▪▪ Foreword by Carl Friedrich von Weizsäcker ▪▪▪▪▪ Acknowledgments ▪▪▪▪▪ Avant-propos: A philosopher’s rallying call ▪▪▪▪▪ Introduction ▪▪▪▪▪ A note to the reader ▪▪▪▪▪ A note on conventions ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART I ▪▪▪▪▪ ▪▪▪▪▪ WHY PHILOSOPHY HAS MADE NO PROGRESS AND HOW IT CAN ▪▪▪▪▪ 1 Philosophical-psychological prelude ▪▪▪▪▪ 2 Putting belief in its place: Its psychology and a needed polemic ▪▪▪▪▪ 3 Turning away from the linguistic turn: From theory of reference to metalogic of reference ▪▪▪▪▪ 4 The stepladder to maximum theoretical generality ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART II ▪▪▪▪▪ THE METALOGIC OF REFERENCE ▪▪▪▪▪ A New Approach to Deductive, Transcendental Philosophy ▪▪▪▪▪ 5 Reference, identity, and identification ▪▪▪▪▪ 6 Self-referential argument and the metalogic of reference ▪▪▪▪▪ 7 Possibility theory ▪▪▪▪▪ 8 Presupposition logic, reference, and identification ▪▪▪▪▪ 9 Transcendental argumentation and the metalogic of reference ▪▪▪▪▪ 10 Framework relativity ▪▪▪▪▪ 11 The metalogic of meaning ▪▪▪▪▪ 12 The problem of putative meaning and the logic of meaninglessness ▪▪▪▪▪ 13 Projection ▪▪▪▪▪ 14 Horizons ▪▪▪▪▪ 15 De-projection ▪▪▪▪▪ 16 Self-validation ▪▪▪▪▪ 17 Rationality: Rules of admissibility ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART III ▪▪▪▪▪ PHILOSOPHICAL APPLICATIONS OF THE METALOGIC OF REFERENCE ▪▪▪▪▪ Major Problems and Questions of Philosophy and the Philosophy of Science ▪▪▪▪▪ 18 Ontology and the metalogic of reference ▪▪▪▪▪ 19 Discovery or invention in general problem-solving, mathematics, and physics ▪▪▪▪▪ 20 The conceptually unreachable: “The far side” ▪▪▪▪▪ 21 The projections of the external world, things-in-themselves, other minds, realism, and idealism ▪▪▪▪▪ 22 The projections of time, space, and space-time ▪▪▪▪▪ 23 The projections of causality, determinism, and free will ▪▪▪▪▪ 24 Projections of the self and of solipsism ▪▪▪▪▪ 25 Non-relational, agentless reference and referential fields ▪▪▪▪▪ 26 Relativity physics as seen through the lens of the metalogic of reference ▪▪▪▪▪ 27 Quantum theory as seen through the lens of the metalogic of reference ▪▪▪▪▪ 28 Epistemological lessons learned from and applicable to relativity physics and quantum theory ▪▪▪▪▪ ▪▪▪▪▪ PART IV ▪▪▪▪▪ HORIZONS ▪▪▪▪▪ 29 Beyond belief ▪▪▪▪▪ 30 _Critique of Impure Reason_: Its results in retrospect ▪▪▪▪▪ ▪▪▪▪▪ SUPPLEMENT ▪▪▪▪▪ The Formal Structure of the Metalogic of Reference ▪▪▪▪▪ APPENDIX I ▪▪▪▪▪ The Concept of Horizon in the Work of Other Philosophers ▪▪▪▪▪ APPENDIX II ▪▪▪▪▪ Epistemological Intelligence ▪▪▪▪▪ References ▪▪▪▪▪ Index ▪▪▪▪▪ About the author. 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Two recent and influential papers, van Rooij 2007 and Lassiter 2012, propose solutions to the proviso problem that make central use of related notions of independence—qualitative in the first case, probabilistic in the second. We argue here that, if these solutions are to work, they must incorporate an implicit assumption about presupposition accommodation, namely that accommodation does not interfere with existing qualitative or probabilistic independencies. We show, however, that this assumption is implausible, as updating beliefs with conditional information does not (...) in general preserve independencies. We conclude that the approach taken by van Rooij and Lassiter does not succeed in resolving the proviso problem. (shrink)

Donkey sentences have existential and universal readings, but they are not often perceived as ambiguous. We extend the pragmatic theory of nonmaximality in plural definites by Križ (2016) to explain how context disambiguates donkey sentences. We propose that the denotations of such sentences produce truth-value gaps — in certain scenarios the sentences are neither true nor false — and demonstrate that Križ’s pragmatic theory fills these gaps to generate the standard judgments of the literature. Building on Muskens’s (1996) Compositional Discourse (...) Representation Theory and on ideas from supervaluation semantics, the semantic analysis defines a general schema for quantification that delivers the required truth-value gaps. Given the independently motivated pragmatic theory of Križ 2016, we argue that mixed readings of donkey sentences require neither plural information states, contra Brasoveanu 2008, 2010, nor error states, contra Champollion 2016, nor singular donkey pronouns with plural referents, contra Krifka 1996, Yoon 1996. We also show that the pragmatic account improves over alternatives like Kanazawa 1994 that attribute the readings of donkey sentences to the monotonicity properties of the embedding quantifier. (shrink)

I propose a new theory of semantic presupposition, which I call dissatisfaction theory. I first briefly review a cluster of problems − known collectively as the proviso problem − for most extant theories of presupposition, arguing that the main pragmatic response to them faces a serious challenge. I avoid these problems by adopting two changes in perspective on presupposition. First, I propose a theory of projection according to which presuppositions project unless they are locally entailed. Second, I reject the standard (...) assumption that presuppositions are contents which must be entailed by the input context; instead, I propose that presuppositions are contents which are marked as backgrounded. I show that, together, these commitments allow us to avoid the proviso problem altogether, and generally make plausible predictions about presupposition projection out of connectives and attitude predicates. I close by sketching a two-dimensional implementation of my theory which allows us to make further welcome predictions about attitude predicates and quantifiers. (shrink)

The Proviso Problem is the discrepancy between the predictions of nearly every major theory of semantic presupposition about what is semantically presupposed by conditionals, disjunctions, and conjunctions, versus observations about what speakers of certain sentences are felt to be presupposing. I argue that the Proviso Problem is a more serious problem than has been widely recognized. After briefly describing the problem and two standard responses to it, I give a number of examples which, I argue, show that those responses are (...) inadequate. I conclude by briefly exploring alternate approaches to presupposition that avoid this problem. -/- . (shrink)

Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the form 'will(φ)', that is based on the classic Russellian analysis of definite descriptions. Todd's analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any further (...) controversial semantical or metaphysical complication. In this paper, we will show that this quasi-Russellian analysis of 'will' both lacks linguistic motivation and faces a variety of significant problems. In particular, we show that the standard arguments for Russell's treatment of definite descriptions fail to apply to statements of the form 'will(φ)'. (shrink)

This presentation traces an historical root of the reductio ad absurdum mode of argumentation in Greek philosophy. I propose a new understanding of the liar paradox as an instance of this mode of argumentation. I show that the paradox was crea ted as part of a refutational argument in the controversy over the justification of realism and the realists concepts of truth and certainty. The paradox was part of the dialectical style of Greek scepticism, which was characterized, inter alia, by (...) the u se of the reductio ad absurdum. The paradox turns out to be a metaphysical and epistemological argument. (shrink)

In an interesting experimental study, Bonini et al. (1999) present partial support for truth-gap theories of vagueness. We say this despite their claim to find theoretical and empirical reasons to dismiss gap theories and despite the fact that they favor an alternative, epistemic account, which they call ‘vagueness as ignorance’. We present yet more experimental evidence that supports gap theories, and argue for a semantic/pragmatic alternative that unifies the gappy supervaluationary approach together with its glutty relative, the subvaluationary approach.

We discuss presupposition, the phenomenon whereby speakers mark linguistically the information that is presupposed or taken for granted, rather than being part of the main propositional content of a speech act. Expressions and constructions carrying presuppositions are called “presupposition triggers”, forming a large class including definites and factive verbs. The article first introduces the range of triggers, the basic properties of presuppositions such as projection and cancellability, and the diagnostic tests used to identify them. The reader is then introducedto major (...) models of presupposition from the last 50 years, separated into three classes: Frege-Strawson derived semantic models, pragmaticmodels such as that offered by Stalnaker, and dynamic models. Finallywe discuss some of the main current issues in presupposition theory. These involve accommodation, which occurs when a hearer's knowledge state is adjusted to meet the speaker's presuppositions; presupposition failure, which occurs when a presupposition is false; the interaction between presuppositions and attitudes; and the triggering problem, i.e., the problem of explaining why presuppositions occur in the first place. (shrink)

Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in (...) the language of science is presented here. This approach preserves compositionality to a large extent. *Received September 2009; revised February 2010. †To contact the author, please write to: Seminar for Philosophy, Logic, and Theory of Science, Hauspostfach 49, Ludwig-Maximilians-Universität, Munich 80539, Germany; e-mail: [email protected]. (shrink)

According to standard mathematical platonism, mathematical entities (numbers, sets, etc.) are abstract entities. As such, they lack causal powers and spatio-temporal location. Platonists owe us an account of how we acquire knowledge of this inaccessible mathematical realm. Some recent versions of mathematical platonism postulate a plenitude of mathematical entities, and Mark Balaguer has argued that, given the existence of such a plenitude, the attainment of mathematical knowledge is rendered non-problematic. I assess his epistemology for such a profligate platonism and find (...) it unsatisfactory because it lacks an adequate semantics, in particular, an adequate account of reference. (shrink)

A Série Investigação Filosófica é uma série de livros de traduções de verbetes da Enciclopédia de Filosofia da Stanford (Stanford Encyclopedia of Philosophy) e de outras plataformas internacionalmente reconhecidas, que intenciona servir tanto como material didático para os professores das diferentes sub-áreas e níveis da Filosofia quanto como material de estudo para a pesquisa e para concursos da área. Nós, professores, sabemos o quão difícil é encontrar bom material em português para indicarmos. E há uma certa deficiência na graduação brasileira (...) de filosofia, principalmente em localizações menos favorecidas, com relação ao conhecimento de outras línguas, como o inglês e o francês. Tentamos, então, suprir essa deficiência, ao introduzirmos essas traduções ao público de língua portuguesa, sem nenhuma finalidade comercial e meramente pela glória da filosofia. (shrink)

It’s not clear what supervaluationists should say about propositional content. Does a vague sentence, e.g., ‘Harry is bald’, express one proposition, or a barrage of propositions, or none at all? Or is the matter indeterminate? The supervaluationist canon is not decisive on the issue; authoritative passages can be cited in favor of each of the proposals just mentioned. Furthermore, some detractors have argued that supervaluationism is incapable of providing any coherent account of propositional content. This paper considers each of the (...) proposals for how many propositions are expressed by a vague sentence: none, some, all, or it’s indeterminate. Most of these proposals turn out to be unworkable in the metalanguage. I conclude that orthodox supervaluationists—those who identify truth with supertruth—must either relax the standard requirement that propositions be bivalent, or else alter the standard relation between sentences and propositions in which a sentence inherits its truth-conditions from the proposition it expresses. The best option going forward for the orthodox supervaluationist is perhaps the most surprising—amend the requirement that propositions be bivalent. I argue that propositions having supervaluational truth-conditions are best suited to fill the propositional roles in the semantic theory of a vague language. These propositions admit of truth-value gaps, and gappy propositions are controversial, but I argue that they earn their keep. (shrink)

In this paper, a solution to the problem of theoretical terms is developed that is based on Carnap’s doctrine of indirect interpretation of theoretical terms. This doctrine will be given a semantic, model-theoretic explanation that is not given by Carnap himself as he remains content with a syntactic explanation. From that semantic explanation, rules for the truth-value assignment to postulates, i.e. sentences that determine the meaning of theoretical terms, are derived. The logical status of postulates will be clarified thereby in (...) such a way that the problem of theoretical terms disappears. (shrink)

The extensions of vague predicates like ‘is bald’, ‘is tall’, and ‘is a heap’ apparently lack sharp boundaries, and this makes such predicates susceptible to soritical reasoning, i.e. reasoning that leads to some version of the notorious sorites paradox. This essay is concerned with a certain kind of theory of vagueness, according to which the symptoms and puzzles of vagueness should be accounted for in terms of a particular species of context sensitivity exhibited by vague expressions. The basic idea is (...) that the extensions of vague predicates vary with certain contextual factors, and that this fact can explain why they appear to lack sharp boundaries. This kind of view is referred to as contextualism about vagueness. A detailed characterisation of contextualism about vagueness is given in chapter two and three. In chapter two, a generic version of contextualism about vagueness is developed, and some alternative forms of context sensitivity are introduced. In chapter three, the specific contextual factors appealed to by different contextualists are discussed. In chapter four, different contextualist diagnoses of the sorites paradox are considered, and found to be problematic in various ways. It is argued that contrary to what some of its proponents have claimed, contextualism about vagueness is not superior to other comparable theories of vagueness when it comes to explaining the appeal of soritical reasoning. In chapter five, a certain version of the sorites paradox, known as the forced march sorites, is discussed. It is argued that “data” about how speakers would behave in the forced march cannot lend any firm support to contextualism about vagueness. In chapter six, some problems concerning the instability of the contextual factors are considered. One problem is that contextualist diagnoses of the sorites which locate a fallacy of equivocation in the reasoning seem to render non-soritical reasoning fallacious as well. A model for treating this problem is suggested, but on closer consideration, it turns out to be problematic. Moreover, this model is of no help in solving the more general problem that even if classical logic remains valid for vague language on some contextualist views, the instability of the extensions of vague predicates makes it difficult to know when a certain piece of reasoning instantiates a valid argument form. Other difficulties arise with respect to speech reports and belief contents. Chapter seven concludes with a summary and some methodological remarks. (shrink)

This volume seeks to further the use of formal methods in clarifying one of the central problems of philosophy: that of our free human agency and its place in our indeterministic world. It celebrates the important contributions made in this area by Nuel Belnap, American logician and philosopher. Philosophically, indeterminism and free action can seem far apart, but in Belnap’s work, they are intimately linked. This book explores their philosophical interconnectedness through a selection of original research papers that build forth (...) on Belnap’s logical and philosophical work. Some contributions take the form of critical discussions of Belnap's published work, some develop points made in his publications in new directions, and others provide additional insights on the topics of indeterminism and free action. In Nuel Belnap’s work on indeterminism and free action, three formal frameworks figure prominently: the simple branching histories framework known as "branching time;" its relativistic spatio-temporal extension, branching space-times; and the “seeing to it that” logic of agency. As those frameworks provide the formal background for the contributed papers, the volume introduction gives an overview of the current state of their development. It also introduces case-intensional first order logic, a general intensional logic offering resources for a first-order extension of the mentioned frameworks and a recent research focus of Belnap’s. The volume also contains an extended biographical interview with Nuel Belnap. (shrink)

In dynamic theories of presupposition, a trigger pp′ with presupposition p and at-issue component p′ comes with a requirement that p should be entailed by the local context of pp′. We argue that some co-speech gestures should be analyzed within a presuppositional framework, but with a twist: an expression p co-occurring with a co-speech gesture G with content g comes with the requirement that the local context of p should guarantee that p entails g; we call such assertion-dependent presuppositions ‘cosuppositions’. (...) We show that this analysis can be combined with earlier theories of local contexts to account for complex patterns of gesture projection in quantified and in attitudinal contexts, and we compare our account to two potential alternatives: one based on supervaluations, and one, due to Cornelia Ebert, that treats co-speech gestures as supplements. We argue that the latter is correct, but for ‘post-speech’ gestures, rather than for co-speech gestures. (shrink)

By force of _causes precede effects_, causality contributes to the temporal meaning of discourse. In case of semantic causal relations, this contribution is straightforward, but in case of epistemic causal relations, it is not. In order to gain insight into the semantics of epistemic causal relations, paradoxical cases are analyzed of text fragments in which temporal and causal meaning seem to be irreconcilable. A solution is proposed consisting of several parts: First, an analysis of epistemic causal coherence relations, in which (...) the effect sentence is argued to be a _belief_ sentence. Secondly, a method for deriving causal coherence relations. And thirdly, a format for representing temporal meaning in which contributions of tense and causality can be reconciled. Finally, it is argued that _understanding_ epistemically causally connected sequences is not equal to being persuaded to _believing_ them. The difference is shown to be expressible in the representation format proposed. (shrink)

This paper provides a new account of positive versus negative antonyms. The data includes well-known linguistic generalizations regarding negative adjectives, such as their incompatibility with measure phrases (cf. two meters tall/ *short) and ratio phrases (twice as tall/ #short) as well as the impossibility of truly crosspolar comparisons (*Dan is taller than Sam is short). These generalizations admit a variety of exceptions, e.g., positive adjectives that do not license measure phrases (cf. #two degrees warm/cold) and rarely also negative adjectives that (...) do (cf. two hours late/early). Furthermore, new corpus data is presented regarding the use of twice with positive and negative adjectives. The analysis the paper presents supposes that grammar associates gradable adjectives with measure functions—mapping of entities to a set of degrees isomorphic to the real numbers (Kennedy, Projecting the adjective: The syntax and semantics of gradability and comparison, 1999). On this analysis, negative adjectives map entities to values that are linearly reversed and linearly transformed in comparison with their values in the positive antonyms. As shown, the generalizations, as well as their exceptions, directly follow. Negative polarity is explained in terms of function reversal, and non-licensing of measure phrases is explained in terms of transformation by an unspecified value. (shrink)

Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the theoretical terms once these (...) terms are introduced through the axioms of a theory. (shrink)

Those inclined to believe in the existence of propositions as traditionally conceived might seek to reduce them to some other type of entity. However, parsimonious propositionalists of this type are confronted with a choice of competing candidates – for example, sets of possible worlds, and various neo-Russellian and neo-Fregean constructions. It is argued that this choice is an arbitrary one, and that it closely resembles the type of problematic choice that, as Benacerraf pointed out, bedevils the attempt to reduce numbers (...) to sets – should the number 2 be identified with the set Ø or with the set Ø, Ø? An “argument from arbitrary identification” is formulated with the conclusion that propositions (and perhaps numbers) cannot be reduced away. Various responses to this argument are considered, but ultimately rejected. The paper concludes that the argument is sound: propositions, at least, are sui generis entities. (shrink)

Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative (...) semantics for classical proof theory. The key features of the account are: there is a single notion of truth—definite truth—and a single notion of validity; sentences can be true, false, or undetermined; all classical theorems and all classical inference rule are valid; the sorites argument is unsound; ‘definitely’ is treated as a meta-language predicate; higher-order vagueness is handled via semantic ascent. (shrink)

This paper presents a novel semantic analysis of unit names (like pound and meter) and gradable adjectives (like tall, short and happy), inspired by measurement theory (Krantz et al. In Foundations of measurement: Additive and Polynomial Representations, 1971). Based on measurement theory’s four-way typology of measures, I claim that different adjectives are associated with different types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the puzzling limited distribution of measure phrases, as well (...) as unit-based comparisons between predicates (as in the table is longer than it is wide). All considered, my analyses support the view that the grammar of natural languages is sensitive to features of measurement theory. (shrink)

Kripke’s theory of truth is arguably the most influential approach to self-referential truth and the semantic paradoxes. The use of a partial evaluation scheme is crucial to the theory and the most prominent schemes that are adopted are the strong Kleene and the supervaluation scheme. The strong Kleene scheme is attractive because it ensures the compositionality of the notion of truth. But under the strong Kleene scheme classical tautologies do not, in general, turn out to be true and, as a (...) consequence, classical reasoning is no longer admissible once the notion of truth is involved. The supervaluation scheme adheres to classical reasoning but violates compositionality. Moreover, it turns Kripke’s theory into a rather complicated affair: to check whether a sentence is true we have to look at all admissible precisification of the interpretation of the truth predicate we are presented with. One consequence of this complicated evaluation condition is that under the supervaluation scheme a more proof-theoretic characterization of Kripke’s theory becomes inherently difficult, if not impossible. In this paper we explore the middle ground between the strong Kleene and the supervaluation scheme and provide an evaluation scheme that adheres to classical reasoning but retains many of the attractive features of the strong Kleene scheme. We supplement our semantic investigation with a novel axiomatic theory of truth that matches the semantic theory we have put forth. (shrink)

It has seemed natural to model phenomena related to vagueness in terms of graded membership. However, so far no satisfactory answer has been given to the question of what graded membership is nor has any attempt been made to describe in detail a procedure for determining degrees of membership. We seek to remedy these lacunae by building on recent work on typicality and graded membership in cognitive science and combining some of the results obtained there with a version of the (...) conceptual spaces framework. (shrink)

The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free logic and supervaluations), and apply the (...) resulting approach to accommodate semantic paradoxes. (shrink)

Thomason (1979/2010)'s argument against competence psychologism in semantics envisages a representation of a subject's competence as follows: he understands his own language in the sense that he can identify the semantic content of each of its sentences, which requires that the relation between expression and content be recursive. Then if the scientist constructs a theory that is meant to represent the body of the subject's beliefs, construed as assent to the content of the pertinent sentences, and that theory satisfies certain (...) 'natural assumptions', then it implies that the subject is inconsistent if the beliefs include arithmetic. I challenge the result by insisting that the motivation for Thomason's principle (ii), via Moore's Paradox, leads to a more complex representation, in which stating the facts and expressing one's beliefs are treated differently. Certain logical connections among expressions of assent, and between expression and statement, are a matter of consequence on pain of pragmatic incoherence, not consequence on pain of classical logical inconsistency. But while this salvages the possibility that a modification of the above sort of representation could be adequate, Thomason's devastating conclusion returns if the scientist identifies himself as the subject of that representation, even when paying heed to the requirement of pragmatic coherence of the sort highlighted by Moore's Paradox. (shrink)

Charles Sanders Peirce was one of the United States’ most original and profound thinkers, and a prolific writer. Peirce’s game theory-based approaches to the semantics and pragmatics of signs and language, to the theory of communication, and to the evolutionary emergence of signs, provide a toolkit for contemporary scholars and philosophers. Drawing on unpublished manuscripts, the book offers a rich, fresh picture of the achievements of a remarkable man.

My purpose in this paper is to argue that the classical notion of entailment is not suitable for non-bivalent logics, to propose an appropriate alternative and to suggest a generalized entailment notion suitable to bivalent and non-bivalent logics alike. In classical two valued logic, one can not infer a false statement from one that is not false, any more than one can infer from a true statement a statement that is not true. In classical logic in fact preserving truth and (...) preserving non-falsity are one and the same thing. They are not the same in non-bivalent logics however and I will argue that the classical notion of entailment that preserves only truth is not strong enough for such a logic. I will show that if we retain the classical notion of entailment in a logic that has three values, true, false and a third value in between, an inconsistency can be derived that can be resolved only by measures that seriously disable the logic. I will show this for a logic designed to allow for semantic presuppositions, then I will show that we get the same result in any three valued logic with the same value ordering. I will finally suggest how the notion of entailment should be generalized so that this problem may be avoided. The strengthened notion of entailment I am proposing is a conservative extension of the classical notion that preserves not only truth but the order of all values in a logic, so that the value of an entailed statement must alway be at least as great as the value of the sequence of statements entailing it. A notion of entailment this strong or stronger will, I believe, be found to be applicable to non-classical logics generally. In the opinion of Dana Scott, no really workable three valued logic has yet been developed. It is hard to disagree with this. A workable three valued logic however could perhaps be developed however, if we had a notion of entailment suitable to non-bivalent logics. (shrink)

Deflationists cannot make sense ofthe notion of referential indeterminacybecause they deny the existence of substantivereference. One way for them to make sense ofthe objective existence of linguisticindeterminacy is by embracing theworldly (or objectual) view ofindeterminacy, the view that indeterminacyexists not in reference relations but in the(non-linguistic) world itself. On this view,the entire world is divided into precisified worlds, just as it is dividedinto temporal slices and (arguably) alethicpossible worlds. Supervaluationism proves tobe neutral with respect to the debate betweenthe worldly view (...) and the referential view ofindeterminacy. (shrink)

In this paper, a new account of empirical claims in structuralism is developed. Its novelty derives from the use that is made of the linguistic approach to scientific theories despite the presumed incompatibility of structuralism with that approach. It is shown how the linguistic approach can be applied to the framework of structuralism if the semantic foundations of that approach are refined to do justice to the doctrine of indirect interpretation of theoretical terms. This doctrine goes back to Carnap but (...) has been advanced until the present day without a proper semantic explanation. (shrink)

Thomason (1979/2010)’s argument against competence psychologism in semantics envisages a representation of a subject’s competence as follows: he understands his own language in the sense that he can identify the semantic content of each of its sentences, which requires that the relation between expression and content be recursive. Then if the scientist constructs a theory that is meant to represent the body of the subject’s beliefs, construed as assent to the content of the pertinent sentences, and that theory satisfies certain (...) ‘natural assumptions’, then it implies that the subject is inconsistent if the beliefs include arithmetic. I challenge the result by insisting that the motivation for Thomason’s principle (ii), via Moore’s Paradox, leads to a more complex representation, in which stating the facts and expressing one’s beliefs are treated differently. Certain logical connections among expressions of assent, and between expression and statement, are a matter of consequence on pain of pragmatic incoherence, not consequence on pain of classical logical inconsistency. But while this salvages the possibility that a modification of the above sort of representation could be adequate, Thomason’s devastating conclusion returns if the scientist identifies himself as the subject of that representation, even when paying heed to the requirement of pragmatic coherence of the sort highlighted by Moore’s Paradox. (shrink)

This paper presents a novel semantic analysis of unit names and gradable adjectives, inspired by measurement theory (Krantz et al 1971). Based on measurement theory's typology of measures, I claim that different predicates are associated with different types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the puzzling limited distribution of measure phrases.