I critically discuss Dale Jacquette’s Frege: A Philosophical Biography. First, I provide a short overview of Jacquette’s book. Second, I evaluate Jacquette’s interpretation of Frege’s three major works, Begriffsschrift, Grundlagen der Arithmetik and Grundgesetze der Arithmetik; and conclude that the author does not faithfully represent their content. Finally, I offer some technical and general remarks.

The paper gives a historically informed reconstruction of Frege's view of statements of number. The reconstruction supports Frege's claim that a statement can be 'about a concept' although it does not contain a singular term referring to the concept. Hence, Frege's philosophy of number is not subject to the problems Frege sees for singular reference to concepts.

The subject of mental processes or mental states is usually assumed to be an individual, and hence the boundaries of mental features – in a strict or metaphorical sense – are naturally regarded as reaching no further than the boundaries of the individual. This chapter addresses various philosophical developments in the 20th and 21st century that questioned this natural assumption. I will frame this discussion by fi rst presenting a historically infl uential commitment to the individualistic nature of the mental (...) in Descartes’ theory. I identify various elements in the Cartesian conception of the mind that were subsequently criticized and rejected by various externalist theories, advocates of the extended mind hypothesis and defenders of embodied cognition. Then I will indicate the main trends in these critiques. (shrink)

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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This paper addresses an issue with the sign ‘⊢’ in Frege’s mature version of Begriffsschrift, i.e., the version in ‘Function and Concept’ and Grundgesetze. The sign is a performative for asserting in that writing down ‘⊢p’ is equivalent to asserting that p. Frege further says that writing ‘ p’ is also equivalent to identifying the reference of ‘p’ with the truth-value True. It looks as if he holds that asserting that p consists in identifying the True with the reference of (...) ‘p’. Frege’s commitment to it, however, seems to encounter a number of tensions. This paper aims to show that these tensions can be avoided by endorsing a non-assertive conception of identification under which making an identification is not making an identity assertion. The suggested reading leads to an entirely di erent understanding of the compositionality of the sign ‘⊢’ as well as Frege’s conception of assertion and judgment. (shrink)

The way Frege presented the Square of Opposition in a reduced form in 1879 and 1910 can be used to develop two distinct versions of the square: The traditional square that displays inferences and a “Table of Oppositions” displaying variations of negation. This Table of Oppositions can be further simplified and thus be made more symmetrical. A brief survey of versions of the square from Aristotle to the present shows how both aspects of the square have coexisted for a very (...) long time without ever being properly distinguished. (shrink)

In this dissertation, I seek to explain G.W.F. Hegel’s view that human accessible conceptual content can provide knowledge about the nature or essence of things. I call this view “Conceptual Transparency.” It finds its historical antecedent in the views of eighteenth century German rationalists, which were strongly criticized by Immanuel Kant. I argue that Hegel explains Conceptual Transparency in such a way that preserves many implications of German rationalism, but in a form that is largely compatible with Kant’s criticisms of (...) the original rationalist version. After providing background on Hegel’s relationship to the traditional rationalist theory of concepts and Kant’s challenge to it, I claim that Hegel’s central task is to provide a theory of conceptual content that allows a relationship to the objective world without being dependent on the specifically sensory aspect of the world, which Kant’s theory of concepts required. Since many interpreters deny that Hegel’s use of the term “concept” is comparable to other historical philosophers (or our own), I first show that Hegel’s critique of standard conceptions of concepts presupposes an agreement of subject matter. I then show how Hegel’s account of the “formal concept” provides the skeleton for a view of conceptual content that relies on negative relations between terms, rather than a relation to sensibility, to provide content. Hegel’s account of conceptual content is completed when he shows how a universal term is further specified so that it can determine singular objects. This occurs in its adequate form in a teleological process. I argue that Hegel’s account of teleology in the Science of Logic is an attempt to explain how and where Conceptual Transparency obtains. A teleological process is one in which a concept constitutes an object, and this means that a concept is perfectly adequate to express that thing’s nature and not merely to represent it. However, in the final chapter, I show that Hegel’s concept of teleology is meant paradigmatically to illuminate how human purposive processes have constituted a social world that is conceptually accessible to us. In this way, the primary “province” of Hegel’s rationalism is the human constructed world. (shrink)

This essay is an attempt to explain Kantian transcendental idealism to contemporary metaphysicians and make clear its relevance to contemporary debates in what is now called ‘meta-metaphysics.’ It is not primarily an exegetical essay, but an attempt to translate some Kantian ideas into a contemporary idiom.

In the section “Validity and Existence in Logik, Book III,” I explain Lotze’s famous distinction between existence and validity in Book III of Logik. In the following section, “Lotze’s Platonism,” I put this famous distinction in the context of Lotze’s attempt to distinguish his own position from hypostatic Platonism and consider one way of drawing the distinction: the hypostatic Platonist accepts that there are propositions, whereas Lotze rejects this. In the section “Two Perspectives on Frege’s Platonism,” I argue that this (...) is an unsatisfactory way of reading Lotze’s Platonism and that the Ricketts-Reck reading of Frege is in fact the correct way of thinking about Lotze’s Platonism. (shrink)

In certain philosophical quarters, a new metaphilosophical position is being discussed—antiphilosophy. Such a position seems to maintain that there is no distinction between philosophy and sophistry, reason and rhetoric, arguing and emoting. This paper examines antiphilosophy. Specifically, it aims to address three interrelated questions: Is antiphilosophy a possible metaphilosophical position? If it is, what characterizes it? And what ramifications would it have? The paper argues that antiphilosophy is possible and is best construed as an attempt to reconstruct philosophical discourse on (...) noncognitive lines. Explicitly, “to assert” and the belief propositional attitude is replaced by “to convince” and a pro‐attitude desire to rhetorically talk someone into something. The paper examines one possible form such a position could take as well as various ramifications of it. (shrink)

SUMMARY Major theories of philosophical psychology and philosophy of mind are examined on the basis of the fundamental questions of ontology, metaphysics, epistemology, semantics and logic. The result is the choice between language of eliminative reductionism and dualism, neither of which answers properly the relation between mind and body. In the search for a non–dualistic and non–reductive language, Wittgenstein’s notion of language–games as the representative links between language and the world is considered together with Peirce’s semeiosis of cognition. The result (...) is a redefined notion of cognition as the goal–oriented ability to instantiate strategies from the rules of the language–games. Cognition is considered within the four-dimensional languagegames: rules/strategies, primitive/complete language-games, family-resemblances/forms of life, and non-temporal continuum as the language-games’ modality. Cognition is seen as a continuum process of non–individualized elements that unites perception, volition, emotion, will and thought against the commonly accepted understandings of cognition in exclusive terms of perception and thinking. The alternative to the mind/body problem is the continuity of cognition where rules and strategies, syntax and semantics, are considered inseparable within language–games. This continuity of cognition is explained in terms of virtual (univocal) identity, replacing the old philosophical paradigm of the mind/body problem. -/- SOMMARIO Le teorie maggiori della psicologia filosofica e filosofia della mente sono esaminate a partire dalle questioni fondamentali di ontologia, metafisica, epistemologia, semantica e logica. Il risultato è la scelta tra un linguaggio riduzionista eliminativo e un dualismo che però non confronta in modo adeguato la relazione tra mente e corpo. Nella ricerca per un linguaggio non-dualistico e non-riduttivo, viene considerata la nozione del gioco linguistico di Wittgenstein come un legame rappresentativo tra il linguaggio e il mondo insieme con la semiosi cognitiva di Peirce. Il risultato è la nozione ridefinita della cognizione come abilità goal-orientata di creare le strategie dalle regole dei giochi linguistici. La cognizione è considerata entro le quattro dimensioni dei giochi linguistici: regole/strategie, giochi linguistici primitivi/completi, somiglianze di famiglia/forme di vita, e la continuità atemporale come la modalità dei giochi linguistici. La cognizione diventa un processo continuo degli elementi non-individualizzati che tende ad unificare la percezione, volizione, emozione, la volontà e il pensiero contro un concetto generalmente accettato di vedere la cognizione nei termini esclusivamente di percezione e di pensiero. L’alternativa al problema della mente/corpo è la continuità della cognizione, dove le regole e le strategie, la sintassi e la semantica, sono considerate inseparabili nei giochi linguistici. Questa continuità della cognizione è spiegata nei termini dell’identità virtuale (univoca) sostituendo un paradigma filosofico previo del problema della mente/corpo. (shrink)

It is commonly thought that logic, whatever it may be, is normative. While accounting for the normativity of logic is a challenge for any view of logic, in this paper I argue that it is particularly problematic for certain types of logical pluralists, due to what I call the normative problem for logical pluralism. I introduce the NPLP, distinguish it from other problems that logical pluralists may face, and show that it is unsolvable for one prominent type of logical pluralism.

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

The theory of object-dependent singular thought is outlined and the central motivation for it, turning on the connection between thought content and truth conditions, is discussed. Some of its consequences for the epistemology of thought are noted and connections are drawn to the general doctrine of externalism about thought content. Some of the main criticisms of the object-dependent view of singular thought are outlined. Rival conceptions of singular thought are also sketched and their problems noted.

Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion of logically equivalent (...) formulas, and presenting the notation's close connection to syntax trees. In the second part, Frege's considerations regarding the design principles underlying the Begriffsschrift are presented. Frege was quite explicit about these in his replies to early criticisms and unfavorable comparisons with Boole's notation for propositional logic. This discussion reveals that the Begriffsschrift is in fact a well thought-out and carefully crafted notation that intentionally exploits the possibilities afforded by the two-dimensional medium of writing like none other. (shrink)

In this paper I argue that propositionalism is what generates a tension between referentialism and harmony. Harmony can be preserved if we replace propositionalism by centred referentialism, according to which referential thoughts and utterances about an object have descriptive contents that must be evaluated relative to a world centred on that object at the relevant time. By disentangling truth-conditions and contents, this move allows us to dissolve the tension between referentialism and descriptivism. The view that emerges has three main components: (...) the truth-conditions of a referential utterance or thought involves its referent ; its reference is determined by causal relations of acquaintance in the context of use ; and its cognitive value is fully explained by associated descriptions or truth-conditional contents. (shrink)

Discussion of Frege’s theory of fiction has tended to focus on the problem of empty names, and has consequently missed the truly problematic aspect of the theory, Frege’s commitment to the view that even fictional sentences that contain no empty names fail to refer. That claim prima facie conflicts with his commitment to the cognitive transparency of sense, and the determination of reference by sense. Resolving this tension compels us to recognize that fiction for Frege is a special kind of (...) force, and that words express a sense capable of picking out a referent only in the presence of the appropriate assertoric force. In effect, Frege’s theory of fiction reveals his commitment to an act-centered rather than an expression-centered semantics. (shrink)

This paper uses the resources of higher-order logic to articulate a Fregean conception of predicate reference, and of word-world relations more generally, that is immune to the concept horse problem. The paper then addresses a prominent style of expressibility problem for views of broadly this kind, versions of which are due to Linnebo, Hale, and Wright.

The 'substitution argument' purports to demonstrate the falsity of Russellian accounts of belief-ascription by observing that, e.g., these two sentences: (LC) Lois believes that Clark can fly. (LS) Lois believes that Superman can fly. could have different truth-values. But what is the basis for that claim? It seems widely to be supposed, especially by Russellians, that it is simply an 'intuition', one that could then be 'explained away'. And this supposition plays an especially important role in Jennifer Saul's defense of (...) Russellianism, based upon the existence of an allegedly similar contrast between these two sentences: (PC) Superman is more popular than Clark. (PS) Superman is more popular than Superman. The latter contrast looks pragmatic. But then, Saul asks, why shouldn't we then say the same about the former? The answer to this question is that the two cases simply are not similar. In the case of (PC) and (PS), we have only the facts that these strike us differently, and that people will sometimes say things like (PC), whereas they will never say things like (PS). By contrast, there is an argument to be given that (LS) can be true even if (LC) is false, and this argument does not appeal to anyone's 'intuitions'. The main goal of the paper is to present such a version of the substitution argument, building upon the treatment of the Fregan argument against Russellian accounts of belief itself in "Solving Frege's Puzzle". A subsidiary goal is to contribute to the growing literature arguing that 'intuitions' simply do not play the sort of role in philosophical inquiry that so-called 'experimental philosophers' have supposed they do. (shrink)

The central claim of this thesis is that concepts, the components from which cognitively significant truth evaluable content (thought) is composed, are unstructured entities an account of whose individuation makes no essential reference to other concepts in the possession of the thinking subject or to any particular means by which the reference of the concept is identified by the thinking subject. This position is called Conceptual Atomism and contrasts with Inferential Role Semantics, according to which concepts are individuated by their (...) inferential roles or their conditions of warranted application. The structure of the argument is as follows. Firstly, a principle called the Transparency Principle is developed. This places constraints on the individuation of concepts across differing contexts. The Transparency Principle is then used to show that Inferential Role Semantics is false because it cannot provide a satisfactory account of cognitive dynamics; that is, of the conditions under which a concept is retained through changes in the epistemic state of the subject over a period of time. A version of Conceptual Atomism is then defended and it is shown that this theory yields the correct individuation of concepts. According to this theory the concepts of an individual subject are individuated in terms of referential episodes, episodes of ongoing reference to an object or property during which it is diachronically transparent to the subject that the same thing is being referred to. The more general notion of a referential practice is then used to account for the sharing of concepts by more than one person. Finally, a novel account of the thoughts expressed using indexical terms is defended in order to show that indexicals present no counterexample to Conceptual Atomism. This account of indexical thoughts is of some consequence in its own right. (shrink)

This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach (...) to mathematics and a top-down naturalisation. Articulating my particular understanding of what realism and naturalism should commit us to, I propose a creative fusion of Badiou’s attention to metamathematical results with a structural-informational metaphysics, proposing a ‘matherialism’ uniting the more daring speculative insights of the former with the naturalist and empiricist commitments motivating the latter. (shrink)

Gottfried Gabriel is interviewed by Todor Polimenov about the relationship between analytic and continental philosophy.

The paper discusses the emergence of Frege's puzzle and the introduction of the celebrated distinction between sense and reference in the context of Frege's logicist project. The main aim of the paper is to show that not logicism per se is mainly responsible for this introduction, but Frege's constant struggle against formalism. Thus, the paper enlarges the historical context, and provides a reconstruction of Frege's philosophical development from this broader perspective.

En su obra de 1884, Die Grundlagen der Arithmetik [Gl.], Frege establece el principio del contexto como uno de sus principios fundamentales y propone valerse de él para dar con el concepto adecuado de número. Así, ofrece una definición de tipo contextual de número cardinal, pero ante una objeción que le resulta insalvable se decide por una definición explicita. La cuestión acerca de cuál ha sido entonces el sentido de establecer con tanto énfasis el principio del contexto admite más de (...) una respuesta. Mi texto polemiza con la interpretación canónica que se ha dado al papel de este principio en Gl., acusándola de permanecer encandilada por lo que se lee de manera inmediata en desmedro de una evaluación más integral y crítica. En particular, defenderé que: i) a diferencia de lo afirmado en Dummett 1991, la definición contextual de número cardinal no es abandonada por Frege al dar su definición explícita de número, ii) el principio del contexto tiene en Gl. un papel erístico fundamental de eliminar posiciones rivales acerca de la naturaleza de los números, iii) dicha definición contextual de número tiene un papel heurístico en el contexto de descubrimiento, en el sentido de que ofrece una intuición clave que permite llegar a la formulación final, iv) a su vez, la definición contextual es una condición necesaria de la definición explícita en el contexto de justificación, siendo que esta última se ha construido a partir de la primera. Por todo ello, sostengo que la función del principio del contexto no es la que prioriza Dummett, i. e., la fallida función de resolver el problema ontológico de la naturaleza de los números, sino que es fundamentalmente metodológica. En efecto, es en su función erística y heurística en donde debe ubicarse su relevancia para la investigación llevada a cabo en Gl. In his masterpiece of 1884, Die Grundlagen der Arithmetik [Gl.] Frege presents the context principle as a fundamental one in his investigation à propos an accurate concept of number. Thus, resting on it he offers a contextual definition of cardinal number; but after analyzing some objections he realizes that this definition does not work and decides himself for an explicit one. The question about what is the purport of the context principle when something that appeared to be the consequence is put aside admits more than a single answer. In this paper I argue against the canonic interpretation for, even while keeping next to the Fregean text, it fails to offer an integral explanation of how the context principle works all along Gl. In particular, I will defend that: i) contrary with Dummett 1991, the contextual definition of cardinal number is not abandoned by Frege when giving his explicit definition of number, ii) the context principle has in Gl. a fundamental eristic role of crossing out rival positions about the nature of numbers, iii) such contextual definition of number has an heuristic role in the discovery context, in the sense it offers a key intuition towards the final formulation, iv) furthermore, the contextual definition is a necessary condition in the justification context for the latest has been built up through the first one. For all this, I maintain that the function of the context principle is not the one Dummett prioritizes, i. e., the failed function of solving the ontological problem of the nature of numbers; the function of the context principle is rather and fundamentally methodological. It is on its eristic and heuristic function that its relevance to the Gl. investigation must be looked for. (shrink)

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)

This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.

Here is Frege in Foundations of Arithmetic, § 64:The judgment 'Line a is parallel to line b', in symbols: ab, can be taken as an identity. If we do this, we obtain the concept of direction, and say: 'The direction of line a is equal to the direction of line b.' Thus we replace the symbol by the more generic symbol =, through removing what is specific in the content of the former and dividing it between a and b. We (...) carve up the content in a way different from the original way, and this yields us a new concept.Something important is going on in this passage. But at the same time it borders on incoherent. For Frege is saying at least the following:'dir(a ) = dir(b )' has the same content as 'ab'reflecting on that .. (shrink)

This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...

A first-person proposition is a proposition that only a single subject can assert or believe. When I assert ‘I am on fire’ I assert a first-person proposition that only I have access to, in the sense that no one else can assert or believe this proposition. This is in contrast to third-person propositions, which can be asserted or believed by anyone.

It is commonly thought that the prevalence of moral dissent poses a problem for the moral cognitivist, forcing her to diagnose either a lot of misunderstanding, or a lot of unexplained observational error. Since mere misunderstanding can be ruled out in most cases of moral dissent, and since the diagnosis of widespread unexplained error is interpretively unstable, prevalent dissent has pushed many philosophers towards non-cognitivism. In this essay, I argue that once a diachronic, pragmatist theory of language along the lines (...) of the latest Wittgenstein is employed, a third interpretive option becomes available to the cognitivist. Besides the diagnostic options of misunderstanding and factual disagreement, she can argue that a given case of moral dissent is an instance of grammatical tension. This interpretation not only saves moral cognitivism, it also has some attractive theoretical implications. Among other things, it yields an elegant way of solving the current debate around moral particularism. (shrink)

The paper surveys two contrasting views of first‐order analyses of classical theistic doctrines about the existence and nature of God. On the first view, first‐order logic provides methods for the adequate analysis of these doctrines, for example by construing ‘God’ as a singular term or as a monadic predicate, or by taking it to be a definite description. On the second view, such analyses are conceptually inadequate, at least when the doctrines in question are viewed against the background of classical (...) theism’s doctrine of divine simplicity, for first‐order analyses presuppose an ontological complexity on the part of the propositions which they analyze, which fits ill with this doctrine. (shrink)

It is a commonplace that in the development of modern logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the mo...

In this essay, I critically discuss Dale Jacquette's new English translation of Frege's work Die Grundlagen der Arithmetik as well as his Introduction and Critical Commentary (Frege, G. 2007. The Foundations of Arithmetic. A Logical-Mathematical Investigation into the Concept of Number . Translated with an Introduction and Critical Commentary by Dale Jacquette. New York: Longman. xxxii + 112 pp.). I begin with a short assessment of Frege's book. In sections 2 and 3, I examine several claims that Jacquette makes in (...) his Introduction and Critical Commentary and put matters in the right perspective. In sections 4-7, I analyse errors and shortcomings in Jacquette's (and Austin's) translation(s) and show how they can be avoided. In this context, I consider several issues of interest for Frege's logic and philosophy of arithmetic. I conclude with general remarks. (shrink)

There is a strong consensus among analytic philosophers that Husserl is an internalist and that his internalism must be understood in conjunction with his methodological solipsism. This paper focuses on Husserl's early work the, Logical Investigations , and explores whether such a reading is justified. It shows that Husserl is not a methodological solipsist: He neither believes that meaning can be reduced to the individual, nor does he assign an explanatory role for meaning to the subject. Explanatory priority is assigned (...) to objects which have an intrinsic property independently of any access or attitude we may have to them. Although not a methodological solipsist, there are nonetheless internalist elements to Husserl's thought: He believes that we can think of non-existent objects and his account of indexicals and demonstratives shows that there are two kinds of meaning: one is context independent and internally individuated, the other is partly determined by context and so externally individuated. The paper leaves it open whether this is sufficient to mark Husserl out as an internalist. However, even if he were considered as such, we can be sure of one thing, namely, that his internalism would not be a species of methodological solipsism. (shrink)

In this paper I shall deal with the role of "understanding a thought" in the debate on the definition of the content of an assertion. I shall present a well known tension in Frege's writings, between a cognitive and semantic notion of sense. This tension is at the source of some of the major contemporary discussions, mainly because of the negative influence of Wittgenstein's Tractatus, which did not give in-depth consideration to the tension found in Frege. However many contemporary authors, (...) after the first attempt by Carnap himself, have tried to make room both for a cognitive and semantic aspect of meaning. I claim that at least some of these attempts (Dummett, Perry and Chalmers) are seriously flawed, mainly due to the difficulty in making a proper connection between the two different conceptions of sense. I shall outline an alternative project, which takes into consideration Frege's requirements on antipsychologism and of the objectivity of thought, while maintaining a close connection between the two aspects of sense. (shrink)

One of the most striking differences between Frege's Begriffsschrift (logical system) and standard contemporary systems of logic is the inclusion in the former of the judgement stroke: a symbol which marks those propositions which are being asserted , that is, which are being used to express judgements . There has been considerable controversy regarding both the exact purpose of the judgement stroke, and whether a system of logic should include such a symbol. This paper explains the intended role of the (...) judgement stroke in a way that renders it readily comprehensible why Frege insisted that this symbol was an essential part of his logical system. The key point here is that Frege viewed logic as the study of inference relations amongst acts of judgement , rather than – as in the typical contemporary view – of consequence relations amongst certain objects (propositions or well-formed formulae). The paper also explains why Frege's use of the judgement stroke is not in conflict with his avowed anti-psychologism, and why Wittgenstein's criticism of the judgement stroke as 'logically quite meaningless' is unfounded. The key point here is that while the judgement stroke has no content , its use in logic and mathematics is subject to a very stringent norm of assertion. (shrink)

Now I may not be an educated man . . . But it seems to me to go against common sense to ask what the poet is ‘trying to say’. The poem isn’t a code for something easily understood. The poem is what he is trying to say.

One particular topic in the literature on Frege’s conception of sense relates to two apparently contradictory theses held by Frege: the isomorphism of thought and language on one hand and the expressibility of a thought by different sentences on the other. I will divide the paper into five sections. In (1) I introduce the problem of the tension in Frege’s thought. In (2) I discuss the main attempts to resolve the conflict between Frege’s two contradictory claims, showing what is wrong (...) with some of them. In (3), I analyze where, in Frege’s writings and discussions on sense identity, one can find grounds for two different conceptions of sense. In (4) I show how the two contradictory theses held by Frege are connected with different concerns, compelling Frege to a constant oscillation in terminology. In (5) I summarize two further reasons that prevented Frege from making the distinction between two conceptions of sense clear: (i) the antipsychologism problem and (ii) the overlap of traditions in German literature contemporary to Frege about the concept of value. I conclude with a hint for a reconstruction of the Fregean notion of ‘thought’ which resolves the contradiction between his two theses. (shrink)

According to an old and attractive view, vagueness must be eliminated before semantic notions — truth, implication, and so on — may be applied. This view was accepted by Frege, but is rarely defended nowadays.1 This..

This paper presents and defends a definition of vagueness, compares it favourably with alternative definitions, and draws out some consequences of accepting this definition for the project of offering a substantive theory of vagueness. The definition is roughly this: a predicate 'F' is vague just in case for any objects a and b, if a and b are very close in respects relevant to the possession of F, then 'Fa' and 'Fb' are very close in respect of truth. The definition (...) is extended to cover vagueness of many-place predicates, of properties and relations, and of objects. Some of the most important advantages of the definition are that it captures the intuitions which motivate the thought that vague predicates are tolerant, without leading to contradiction, and that it yields a clear understanding of the relationships between higher-order vagueness, sorites susceptibility, blurred boundaries, and borderline cases. The most notable consequence of the definition is that the correct theory of vagueness must countenance degrees of truth. (shrink)

It's generally agreed that, for a certain a class of cases, a rational subject cannot be wrong in treating two elements of thought as co-referential. Even anti-individualists like Tyler Burge agree that empirical error is impossible in such cases. I argue that this immunity to empirical error is illusory and sketch a new anti-individualist approach to concepts that doesn't require such immunity.

Assume that the only thing before you is a statue made of some alloy. Call those who think that there is one thing before you in such a case monists. Call those who think there are at least two things before you in such a case pluralists. The most common arguments for pluralism run as follows. The statue is claimed to have some property P that the piece of alloy lacks (or vice versa), and hence it is concluded that they (...) are distinct. Most often, the predicates employed in such arguments to express the crucial property are predicates expressing ‘temporal properties’, such as existing at a certain time; or ‘modal properties’, such as possibly being spherical; or ‘constitution properties’, such as being made of a certain sort of material. In a recent paper, Kit Fine has noted that such predicates suffer from various defects that make it possible for the monist to plausibly resist the relevant versions of the pluralist's arguments. For this reason, Fine considers a number of predicates that do not suffer from these defects, and constructs new versions of the above argument using them. Fine argues that any attempt on the monist's part to resist his versions of the argument force the monist to adopt implausible positions in the philosophy of language. As against this, I argue that the monist has perfectly plausible responses to Fine's arguments that require the monist to adopt only quite reasonable positions in the philosophy of language. (shrink)

Provides a certain conception of the target of a theory of intentionality in terms of five properties (aboutness, non-existence, aspectuality, generality, and semantic normativity) and provides a guided tour of how different styles of theories of intentionality can meet up these requirements.

According to a certain conception of language, any sentence can, when used on an occasion, have any of indefinitely many truth-conditions. Such a conception of language gives us reason to think that the question of whether the notion of truth has a distinctive content cannot be settled by looking solely at the predication of truth. By focusing on the predicate ‘true’ when trying to determine the significance of the notion of truth, we may have been looking in the wrong place.

A speculative investigation of how Frege's logical views change between Begriffsschrift and Grundgesetze and how this might have affected the formal development of logicism.

It is almost universally accepted that the Frege–Geach Point is necessary for explaining the inferential relations and compositional structure of truth-functionally complex propositions. I argue that this claim rests on a disputable view of propositional structure, which models truth-functionally complex propositions on atomic propositions. I propose an alternative view of propositional structure, based on a certain notion of simulation, which accounts for the relevant phenomena without accepting the Frege–Geach Point. The main contention is that truth-functionally complex propositions do not include (...) as their parts truth-evaluable propositions, but their simulations, which are neither forceful nor truth-evaluable. The view makes room for the idea that there is no such thing as the forceless expression of propositional contents and is attractive because it provides the resources for avoiding a fundamental problem generated by the Frege–Geach Point concerning the relation between forceless and forceful expressions of propositional contents. I further argue that the acceptance of the Frege–Geach Point mars Peter Hanks’ and François Recanati’s recent attempts to resist the widespread idea that assertoric force is extrinsic to the expression of propositional contents. Rejecting this idea, I maintain, requires a deeper break with the tradition than Hanks and Recanati have allowed for. (shrink)