Consider the Unshareability View, namely, the view that first person thought or self-thought—thought as typically expressed via the first person pronoun—is not shareable from subject to subject. In this article, I show that a significant number of Fregean and non-Fregean commentators of Frege have taken the Unshareability View to be the default Fregean position, rehearse Frege’s chief claims about self-thought and suggest that their combination entails the Unshareability View only on the assumption that there is a one-to-one correspondence between way (...) of thinking and thought-individuating cognitive value, outline an account of self-thought that rejects the assumption and keeps intact all of Frege’s chief claims, and respond to a number of worries to the effect that this proposal yields undesirable results from the point of view of the individuation of self-thought at the level of cognitive value. (shrink)

The paper offers an account of inference. The account underwrites the idea that inference requires that the reasoner takes her premises to support her conclusion. I reject views according to which such ‘takings’ are intuitions or beliefs. I sketch an alternative view on which inferring consists in attaching what I call ‘inferential force’ to a structured collection of contents.

Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such asreductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th (...) century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titledSpecimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule ofreductio ad absurdumin a purely categorical calculus in which every proposition is of the formA is B. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule ofreductio ad absurdum, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic known as RMI$_{{}_ \to ^\neg }$. (shrink)

Many normative nonnaturalists find normative naturalism to be completely implausible. Naturalists and nonnaturalists agree, provided they are realists, that there are normative properties, such as moral ones. Naturalists hold that these properties are similar in all metaphysically important respects to properties that all would agree to be natural ones, such as such as meteorological or economic ones. It is this view that the nonnaturalists I have in mind find to be hopeless. They hold that normative properties are just too different (...) from natural properties for it to be possible they are natural properties. I aim to defuse this intuition. “Non-analytic naturalism” has made progress in defusing the intution. According to non-analytic naturalists, normative properties can be represented in thought in two ways, by an ordinary normative concept and by a naturalistic concept, where, the non-analytic naturalist concedes, normative concepts are not, and are not analyzable in terms of, naturalistic concepts. Non-analytic naturalism seems to avoid many of the standard objections to naturalism, but the Just Too Different intuition is resilient in the face of non-analytic naturalism, for even if one thinks that normative concepts are not analyzable at all, one might think that clarity about the concepts can show that naturalism is hopeless. I therefore think it is important for naturalists to address the intuition directly. In this paper, I argue that the intuition plausibly rests on certain characteristic pre-theoretical ways of thinking of the normative properties that we acquire in the ordinary course of moral learning, together with a drive to vindicate these ways of thinking, something of which people may be unaware. This drive to vindicate our ways of thinking is pervasive, and it is characteristic of rational agents. It explains our tendency to think well of those we love, for example, and to think ill of those with whom we are angry. It also explains a strong inclination to form beliefs that, if true, would seemingly vindicate our ways of thinking of normative properties. A result of this, I contend, is the intuition that normative naturalism cannot be true. Yet, as I further argue, the vindication process does not track the truth and the drive to vindicate our states of mind cannot be relied on as a guide to the metaphysics of normativity. (shrink)

The two different layers of logical theory—epistemological and ontological—are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions serve to establish the holding of consequence from antecedent propositions to succedent proposition.

In the past century the received view of definition in mathematics has been the stipulative conception, according to which a definition merely stipulates the meaning of a term in other terms which are supposed to be already well known. The stipulative conception has been so absolutely dominant and accepted as unproblematic that the nature of definition has not been much discussed, yet it is inadequate. This paper examines its shortcomings and proposes an alternative, the heuristic conception.

The deviation of mathematical proof—proof in mathematical practice—from the ideal of formal proof—proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as a (...) necessary prerequisite to first possess a clear picture of what the deviation of mathematical proof from formal proof consists in. The present work aims to contribute building such a picture by investigating the relation between the elementary steps of deduction constituting the two types of proofs—mathematical inference and logical inference. Many claims have been made in the literature regarding the relation between mathematical inference and logical inference, most of them stating that the former is lacking properties that are constitutive of the latter. Such differentiating claims are, however, usually put forward without a clear conception of the properties occurring in them, and are generally considered to be immediately justified by our direct acquaintance, or phenomenological experience, with the two types of inferences. The present study purports to advance our understanding of the relation between mathematical inference and logical inference by developing a detailed philosophical analysis of the differentiating claims, that is, an analysis of the meaning of the differentiating claims—through the properties that occur in them—as well as the reasons that support them. To this end, we provide at the outset a representative list of the different properties of logical inference that have occurred in the differentiating claims, and we notice that they all boil down to the three properties of formality, generality, and mechanicality. For each one of these properties, our analysis proceeds in two steps: we first provide precise conceptual characterizations of the different ways logical inference has been said to be formal, general, and mechanical, in the philosophical and logical literature on formal proof; we then examine why mathematical inference does not appear to be formal, general, and mechanical, for the different variations of these notions identified. Our study results in a precise conceptual apparatus for expressing and discussing the properties differentiating mathematical inference from logical inference, and provides a first inventory of the various reasons supporting the observations of those differences. The differentiating claims constitute thus a set of data that any philosophical account of mathematical inference and proof purporting to be more faithful to mathematical practice ought to be able to accommodate and explain. (shrink)

This paper explores the nature of the concept of truth. It does not offer an analysis or definition of truth, or an account of how it relates to other concepts. Instead, it explores what sort of concept truth is by considering what sorts of thoughts it enables us to think. My conclusion is that truth is a part of each and every propositional thought. The concept of truth is therefore best thought of as the ability to token propositional thoughts. I (...) explore what implications this view has for existing accounts of concepts, and argue that truth is a concept unlike any other. (shrink)

This paper motivates and explores an expressivist theory of vagueness, modelled on Allan Gibbard’s normative expressivism. It shows how Chris Kennedy’s semantics for gradable adjectives can be adjusted to fit into a theory on Gibbardian lines, where assertions constrain not just possible worlds but plans for action. Vagueness, on this account, is literally indecision about where to draw lines. It is argued that the distinctive phenomena of vagueness, such as the intuition of tolerance, can be explained in terms of practical (...) constraints on plans, and that the expressivist view captures what is right about several contending theories of vagueness. (shrink)

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...) We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis. (shrink)

Quine’s philosophy comprises a bewildering set of views whose integrating principle is his “confirmed extensionalism”. The paper offers a historical as well as an intellectual reconstruction of extensionalism. Traditional extensionalism (Boole) freed logic from Aristotelian essentialism that had inhibited the development of logic. Quine’s confirmed extensionalism is the acceptance, as a matter of course, of the validity of Frege’s criticism of [Boole’s] extensionalism. His confirmed extensionalism is a generalized version of the philosophy of science known as conventionalism. As such, it (...) places the advancement of science outside the province of science proper. It is, thus, at odds with Quine’s repeated expressions of alliance with the Popperian (hypothetico-deductive) model of science. (shrink)

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)

Although at present analytic philosophy is practiced mainly in the English-speaking world, it is to a considerable part the invention of German speakers. Its emergence owes much to Russell, Moore, and American Pragmatism, but even more to Frege, Wittgenstein, and the logical positivists of the Vienna Circle. No one would think of analytic philosophy as a specifically Anglophone phenomenon, if the Nazis had not driven many of its pioneers out of central Europe.

open journal of Philosophical Investigations (PI) is an international journal dedicated to the latest advancements in philosophy. The goal of this journal is to provide a platform for academicians all over the world to promote, share, and discuss various new issues and developments in different areas of philosophy. -/- All manuscripts to be prepared in English or Persian and are subject to a rigorous and fair peer-review process. Generally, accepted papers will appear online. The journal publishes papers including the following (...) fields: -/- · Analytic Philosophy · Ancient Greek and Roman Philosophy · Art Aesthetics · Comparative Philosophy West and Chinese · Eastern Philosophy . Islamic philosophy · Epistemology · Ethics · Hermeneutics · History of Religious Thought · History of Western Philosophy · Language Logic . (shrink)

Adrian Moore develops a helpful distinction between good and bad metaphysics. Employing this distinction, I argue, first, that some contemporary metaphysical theories might be ‘bad’, insofar as they employ, unreflectively, concepts akin to Kant’s Ideas of reason. Second, I investigate the difficulty Kant himself has with explaining our craving for bad metaphysics. Third, I raise some problems for Kant’s doctrine of ‘transcendental cognition’, which rests on the difficult assumption that Ideas have objective reality. I conclude that, while Kant has given (...) us means to combat certain bad metaphysics, his own philosophy is not entirely free of it either. (shrink)

Over the past fifty years the philosophy of language and mind has been dominated by a nondescriptivist approach to content and reference. This book attempts to recast and systematize that approach by offering an indexical model in terms of mental files. According to Recanati, we refer through mental files, the function of which is to store information derived through certain types of contextual relation the subject bears to objects in his or her environment. The reference of a file is determined (...) relationally, not satisfactionally, so a file is not to be equated to the body of (mis-)information it contains. Mental files are the mental equivalent of singular terms, and the reference of linguistic expressions is inherited from that of the files we associate with them. On this approach, mental files, the vehicles of singular thought, do all the work of so-called 'modes of presentation' in Fregean and neo-Russellian theories. (shrink)

The purpose of this paper is to reconstruct Frege’s argument against the relativity of truth contained in his posthumous writing Logic from 1897. Two points are made. The first is that the argument is a performative version of the common objection that truth relativism is incoherent: it is designed to show that the assertion of the relativity of truth involves a performative incoherence, because the absoluteness of truth is a success condition for making assertions. From a modern point of view, (...) the central premise of the argument, that the successful making of assertions depends on the absoluteness of truth, is highly doubtful. The second point is that this premise can be made plausible within the framework of Frege’s conception of truth and assertion: it can be derived from his thesis that, in order to put something forward as true, we do not need the word ‘true’, but only the assertoric force. (shrink)

The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.

I argue that a theory of distributive justice is sensitive to desert if and only if it does not require an institutional scheme that prevents individuals from treating one another as they deserve, and requires a desert ethos. A desert ethos is a set of principles that, though not embodied in a society’s basic coercive structure, nevertheless governs interpersonal relations between citizens. These two necessary conditions are jointly sufficient for ‘giving desert its due’ in a theory of justice. I therefore (...) reject the received view that a desert-sensitive theory must endeavor to guarantee distributions patterned according to desert. (shrink)

Frege's philosophical writings, including the “logistic project,” acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing their (...) own intelligibility. This article is based on more technical analyses of Frege which Claude Imbert has previously offered in other writings. (shrink)

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

This two-part paper reviews a scholarly debate on an alleged tension in Frege ’s philosophy of logic. In Section 1 of Part I, I discuss Frege ’s view that logic is concerned with establishing norms for correct thinking and is therefore a normative science. In Section 2, I explore a different understanding of the role of logic that Frege seems to advance: logic is constitutive of the very possibility of thought, because it sets forth necessary conditions for thought. Hence, the (...) tension the view according to which logic is normative for thought seems to be incompatible with the idea that abiding by the laws of logic forms a precondition for thought. In Section 1 of Part II, I survey a number of interpretations of Frege ’s conception of logic that deal with this question. I show that they are for the most part either normative readings or constitutive readings. Finally, in Section 2, I adjudicate the debate and aim at reconciling the normative and the constitutive strands in Frege ’s conception of logic. (shrink)

This two-part paper reviews a scholarly debate on an alleged tension in Frege's philosophy of logic. In Section 1 of Part I, I discuss Frege's view that logic is concerned with establishing norms for correct thinking and is therefore a normative science. In Section 2, I explore a different understanding of the role of logic that Frege seems to advance: logic is constitutive of the very possibility of thought, because it sets forth necessary conditions for thought. Hence, the tension the (...) view according to which logic is normative for thought seems to be incompatible with the idea that abiding by the laws of logic forms a precondition for thought. In Section 1 of Part II, I survey a number of interpretations of Frege's conception of logic that deal with this question. I show that they are for the most part either normative readings (emphasising the former understanding of the nature of logic) or constitutive readings (emphasising the latter). Finally, in Section 2, I adjudicate the debate and aim at reconciling the normative and the constitutive strands in Frege's conception of logic. (shrink)

I argue that the concept of direction of fit is best seen as picking out a certain inferential property of a psychological attitude. The property in question is one that believing shares with assuming and fantasizing and fails to share with desire. Unfortunately, the standard analysis of DOF obscures this fact because it conflates two very different properties of an attitude: that in virtue of which it displays a certain DOF, and that in virtue of which it displays certain revision (...) conditions. I claim that the latter corresponds with the aim of an attitude, not its DOF. In order to remedy this failure of the standard analysis, I offer an alternative account of DOF, which I refer to as the two-content analysis. (shrink)

In (1959), Carnap famously attacked Heidegger for having constructed an insane metaphysics based on a misconception of both the logical form and the semantics of ordinary language. In what follows, it will be argued that, once one appropriately (i.e., in a Russellian fashion) reads Heidegger’s famous sentence that should paradigmatically exemplify such a misconception, i.e., “the nothing nothings”, there is nothing either logically or semantically wrong with it. The real controversy as to how that sentence has to be evaluated—not as (...) to its meaning but as to its truth—lies at the metaphysico- ontological level. For in order for the sentence to be true one has to endorse an ontology of impossibilia and Leibniz’s principle of the identity of indiscernibles. (shrink)

While it is highly controversial whether Frege's criterion of sameness and difference for sense is true, it is relatively uncontroversial that that principle is inconsistent with Millian–Russellian views of content. I argue that this should not be uncontroversial. The reason is that it is surprisingly difficult to come up with an interpretation of Frege's criterion which implies anything substantial about the sameness or difference of content of anything.

In the first part ("Determination"), I consider different notions of determination, contrast and compare modal with non-modal accounts and then defend two a-modality theses concerning essence and supervenience. I argue, first, that essence is a a-modal notion, i.e. not usefully analysed in terms of metaphysical modality, and then, contra Kit Fine, that essential properties can be exemplified contingently. I argue, second, that supervenience is also an a-modal notion, and that it should be analysed in terms of constitution relations between properties. (...) In the second part ("A Theory of Truthmaking"), I first review the literature on ontological commitment, and argue that the notion of truthmaking is better suited to play its explanatory rôle. I then argue that we should take truthmaker theory seriously, and that we should provide actual truthmakers for all truths there are. In the last chapter of this part, I review Armstrong's truthmaker theories and argue that they are unsatisfactory. I generalise my criticism to an argument against truthmaker necessitarianism, the view that truthmakers necessarily make true the truths they are truthmakers of. In the third part ("Properties and their Kind(s)"), I discuss qualitative determination. I present and endorse the truthmaker argument for universals, and defend universalism against friends of tropes, states of affairs and facts. I then give a novel characterisation of the important class of intrinsic properties, building on Lewis' work. With a workable notion of intrinsicness at hand, I argue that relations are ontologically – but not "ideologically" – dispensable: qualitative determination in general is a matter of intrinsic structure. In the future, I plan to add two parts and to publish my thesis as a book: In the fourth part ("Exemplification"), I argue for the existence of an exemplification relation tying universals and particulars together. I derive theoretical benefits from this relation by providing adverbialist theories of modality and tense and identify exemplification with a type of parthood. In the fifth part ("Qua qua qua"), I investigate the curious and interesting ontological category of so-called "qua-objects" (Picasso-as-a-painter, for example) and argue that they exist, are not identical with transworld indidivuals or modal parts and that they provide (contingent) truthmakers for all true predications. (shrink)

Hans Herzberger as a philosopher and logician has shown deep interest both in the philosophy of Gottlob Frege, and in the topic of the inexpressible and the ineffable. In the fall of 1982, he taught at the University of Toronto, together with André Gombay, a course on Frege's metaphysics, philosophy of language, and foundations of arithmetic. Again, in the fall of 1986, he taught a seminar on the philosophy of language that dealt with 'the limits of discursive symbolism in several (...) domains of human experience.' The course description continues by saying: 'Special attention will be given to the paradoxes underlying various doctrines of the inexpressible and the tensions inherent in those paradoxes. Some doctrines of .. (shrink)

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two (...) senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory. (shrink)

Philosophers of the modern period are often presented as having made an elementary error: that of confounding the attitude one adopts toward a proposition with its content. By examining the works of Locke and the Port-Royalians, I show that this accusation is ill-founded and that Locke, in particular, has the resources to construct a theory of propositional attitudes.

In the late nineteenth century there were two very active lines of research in the field of formal logic. First, logicians (mostly in English-speaking countries) were engaged in formulating a generally traditional logic as an algebra, a part of mathematics; second, logicians (mostly on the continent) were busy building a non-traditional logic that could serve, not as a part of, but as the foundation of, mathematics. By the end of the First World War the former line had been pretty well (...) abandoned while the second continued to expand. However, that old abandoned line, stretching from Aristotle, through the Scholastics and then Leibniz to the nineteenth century algebraists, had not been completely forgotten. One of those logicians who has recently worked on the restoration (and, importantly, the extension) of that line is Fred Sommers. His Term Logic preserves a number of traditional insights (especially involving the theory of logical syntax), while also enjoying a power to account for formal inference at least comparable to that of the standard logic now in place. (shrink)

Are Fregean thoughts compositionally complex and composed of senses? We argue that, in Begriffsschrift, Frege took 'conceptual contents' to be unstructured, but that he quickly moved away from this position, holding just two years later that conceptual contents divide of themselves into 'function' and 'argument'. This second position is shown to be unstable, however, by Frege's famous substitution puzzle. For Frege, the crucial question the puzzle raises is why "The Morning Star is a planet" and "The Evening Star is a (...) planet" have different contents, but his second position predicts that they should have the same content. Frege's response to this antinomy is of course to distinguish sense from reference, but what has not previously been noticed is that this response also requires thoughts to be compositionally complex, composed of senses. That, however, raises the question just how thoughts are composed from senses. We reconstruct a Fregean answer, one that turns on an insistence that this question must be understood as semantic rather than metaphysical. It is not a question about the intrinsic nature of residents of the third realm but a question about how thoughts are expressed by sentences. (shrink)

John MacFarlane explores how we might make sense of the idea that truth is relative. He provides new, satisfying accounts of parts of our thought and talk that have resisted traditional methods of analysis, including what we mean when we talk about what is tasty, what we know, what will happen, what might be the case, and what we ought to do.

L'extraordinaire progrès quantitatif de la science contemporaine masque souvent sa dimension qualitative. En mathématiques, la compréhension actuelle des phénomènes théoriques fondamentaux va bien au-delà de celle des périodes antérieures, fussent-elles récentes. Cette évolution s'accompagne par ailleurs d'une prise de distance à l'égard du structuralisme classique et du réductionnisme logique et, corrélativement, d'une attitude plus œverte, plus attentive à sa richesse et sa complexité, lorsqu'il s'agit de penser la nature du travail mathématique. Ces changements attendent pourtant toujours largement d'être théorisés philosophiquement. (...) Ce sera le propos de cet article que de les envisager au filtre de thèmes bachelardiens. (shrink)

Pragmatist reinterpretations of both deliberative‐communicative theory and legal positivism point out the mentalist fallacy entailed by these prevalent models. I argue that pragmatist approaches imply analogous erroneous beliefs since they presuppose as given the shared perception of social contexts. Therefore they take for granted the shared interpretation of social problems and shared selection of common goals. Hence I advance the necessity of inquiring into the possibility conditions for a shared perception of social contexts. This would entail the organization of institutional (...) incentives meant to extend the scope and inclusiveness of the immediate perception of social context expressed by different agents. (shrink)

Grice coined the term ‘conventional implicature’ in a short passage in ‘Logic and conversation’. The description is intuitive and deeply intriguing. The range of phenomena that have since been assigned this label is large and diverse. I survey the central factual motivation, arguing that it is loosely uni- fied by the idea that conventional implicatures contribute a separate dimen- sion of meaning. I provide tests for distinguishing conventional implicatures from other kinds of meaning, and I briefly explore ways in which (...) one can incorporate multiple dimensions of meaning into a single theory. (shrink)

This article is about the understanding of the definition of the number concept and its content in the context of arithmeticisation of analysis and discussions on the basis of mathematics in the nineteenth century. The issue will be addressed historically first and then the proposals for solutions by mathematicians such as Dedekind, Cantor, Peano, as well as by Frege, a logician, will be examined. The discussions on the foundations of arithmetic in the 1870s gained intensity. For mathematics to be a (...) consistent and reliable science free from contradictions, the concept of number, the cornerstone of arithmetic, had to be precisely defined. In this article, the answer to the question of what the concept of number is and what its meaning is will be discussed. (shrink)

This dialogue on thought and language is a sequel to my dialogue ‘Thought and Thinking’, but can be read independently of it. The five disputants are the same as in the previous dialogue, namely Socrates; an imaginary neuroscientist from California ; an Oxford don from the 1950s ; a Scottish post-doctoral student; and John Locke. The discussion takes place in Elysium in the early evening after dinner. They discuss the relationship between what one thinks and what one says, examine the (...) reasons for supposing that there must be a language of thought and show why there cannot be one, investigate the supposition that thought must have a medium – that one must think in something – and demonstrate that it cannot have one. They investigate whether there can be non-linguistic thinking and whether non language-using animals can be said to think, and determine the limits of thought and thinking. (shrink)

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)

The paradox that appears under Burali-Forti’s name in many textbooks of set theory is a clever piece of reasoning leading to an unproblematic theorem. The theorem asserts that the ordinals do not form a set. For such a set would be—absurdly—an ordinal greater than any ordinal in the set of all ordinals. In this article, we argue that the paradox of Burali-Forti is first and foremost a problem about concept formation by abstraction, not about sets. We contend, furthermore, that some (...) hundred years after its discovery the paradox is still without any fully satisfactory resolution. A survey of the current literature reveals one key assumption of the paradox that has gone unquestioned, namely the assumption that ordinals are objects. Taking the lead from Russell’s no class theory, we interpret talk of ordinals as an efficient way of conveying higher-order logical truths. The resulting theory of ordinals is formally adequate to standard intuitions about ordinals, expresses a conception of ordinal number capable of resolving Burali-Forti’s paradox, and offers a novel contribution to the longstanding program of reducing mathematics to higher-order logic. (shrink)

Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...) theoretically satisfying treatment of their favoured epistemic source. It is argued, first, that intuitions and perceptual experiences are at a certain level of abstraction the same type of mental state, presentations, which are distinct from beliefs, hunches, inclinations, attractions, and seemings. The notion of a presentation is given a positive explication, which identifies its characteristic features, accounts for several of its substantive psychological roles, and systematically locates it in a threefold division among types of contentful states. Subsequently, it is argued that presentations, intuitive no less than sensory, are by their nature poised to play a distinctive epistemic role. Specifically, in the case of intuition, we encounter an intellectual state that is so structured as to provide justification without requiring justification in turn—something which may, thus, be thought of as ‘given’. (shrink)

The ArgumentStarting from the thesis that a science constructs the knowledge of the part of the world allotted to it, the present paper aims at bringing together all the various aspects of physics under a unified conceptual framework — that provided by the Marxian concept “mode of production.” After an introduction providing the initial plausibility grounds for the undertaking, the concept is analyzed into its conceptual elements in Part I of the paper. The analysis presents the reconstruction initiated by Louis (...) Althusser and developed by his followers. Part II starts from a characterization of physical problems. This offers a basis for “reading” physics in the terms introduced in Part I. The rest of Part II is devoted to the identification of all the aspects of physics with the conceptual elements in question. The paper aims at three things: to uncover the connections holding among seemingly disparate aspects of physics, usually discussed in almost total independence from each other; to take full account of the social dimensions of physics without vindicating social constructivism; to show that the boundaries separating the disciplines of philosophy, history and sociology of science are more arbitrary than usually considered. (shrink)

The Frege-Russell view is that existence is a second-order property rather than a property of individuals. One of the most compelling arguments for this view is based on the premise that there is an especially close connection between existence and number. The most promising version of this argument is by C.J.F Williams (1981, 1992). In what follows, I argue that this argument fails. I then defend an account according to which both predications of number and existence attribute properties to individuals.

One of the most striking features of twentieth-century philosophy has been its obsession with language. For the most part, this phenomenon is greeted with hostile incredulity by external observers. Surely, they say, if philosophy is the profound and fundamental discipline which it has purported to be for more than two millennia, it must deal with something more serious than mere words, namely the things they stand for, and ultimately the essence of reality or of the human mind.

Is linguistic understanding a form of knowledge? I clarify the question and then consider two natural forms a positive answer might take. I argue that, although some recent arguments fail to decide the issue, neither positive answer should be accepted. The aim is not yet to foreclose on the view that linguistic understanding is a form of knowledge, but to develop desiderata on a satisfactory successor to the two natural views rejected here.

A model-theoretic approach to the semantics of set-theoretic discourse.