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.

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)

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.

Frege is celebrated as an arch-Platonist and arch-realist. He is renowned for claiming that truths of arithmetic are eternally true and independent of us, our judgments and our thoughts; that there is a third realm containing nonphysical objects that are not ideas. Until recently, there were few attempts to explicate these renowned claims, for most philosophers thought the clarity of Frege's prose rendered explication unnecessary. But the last ten years have seen the publication of several revisionist interpretations of Frege's writings (...) — interpretations on which these claims receive a very different reading. In Frege on Knowing the Third Realm, Tyler Burge attempts to undermine this trend. Burge argues that Frege is the very Platonist most have thought him — that revisionist interpretations of Frege's Platonism, mine among them, run afoul of the words on Frege's pages. This paper is a response to Burge's criticisms. I argue that my interpretation is more faithful than Burge's to Frege's texts. (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)

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

C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed with (...) many fortunate circumstances, not least of which was entering the field when mathematical logic, after only six decades of toil, had just reaped one of its most important harvests with publication of the monumental Principia Mathematica. It was a time of joyful optimism which demanded an historical account and a sober philosophical critique. Lewis was one of the first to apply to mathematical logic the Aristotelian dictum that we do not understand a living institution until we see it growing from its birth. (shrink)

Friederike Moltmann has recently proposed an account of truth-bearers that draws on Kazimierz Twardowski’s action/product distinction. Her account is meant to provide a third way between the dominant view of primary truth-bearers as mind-independent entities and the recently revived construal of them as mental or linguistic acts. This paper argues that there is no room for Twardowskian accounts because they are based on a notion of “nonenduring product” that defies comprehension, and no need for them because the linguistic data that (...) Twardowskians take to refute the act-theoretic approach can, in fact, be handled by that approach. (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)

In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.

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 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)

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)

This paper is about first‐person thoughts—thoughts about oneself that are expressible through uses of first‐person pronouns. It is widely held that first‐person thoughts cannot be shared. My aim is to postpone rejection of the more natural view that such thoughts about oneself can be shared. I sketch an account on which such thoughts can be shared and indicate some ways in which deciding the fate of the account will depend upon further work.

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)

In Hanks I defend a theory of propositions that locates the source of propositional unity in acts of predication that people perform in thought and speech. On my account, these acts of predication are judgmental or assertoric in character, and they commit the speaker to things being the way they are represented to be in the act of predication. This leads to a problem about negations, disjunctions, conditionals, and other kinds of embeddings. When you assert that a is F or (...) b is G you do not assert that a is F, nor do you commit yourself to a’s being F. According to my theory, however, in uttering the disjunction you predicate F of a. What is going on? I account for these cases using the concept of cancellation. In uttering the disjunction, the act of predicating F of a is cancelled, and when an act of predication is cancelled it does not count as an assertion and does not commit the speaker to anything. But what is it for an act of predication to be cancelled? One immediate concern is that cancelled predication won’t provide a unified proposition to be the input to disjunction. In this paper I answer this and related objections by explaining and defending my concept of cancellation. (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)

Fred Sommers passed away in October of 2014 in his 92nd year. Having begun his teaching at Columbia University, he eventually became the Harry A. Wolfson Chair in Philosophy at Brandeis University, where he taught from 1963 to 1993. During his long and productive career, Sommers authored or co-authored over 50 books, articles, reviews, etc., presenting his ideas on numerous occasions throughout North America and Europe. His work was characterized by a commitment to the preservation and application of historical insights (...) and to the value of a well-articulated, coherent logical system. He was recognized for his independence and refusal to accept any view on the basis of authority alone. This made him a formidable critic but accounted in part for his many innovative and original ideas. In spite of his general contrariness in logic, Sommers earned the respect of the majority of his contemporaries, including Russell, Quine, van Benthem, Hacking, Suppes, and Strawson. In 2005, he was the subjec... (shrink)

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)

Mental files, in Recanati's framework, function as 'singular terms in the language of thought' ; they serve to think about objects in the world (and to store information about them). But they have a derived, metarepresentational function : they serve to represent how other subjects think about objects in the world. To account for the metarepresentational use of files, Recanati introduces the notion of an 'indexed file', i.e. a vicarious file that stands, in the subject's mind, for another subject's file (...) about an object. Using that notion, he argues, one can provide an analysis of attitude ascriptions and the conniving use of empty singular terms. (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 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)

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)

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.

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)

What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of definitions. Specifically, I pursue this issue via an examination of Frege’s views about the scientific unification of logic and arithmetic. In my view, what interpreters have failed to appreciate is that logicism is a project of unification, not reduction. For Frege, unification involves two separate steps: (1) an account of the (...) content expressed by arithmetical claims and (2) the justification of that content. The distinction between these steps allows us to see that there are two notions of definition at play in Frege’s logicist work, viz., one concerned with conceptual analysis, the other concerned with the construction of gap-free proof. I then use this discussion to explain how Frege employs his definitions to defend an epistemological thesis about arithmetic, and to clarify Grundlagen’s fruitfulness condition of definitions, and thereby address two interpretive puzzles from the recent literature. (shrink)

Frege writes in Numbers and Arithmetic about kindergarten-numbers and “an a priori mode of cognition” that they may have “a geometrical source.” This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege’s later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent logicism is compatible with intuitionism.

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.

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)

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)

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)

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)

This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in. It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neo-logicist position on the issues of: what's required for proofs of existence; the connection between models, consistency, and existence; (...) and the prospects for a logical grounding of arithmetic in the wake of the paradox. (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)

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)

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)

We identify two senses of ‘pragmatics’ and related terms that give rise to two different methods of propositional individuation. The first one is the contextualist approach that essentially acknowledges contextual information to take part in the determination of what is said by the utterance of a sentence. In this sense, Pragmatics relies on the Principle of Compositionality and interprets propositions as structured entities. It epitomises the Building-block Model of Propositional Individuation. The general approach that makes what the agents do the (...) grounding level of philosophical and linguistic analysis characterizes the second sense, Pragmatism. It finds its clearest expression in Peirce’s Pragmatist Maxim, and it relies on the Fregean Principle of Context, and supports a view of propositions as unstructured entities. This is the Organic Model of Propositional Individuation. There is a test, the Analytic Equivalence Test, that tells apart the two models. According to it, the answer to the question whether a theory makes room for different but analytically equivalent propositions determines the model the theory belongs in. A positive answer classifies the theory as belonging to the building-block model; a negative answer allocates the theory within the organic model. (shrink)

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 issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.

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.

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.