One ought to be logically consistent. This is sometimes referred to as the Normativity Thesis about logic. But why do we acknowledge it? This is the “source question”. This paper shows that Frege provided a promising, yet often ignored, answer to that question. Frege held that the logical consequence relation |= is not intrinsically normative. Rather, the normativity of logic is derived from something other than logic itself, namely the norm that one ought to judge truly and not falsely. I (...) demonstrate that this carves out a spectrum of two opposed views on why logic is normative. I call Frege’s view extrinsicism, which contrasts with intrinsicism. The extrinsicist view, from an exegetical point of view, is basically absent from all interpretations of Frege’s view on the normativity of logic. From a systematic point of view, it offers a sound alternative to the widely accepted assumption that logic is demarcated from other disciplines such as microphysics, biology or arithmetic through a distinct and exceptional kind of normative force over how to judge and reason about the world, because it is taken to have a direct relation to truth and truth preservation. (shrink)

Criticizing psychologism about logic in the Foreword of Grundgesetze, Frege examines an answer to the question of how we can justify our acknowledgment of logical axioms as true—the logical laws that cannot be proved from other laws. The answer he entertains states that we cannot reject logical axioms if we do not want to give up our judgment altogether. Suspending his judgment about this answer, Frege points out that it is still compatible with his anti-psychologist conception of logic. There are (...) two issues with this paragraph. First, it is difficult to read this paragraph consistently. Second, it is not clear why Frege brings up this particular view regarding the justification for logical axioms in the middle of his criticism of psychologism. This paper develops a consistent interpretation of this paragraph. The view on the justification for logical axioms, which Frege is dealing with, is neo-Kantian. In the paragraph, Frege is criticizing a psychologistic misunderstanding of the neo-Kantian justification for logical axioms. The way Frege explains away this misunderstanding shows that he takes the neo-Kantian justification for logical axioms to be a non-evidential epistemic warrant if it is an epistemic warrant. It is this notion of non-evidential epistemic warrant that Frege suspends his judgment about. Thus, the paragraph shows that Frege has a reason to have reservations about neo-Kantianism. Furthermore, it turns out that the sole issue between Frege and psychological logicians is whether truth is objective, which provides a different way to explain away a much-discussed tension between Begriffsschrift and Frege's anti-psychologism. (shrink)

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear in every (...) one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising. (shrink)

Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing we (...) search for and specify during investigation or inquiry. I support this epistemological conception of objects by studying specificational sentences, a class of sentences which includes Frege's original example. I defend an analysis of such sentences as question-answer pairs, and show how to formally represent this analysis using game-theoretical semantics. (shrink)

In this paper, I address some puzzles about Frege’s conception of how we “grasp” thoughts. I focus on an enigmatic passage that appears near the end of Frege’s great essay “The Thought.” In this passage Frege refers to a “non-sensible something” without which “everyone would remain shut up in his inner world.” I consider and criticize Wolfgang Malzkorn’s interpretation of the passage. According to Malzkorn, Frege’s view is that ideas [Vorstellungen] are the means by which we grasp thoughts. My counter-proposal (...) is that language enables us to grasp thoughts (ideas are merely their baggage or “trappings,” as Frege puts it). One significant consequence of my interpretation is that it helps challenge the standard reading of Frege according to which he is a metaphysical platonist about thoughts. My interpretation thus provides support for the deflationary, anti-ontological reading spelled out by readers like Thomas Ricketts and Wolfgang Carl. As Ricketts puts it, Frege’s distinction between the objective and the subjective, rather than being an ontological doctrine, “lodges in the contrast between asserting something and giving vent to a feeling.”. (shrink)

In this paper I examine the question of logic’s normative status in the light of Carnap’s Principle of Tolerance. I begin by contrasting Carnap’s conception of the normativity of logic with that of his teacher, Frege. I identify two core features of Frege’s position: first, the normative force of the logical laws is grounded in their descriptive adequacy; second, norms implied by logic are constitutive for thinking as such. While Carnap breaks with Frege’s absolutism about logic and hence with the (...) notion that any system of logic should have a privileged claim to correctness, I argue that there is a sense in which Carnap’s framework-relative conception of logical norms has a constitutive role to play: though they are not constitutive for the conceptual activity for thinking, they do nevertheless set the ground rules that make certain forms of scientific inquiry possible in the first place. I conclude that Carnap’s principle of tolerance is tamer than one might have thought and that, despite remaining differences, Frege’s and Carnap’s conceptions of logic have more in common than one might have thought. (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 paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary and sufficient (...) for possession of mathematical concepts will always face counterexamples of the kind illustrated by Cardano. I close by suggesting that we should rely more heavily on resources of Anti-Individualism as a framework for understanding the acquisition and possession of concepts of abstract subject matters. (shrink)

This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic—what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics—Logicism, Intuitionism, Formalism, Realism—and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam (...) are among the philosophers considered along the way. (shrink)

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 thesis discusses some central aspects of Wittgenstein's conception of language and logic in his Tractatus Logico-Philosophicus and brings them into relation with the philosophies of Frege and Russell. The main contention is that a fruitful way of understanding the Tractatus is to see it as responding to tensions in Frege's conception of logic and Russell's theory of judgement. In the thesis the philosophy of the Tractatus is presented as developing from these two strands of criticism and thus as the (...) culmination of the philosophy of logic and language developed in the early analytic period. Part one examines relevant features of Frege's philosophy of logic. Besides shedding light on Frege's philosophy in its own right, it aims at preparing the ground for a discussion of those aspects of the Tractatus' conception of logic which derive from Wittgenstein's critical response to Frege. Part two first presents Russell's early view on truth and judgement, before considering several variants of the multiple relation theory of judgement, devised in opposition to it. Part three discusses the development of Wittgenstein's conception of language and logic, beginning with Wittgenstein's criticism of the multiple relation theory and his early theory of sense, seen as containing the seeds of the picture theory of propositions presented in the Tractatus. I then consider the relation between Wittgenstein's pictorial conception of language and his conception of logic, arguing that Wittgenstein's understanding of sense in terms of bipolarity grounds his view of logical complexity and of the essence of logic as a whole. This view, I show, is free from the internal tensions that affect Frege's understanding of the nature of logic. (shrink)

Gottlob Frege is often called a "platonist". In connection with his philosophy we can talk about platonism concerning three kinds of entities: numbers, or logical objects more generally; concepts, or functions more generally; thoughts, or senses more generally. I will only be concerned about the first of these three kinds here, in particular about the natural numbers. I will also focus mostly on Frege's corresponding remarks in The Foundations of Arithmetic (1884), supplemented by a few asides on Basic Laws of (...) Arithmetic (1893/1903) and "Thoughts" (1918). My goal is to clarify in which sense the Frege of Foundations and Basic Laws is a platonist concerning the natural numbers.1.. (shrink)

What is the true worth of Wittgenstein's contribution to philosophy? Answers to this question are strongly divided. However, most assessments rest on certain popular misreadings of his purpose. This book challenges both "theoretical" and "therapeutic" interpretations. In their place, it seeks to establish that, from beginning to end, Wittgenstein regarded clarification as the true end of philosophy. It argues that, properly understood, his approach exemplifies rather than betrays critical philosophy and provides a viable alternative to other contemporary offerings.

This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. a matter (...) of recognizing trutlis wliich had previoasly been unrecognized, but of extending the domain of what is true. (shrink)

The historical consensus is that logical evidence is special. Whereas empirical evidence is used to support theories within both the natural and social sciences, logic answers solely to a priori evidence. Further, unlike other areas of research that rely upon a priori evidence, such as mathematics, logical evidence is basic. While we can assume the validity of certain inferences in order to establish truths within mathematics and test scientifi c theories, logicians cannot use results from mathematics or the empirical sciences (...) without seemingly begging the question. Appeals to rational intuition and analyticity in order to account for logical knowledge are symptomatic of these commitments to the apriority and basicness of logical evidence. This chapter argues that these historically prevalent accounts of logical evidence are mistaken, and that if we take logical practice seriously we fi nd that logical evidence is rather unexceptional, sharing many similarities to the types of evidence appealed to within other research areas. (shrink)

While anti-exceptionalism about logic is now a popular topic within the philosophy of logic, there’s still a lack of clarity over what the proposal amounts to. currently, it is most common to conceive of AEL as the proposal that logic is continuous with the sciences. Yet, as we show here, this conception of AEL is unhelpful due to both its lack of precision, and its distortion of the current debates. Rather, AEL is better understood as the rejection of certain traditional (...) properties of logic. The picture that results is not of one singular position, but rather a cluster of often connected positions with distinct motivations, understood in terms of their rejection of clusters of the various traditional properties. In order to show the fruitfulness of this new conception of AEL, we distinguish between two prominent versions of the position, metaphysical and epistemological AEL, and show how the two positions need not stand or fall together. (shrink)

This monograph discusses the question of what it is to be a reason – mainly in practical ethics – and proposes an original contribution to metaethics.It critically examines theories of metaethical realism, constructivism and error theory and identifies several misunderstandings or unclarities in contemporary debates. Based on this examination, the book suggests a distinction between a conceptual question, that can be answered by pure first-personal thinking, and a material question, that targets responses to reasons as a natural phenomenon in space (...) and time and that can be answered by help of the sciences. While this book defends a sharp distinction between these approaches, it also argues that the insights gained by the distinct approaches can be fruitfully integrated into a comprehensive picture.The comprehensive picture promoted in this book, based on both philosophical analysis and resources from psychology and cognitive science, is a picture of reasons as items in a collective archive of mind – reconfiguring the “domain of reasons” as a collectively established and socially cultivated fund of considerations with normative weight. The developed Collective Archive View combines Reasons Fundamentalism as an answer to the conceptual question, with a social ontological proposal, similar to Haslanger’s critical realism, as an answer to the material question.Thereby, it introduces central ideas from the field of social metaphysics into metaethics. At the same time, it offers a way of settling some controversies within metaethics, going on between proponents of Reasons Fundamentalism and Constitutivism, realism and constructivism, as well as proponents of mind-dependence and mind-independence of normative facts. Finally, the proposal enables us to envision and conceptualize genuine normative change within a metaethical theory. (shrink)

The phenomenological movement begins in the Prolegomena to Husserl’s Logical Investigations as a philosophy of logic. Despite this, remarkably little attention has been paid to Husserl’s arguments in the Prolegomena in the contemporary philosophy of logic. In particular, the literature spawned by Gilbert Harman’s work on the normative status of logic is almost silent on Husserl’s contribution to this topic. I begin by raising a worry for Husserl’s conception of ‘pure logic’ similar to Harman’s challenge to explain the connection between (...) logic and reasoning. If logic is the study of the forms of all possible theories, it will include the study of many logical consequence relations; by what criteria, then, should we select one consequence relation as correct? I consider how Husserl might respond to this worry by looking to his late account of the ‘genealogy of logic’ in connection with Gurwitsch’s claim that ‘[i]t is to prepredicative perceptual experience … that one must return for a radical clarification and for the definitive justification of logic’. Drawing also on Sartre and Heidegger, I consider how prepredicative experience might constrain or guide our selection of a logical consequence relation and our understanding of connectives like implication and negation. (shrink)

Bogusław Wolniewicz – polski tłumacz Pism semantycznych Gottloba Fregego – przełożył termin Bedeutung na język polski jako „znaczenie”, zauważając w przypisie, że wątpliwości, jakie może budzić w tym przypadku użycie tego słowa, budzi również użycie w języku niemieckim przez Fregego słowa Bedeutung. Jednocześnie Wolniewicz, w tym samym przypisie, twierdzi, że „to, co Frege nazywa znaczeniem znaku, pokrywa się z tym, co w dzisiejszej terminologii semantycznej zwykło się nazywać »denotacją« albo »denotatem«” (Frege, 2014a, s. 62, przypis 27). W niniejszym artykule postaram (...) się przedstawić rozumienie Fregowskiej kategorii znaczenia (Bedeutung), które oddawałoby sposób, w jaki posługiwał się nim niemiecki filozof, tj. zarówno w odniesieniu do nazw, zdań, jak i predykatów. W części pierwszej przedstawię pokrótce wzajemny stosunek podziałów na przedmioty i funkcje oraz na sens i znaczenie wyrażeń. W drugiej zarysuję sposób, w jaki Frege podchodził do problemów językowych i filozoficznych. W części trzeciej dokonam szczegółowej interpretacji kategorii znaczenia dla nazw, zdań pojedynczych i złożonych, a także predykatów. Część ostatnia dotyczy kwestii Fregowskiego realizmu, która jest kluczowa z punktu widzenia późniejszych krytyk forsowanej przeze mnie interpretacji Bedeutung. (shrink)

As Quine observed, the following sentence has a reading which, if true, would be of special interest to the authorities: Ralph believes that someone is a spy. This is the reading where the quantifier is naturally understood as taking wide scope relative to the attitude verb and as binding a variable within the scope of the attitude verb. This essay is interested in addressing the question what the semantic analysis of this kind of reading should look like from a Fregean (...) perspective—a perspective according to which attitude states are generally relations to structured Fregean thoughts composed of senses. The Fregean view faces a challenge of compositionality here. This essay describes the challenge and offers a response on the Fregean's behalf. (shrink)

This paper develops a criterion for sameness of Fregean senses. I consider three criteria: logical equivalence, intensional isomorphism, and epistemic equipollence. I reject the first two and argue for a version of the third.

Commentators regularly attribute to Frege realist, idealist, and quietist responses to metaphysical questions concerning the abstract objects he calls ‘thoughts’. But despite decades of effort, the evidence offered on behalf of these attributions remains unconvincing. I argue that Frege deliberately avoids commitment to any of these positions, as part of a metaphysical separatist policy motivated by the fact that logic is epistemologically autonomous from metaphysics. Frege’s views and arguments prove relevant to current attempts to argue for epistemological autonomy, particularly that (...) of ethics. (shrink)

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)

How is Frege able to claim that the notion of judgement is essential to his logic without introducing a form of psychologism? I argue first that Frege’s logical notion of judgement is to be distinguished from an empirical notion of judgement, that it cannot be understood as an abstract, idealized notion, and that there are doubts concerning a transcendental reading of Frege’s writings. Then, I explain that the logical notion of judgement has to be understood from a first-person perspective, to (...) be contrasted with a third-person perspective, in which judgement is understood as an empirical, psychological phenomenon. Frege’s logic is essentially a first-person engagement, as each of us can make use of the ideography as a science of logic only if we ourselves have made the relevant judgements. Finally, I claim that the judging agent as conceived by Frege can, after all, be understood as a transcendental ego. (shrink)

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)

Abstract‘Logical Realism’ is taken to mean many different things. I argue that if reality has a privileged structure, then a view I call metaphysical logical realism is true. The view says that, first, there is ‘One True Logic’; second, that the One True Logic is made true by the mind‐and‐language‐independent world; and third, that the mind‐and‐language‐independent world makes it the case that the One True Logic is better than any other logic at capturing the structure of reality. Along the way, (...) I discuss a few alternatives, and clarify two distinct kinds of metaphysical logical realism. (shrink)

This article aims to analyse Wittgenstein’s 1929–1932 notes concerning Frege’s critique of what is referred to as old formalism in the philosophy of mathematics. Wittgenstein disagreed with Frege’s critique and, in his notes, outlined his own assessment of formalism. First of all, he approvingly foregrounded its mathematics-game comparison and insistence that rules precede the meanings of expressions. In this article, I recount Frege’s critique of formalism and address Wittgenstein’s assessment of it to show that his remarks are not so much (...) a critique of Frege as rather a defence of the formalist anti-metaphysical investment. (shrink)

Las interpretaciones tradicionales de Frege tienden a explicar su antipsicologismo como indicando que ninguna consideración subjetivista debe interferir en la elaboración de un lenguaje lógico; dichas interpretaciones, sin embargo, tienen problemas para explicar el énfasis dado por el mismo Frege a conceptos como el de fuerza asertiva. Este artículo pretende solucionar esta extrañeza investigando, a partir de su concepto de ciencia, algunas de las ideas epistemológicas de Frege. Esto nos llevará a concluir que una concepción de la verdad como fenómeno (...) esencialmente público puede resolver este y otros problemas interpretativos. (shrink)

Explores the stable core of Wittgenstein's philosophy as developed from the Tractatus to the Philosophical Investigations.

William Tait's standing in the philosophy of mathematics hardly needs to be argued for; for this reason the appearance of this collection is especially welcome. As noted in his Preface, the essays in this book ‘span the years 1981–2002’. The years given are evidently those of publication. One essay was not previously published in its present form, but it is a reworking of papers published during that period. The Introduction, one appendix, and some notes are new. Many of the essays (...) will be familiar to the readers of this journal; indeed two first appeared here.It should be no surprise to those who know Tait's work that this is a very rich collection, with contributions on a wide variety of issues, both systematic and historical. That poses a problem for a reviewer, because a serious discussion of even all the major issues would be beyond the scope of a review.Before the essays in this collection, Tait's publications were almost all in mathematical logic, especially proof theory. He was a leading actor in the work on the revised Hilbert program stimulated after the war by Georg Kreisel, Kurt Schütte, and Gaisi Takeuti. Tait thus has an experience in mathematical research that is rare among those whose careers have been institutionally in philosophy. In the 1970s Tait became disillusioned with the proof-theoretic program on which he had worked. However, he draws on that background in several of these essays, and he has continued to work on mathematical questions. In particular, the set-theoretic project reflected in essay 6 is as much mathematical as philosophical.It is not easy to characterize Tait's philosophical viewpoint briefly. Both the title of the book and some of its content mark him as a rationalist. His hero in the earlier history …. (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)

Why does Frege claim that logical axioms are ‘self‐evident,’ to be recognized as true ‘independently of other truths,’ and then offer arguments for those axioms? I argue that he thinks the arguments provide us with the justification that we need for accepting the axioms and that this is compatible with his remarks about self‐evidence. This compatibility depends on philosophical considerations connected with the ‘critical method’: an interesting approach to the justification of axioms endorsed by leading philosophers at the time.

Sets are multitudes which are also unities. It is surprising that the fact that multitudes are also unities leads to no contradictions: this is the main fact of mathematics.Kurt Gödel (Hao Wang,A Logical Journey: From Gödel to Philosophy)In what sense can something be at the same time one and many? The problem is familiar since Plato (for example,Republic524e). In recent times, Whitehead and Russell, inPrincipia Mathematica,have been struck by the difficulty of the problem: ‘If there is such an object as (...) a class, it must be in some senseoneobject, yet it is only of classes that many can be predicated. Hence, if we admit classes as objects, we must suppose that the same object can be both one and many, which seems impossible.' It is, however, in Frege's great work,The Foundations of Arithmetic(henceforth,Grundlagen),that many see the final resolution of the old question: how can something be at the same time one and many? (shrink)

The paper scrutinizes Frege's Euclideanism - his view of arithmetic and geometry as resting on a small number of self-evident axioms from which non-self-evident theorems can be proved. Frege's notions of self-evidence and axiom are discussed in some detail. Elements in Frege's position that are in apparent tension with his Euclideanism are considered - his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential (...) abilities. The resolution of the tensions indicates that Frege maintained a sophisticated and challenging form of rationalism, one relevant to current epistemology and parts of the philosophy of mathematics. (shrink)

This paper is divided into two main sections. In the first, I attempt to show that the characterization of Frege as a redundancy theorist is not accurate. Using one of Wolfgang Carl's recent works as a foil, I argue that Frege countenances a realm of abstract objects including truth, and that Frege's Platonist commitments inform his epistemology and embolden his antipsychologistic project. In the second section, contrasting Frege's Platonism with pragmatism, I show that even though Frege's metaphysical position concerning truth (...) has been criticized as reproachable, I argue that it may be useful for people to think like Platonists while conducting their scientific and philosophical inquiries. (shrink)

Em sua obra, Robert Brandom apresenta uma teoria expressivista da lógica. Segundo o autor, a lógica tem o papel expressivo de tornar explı́citas as relações inferenciais implı́citas em nossas práticas linguı́sticas. Estas relações inferenciais conferem conteúdo aos conceitos. Neste artigo, exploraremos a tese de que o expressivismo lógico de Brandom é uma teoria antirrealista acerca da lógica. Realistas lógicos costumam defender a existência independente de fatos lógicos em relação a nossas práticas cognitivas e linguı́sticas, de modo que a lógica, uma (...) vez que seria capaz de representar estes fatos, descreveria verdadeiramente a estrutura da realidade. Por contraste, antirrealistas lógicos não se comprometem com a existência independente de fatos lógicos para entenderem a natureza da lógica. Em contraste com uma visão realista, mostramos que o antirrealismo de Brandom tem como consequências uma ontologia simples e econômica e a fundação de uma alternativa pragmatista para se examinar a normatividade da lógica, o fenômeno da pluralidade de lógicas rivais e a natureza de nossa racionalidade. (shrink)

I dub a certain central tradition in philosophy of language (and mind) the de re tradition. Compelling thought experiments show that in certain common cases the truth conditions for thoughts and public-language expressions categorically turn on external objects referred to, rather than on linguistic meanings and/or belief assumptions. However, de re phenomena in language and thought occur even when the objects in question don't exist. Call these empty de re phenomena. Empty de re thought with respect to numeration is explored (...) in this paper, and such thought with respect to hallucinations is touched on. (shrink)