At the beginning of Die Grundlagen der Arithmetik [1884], Frege observes that “it is in the nature of mathematics to prefer proof, where proof is possible”. This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of self-evidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that both (...) programs are undermined at a crucial point, namely when self-evidence is supported by holistic and even pragmatic considerations. (shrink)

(2013). In the beginning was the doing: the premises of the practical syllogism. Canadian Journal of Philosophy: Vol. 43, No. 3, pp. 303-321.

In this paper I suggest an answer to the question of what Frege means when he says that his logical system, the Begriffsschrift, is like the language Leibniz sketched, a lingua characteristica, and not merely a logical calculus. According to the nineteenth century studies, Leibniz’s lingua characteristica was supposed to be a language with which the truths of science and the constitution of its concepts could be accurately expressed. I argue that this is exactly what the Begriffsschrift is: it is (...) a language, since, unlike calculi, its sentential expressions express truths, and it is a characteristic language, since the meaning of its complex expressions depend only on the meanings of their constituents and on the way they are put together. In fact it is in itself already a science composed in accordance with the Classical Model of Science. What makes the Begriffsschrift so special is that Frege is able to accomplish these goals with using only grammatical or syncategorematic terms and so has a medium with which he can try to show analyticity of the theorems of arithmetic. (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)

The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...) did not hold the relevant sense-identity claim regarding basic law V. (shrink)

This paper concentrates on some aspects of the history of the analyticsynthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio exprincipiis. But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (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.

‘Quantified pure existentials’ are sentences (e.g., ‘Some things do not exist’) which meet these conditions: (i) the verb EXIST is contained in, and is, apart from quantificational BE, the only full (as against auxiliary) verb in the sentence; (ii) no (other) logical predicate features in the sentence; (iii) no name or other sub-sentential referring expression features in the sentence; (iv) the sentence contains a quantifier that is not an occurrence of EXIST. Colin McGinn and Rod Girle have alleged that standard (...) first-order logic cannot adequately deal with some such existentials. The article defends the view that it can. (shrink)

The impartial reader notices that Frege, in Die Verneinung, treats an opposing conception of negation, but without specifically naming its proponent. In this paper, it is proven for the first time that the view in question is that of his colleague in Jena, Bruno Bauch. Besides their different views, concerning above all the status of false thoughts, there are nonetheless broader points of agreement between the ideas of Bauch and Frege. These points of agreement cast light on both thinkers as (...) representatives of a current of Neo-Kantianism, having its source in Lotze, in which Kantian and Platonic elements are fused to form a ?transcendental Platonism? (shrink)

Michael Dummett argued that Frege was a realist while Hans Sluga countered that he was an objective idealist in the rationalist tradition of Kant and Lotze. Sluga ties Frege's idealism to the context principle which he argues Frege never gave up. It is argued that Sluga has correctly interpreted the pre?1891 Frege while Dummett is correct concerning the later period. It is also claimed that the context principle was dropped prior to 1891 to be replaced by the doctrine of unsaturated (...) entities. (shrink)

Frege holds the distinction between complete (saturated) and incomplete (unsaturated) things to be a basic distinction of logic. Many disagree. In this paper I will argue that one can defend Frege's distinction against criticism if one takes, inspired by Frege, a wh -question to be the paradigm incomplete expression.

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

In his recent book, "The Metaphysicians of Meaning" (2000), Gideon Makin argues that in the so-called "Gray's Elegy" argument (the GEA) in "On Denoting", Russell provides decisive arguments against not only his own theory of denoting concepts but also Frege's theory of sense. I argue that by failing to recognize fundamental differences between the two theories, Makin fails to recognize that the GEA has less force against Frege's theory than against Russell's own earlier theory. While I agree with many aspects (...) of Makin's interpretation of the GEA, I differ with him regarding some significant details and present an interpretation according to which the GEA emerges as simpler, stronger, and more integrated. (shrink)

This paper aims to determine what kind of problem Frege's famous “Julius Caesar problem” is. whether it is to be understood as the metaphysical problem of determining what kind of things abstract objects like numbers or value‐courses are, or as the epistemological problem of providing a means of recognizing these objects as the same again, or as the logical problem of providing abstract sortal concepts with a sharp delimitation in order to fulfill the law of excluded middle, or as the (...) semantic problem of fixing the referents of the corresponding abstract singular terms. It is argued that, for Frege, the Caesar problem is a bundle of related problems of which the semantic problem is the most basic one. (shrink)

It is shown that the coherence of de re belief ascriptions is doubtful in view of certain plausible principles. Subsequently, it is argued, the standard argument against substitutivity in de dicto ascriptions loses some of its power. Also, some possible reactions to these results are considered.

In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic distinctions (...) between sentences that, from a Fregean perspective, do not differ in meaning. This is what we call the ‘new problem’ of hyperintensionality to distinguish it from the ‘old problem’ that faced the intensional theory. We show that our semantic framework offers a joint solution to both these problems by virtue of satisfying a version of Frege’s so-called ‘equipollence principle’ for sense individuation. Frege’s principle, we argue, not only captures the semantic intuitions that give rise to the old and the new problem of hyperintensionality, but also points the way to an independently motivated solution to both problems. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

In this paper, I critically discuss Frege’s philosophy of geometry with special emphasis on his position in The Foundations of Arithmetic of 1884. In Sect. 2, I argue that that what Frege calls faculty of intuition in his dissertation is probably meant to refer to a capacity of visualizing geometrical configurations structurally in a way which is essentially the same for most Western educated human beings. I further suggest that according to his Habilitationsschrift it is through spatial intuition that we (...) come to know the axioms of Euclidean geometry. In Sect. 3, I argue that Frege seems right in claiming in The Foundations, §14 that the synthetic nature of the Euclidean axioms follows from the fact that they are independent of one another and of the primitive laws of logic. If the former were dependent on the latter, they would be analytic in Frege’s sense of analyticity. But then they would not be independent of one another and due to their mutual provability would lose their status as axioms of Euclidean geometry, since according to Frege an axiom of a theory T is per definitionen unprovable in T. I further argue that only by invoking pure spatial intuition can Frege “explain” the epistemological status of the axioms of Euclidean geometry completely: their synthetic a priori nature. Finally, I argue that his view about independence in The Foundations, §14 seems to clash with his conception of independence in his mature period. In Sect. 4, I scrutinize Frege’s somewhat vague, but unduly neglected remarks in The Foundations, §26 on space, spatial intuition and the axioms of Euclidean geometry. I argue that for the sake of coherence Frege should have said unambiguously that space is objective, that it is independedent not only of our spatial intuition, but of our mental life altogether including our judgements about space, instead of encouraging the possible conjecture that in his view it contains an objective and a subjective component. I further argue that for Frege the objectivity of both space and the axioms of Euclidean geometry manifests itself in our universal and compulsory acknowledgement of the Euclidean axioms as true. I conclude Sect. 4 by arguing that there is a conflict between the subjectivity of our spatial intuitions as stressed in The Foundations, §26 and Frege’s thesis in his dissertation that the axioms of Euclidean geometry derive their validity from the nature of our faculty of intuition. To resolve this conflict, I propose that in the light of his avowed realism in The Foundations Frege could have replaced his early thesis by saying that although we come to know the axioms of Euclidean geometry through spatial intuition and are justified in acknowledging them as true on the basis of geometrical intuition, their truth is independent not only of the nature of our faculty of intuition and singular acts of intuition, but of our mental processes and activities in general, including the inner mental act of judging. In Sect. 5, I argue that Frege most likely did not adopt Kant’s method of acquiring geometrical knowledge via the ostensive construction of concepts in spatial intuition. In contrast to Kant, Frege holds that the axioms of three-dimensional Euclidean geometry express state of affairs about space obtaining independently of our spatial intuition. In Sect. 6, I conclude with a summarized assessment of Frege’s philosophy of geometry. (shrink)

Remarks on the Relations between Neurophysiology and Psychology. In the last decades of Analytical Philosophy, contributions to the so-called mind-body-problem have been suffering by several serious methodological misunderstandings: they have failed, for instance, to distinguish between explanations of particular and strictly general properties and between two important senses of existential statements; and they have overlooked the role conceptual explanations play in the development of science. Changing our methodological premisses, we should be able to put questions like that of the relation (...) between physiological and psychological phenomena in a new way - and we should be able to see that such newly understood questions allow answers which evade the pitfalls of both reductionist and holistic positions. The paper tries to illustrate and to defend these contentions by reference to a very elementary example: the rational re-building of our concepts to identify behaviour by which a subject controls the position of his body in space. (shrink)

British Journal for the History of Philosophy, Volume 21, Issue 1, Page 189-200, January 2013.

A detailed chronology is offered for the writing of Frege's central philosophical essays from the early 1890s. Particular attention is given to (the distinction between) Sinn and Bedeutung. Suggestions are made as to the origin of the examples concerning the Morning Star/Evening Star and August Bebel's views on the return of Alsace-Lorraine. Likely sources are offered for Frege's use of the terms Bestimmungsweise, Art des Gegebenseins and Sinn und Bedeutung.

This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis . But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)

In the opening to his late essay, Der Gedanke, Frege asserts without qualification that the word "true" points the way for logic. But in a short piece from his Nachlass entitled "My Basic Logical Insights", Frege writes that the word true makes an unsuccessful attempt to point to the essence of logic, asserting instead that "what really pertains to logic lies not in the word "true" but in the assertoric force with which the sentence is uttered". Properly understanding what Frege (...) takes to be at issue here is crucial for understanding his conception of logic and, in particular, what he takes to be its normative status vis-à-vis judgement, assertion, and inference. In this paper, I focus my attention on clarifying the latter claim and Frege's motivations for making it, exposing what I take to be a fundamental tension in Frege's conception of logic. Finally, I discuss whether Frege's deployment of the horizontal in his mature Begriffsschrift helps to resolve this tension. (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)

Lecture notes from Husserl's logic lectures published during the last 20 years offer a much better insight into his doctrine of the forms of meaning than does the fourth Logical Investigation or any other work published during Husserl's lifetime. This paper provides a detailed reconstruction, based on all the sources now available, of Husserl's system of logical grammar. After having explained the notion of meaning that Husserl assumes in his later logic lectures as well as the notion of form of (...) meaning as it features in ‘doctrine of the forms of meaning’, I present a system of rules that describes all the various forms of meaning that Husserl singles out in his lectures. (shrink)

This paper identifies a tension in Frege’s philosophy and offers a diagnosis of its origins. Frege’s Context Principle can be used to dissolve the problem of propositional unity. However, Frege’s official response to the problem does not invoke the Context Principle, but the distinction between ‘saturated’ and ‘unsaturated’ propositional constituents. I argue that such a response involves assumptions that clash with the Context Principle. I suggest, however, that this tension is not generated by deep-seated philosophical commitments, but by Frege’s occasional (...) attempt to take a dubious shortcut in the justification of his conception of propositional structure. (shrink)

This article discusses the problems which concepts pose for the attribution of thoughts to animals. It locates these problems within a range of other issues concerning animal minds (section 1), and presents a ‘lingualist master argument’ according to which one cannot entertain a thought without possessing its constituent concepts and cannot possess concepts without possessing language (section 2). The first premise is compelling if one accepts the building-block model of concepts as parts of wholes – propositions – and the idea (...) that intentional verbs signify relations between subjects and such propositions. But I shall find fault with both (section 3). This opens the way for recognizing a form of ‘holodoxastic’ thought-ascription which does not presuppose concept-possession on the part of the subject (section 4). Section 5 defends this idea against objections. Section 6 turns to the second premise of the lingualist master argument. I press the idea of judgement into service as a label for conceptual thought that need not be linguistic and argue that the possession of concepts is an ability. Section 7 accepts that concept-possession requires the ability to classify rather than merely to discriminate, but suggests that this need not disqualify animals. In the final section I confirm this verdict by returning to the notion of judgement: classification is the deliberate and considered response to a range of options in a sorting or discrimination task. Notwithstanding appearances to the contrary, the capacity for such a response does not presuppose the linguistic ability to answer questions. Judgement is a feature of a type of problem-solving that we share with some non-linguistic creatures. (shrink)

The concept of quantity (Größe) plays a key role in Frege's theory of real numbers. Typically enough, he refers to this theory as ?theory of quantity? (?Größenlehre?) in the second volume of his opus magnum Grundgesetze der Arithmetik (Frege 1903). In this essay, I deal, in a critical way, with Frege's treatment of the concept of quantity and his approach to analysis from the beginning of his academic career until Frege 1903. I begin with a few introductory remarks. In Section (...) 2, I first analyze Frege's use of the term ?source of knowledge? (?Erkenntnisquelle?) with particular emphasis on the logical source of knowledge. The analysis includes a brief comparison between Frege and Kant's conceptions of logic and the logical source of knowledge. In a second step, I examine Frege's theory of quantity in Rechnungsmethoden, die sich auf eine Erweiterung des Größenbegriffes gründen (Frege 1874). Section 3 contains a couple of critical observations on Frege's comments on Hankel's theory of real numbers in Die Grundlagen der Arithmetik (Frege 1884). In Section 4, I consider Frege's discussion of the concept of quantity in Frege 1903. Section 5 is devoted to Cantor's theory of irrational numbers and the critique deployed by Frege. In Section 6, I return to Frege's own constructive treatment of analysis in Frege 1903 and succinctly describe what I take to be the quintessence of his account. (shrink)

In his paper on ‘Frege's Theory of Sense and Reference’ Saul Kripke remarks: “Like the present account, Künne stresses that for Frege times, persons, etc. can be part of the expression of the thought. However, his reading is certainly not mine in significant respects . . .”. On both counts, he is right. As regards the differences between our readings, in some respects I shall confess to having made a mistake, in several others I shall remain stubbornly unmoved. Thus I (...) shall insist on the need for distinguishing Fregean sense from linguistic (lexico-grammatical) meaning, I shall resist Kripke's function-theoretic account of ‘hybrid’ thought-expressions, and I shall deplore his transformation of Gottlob Frege into Gottrand Fressell. As regards this transformation, I shall argue that some of the main points Kripke wants to drive home do not depend on it. (shrink)

The aim of this essay is a criticism of reductionism ? both in its ?static? interpretation (usually referred to as the layer model or level?picture of science) and in its ?dynamic? interpretation (as a theory of the growth of scientific knowledge), with emphasis on the latter ? from the point of view of Popperian fallibilism and Feyerabendian pluralism, but without being committed to the idiosyncrasies of these standpoints. In both aspects of criticism, the rejection is based on the proposal of (...) a global alternative. Hummell and Opp's research programme for the reduction of sociology to psychology is used as a starting?point and taken as the primary object of criticism. Following the introductory Section I, Section II analyses the three crucial notions of Hummell and Opp's research programme ? their explications of the notions of ?sociology?, ?psychology? and the concept of reduction itself ? and criticizes the authors? deficient ?logic of reduction?. Although the ?local? shortcomings of our authors? ?logic of reduction? do not affect reductionism as such, i.e. logically sound versions of reductionism as devised by Kemeny, Nagel, Oppenheim, Putnam, Woodger et al., it is argued that the logical soundness of sophisticated reductionism cannot compensate for its additional epistemological and methodological deficiencies. Section III analyses the ?dynamic? interpretation of reductionism as a particular developmental pattern of scientific growth. It is argued that even reductionism at its best can produce only cumulative progress, thus ?a priori? excluding scientific revolutions which are inevitably counter?inductive as well as counter?reductive. Section IV discusses the philosophical background of modern reductionism, and examines the effects both of reductionism and of anti?reductionistic pluralism on the autonomy of scientific fields. It is argued that pluralistic anti?reductionism undermines spurious claims for autonomy much more effectively than reductionism. As a ?local? improvement of the reductionistic research programme, the replacement of the predominant one?way reductionism by a less restrictive many?way reductionism is proposed. It is argued that the appropriate treatment for an allegedly backward science (say sociology) is not its reduction to an allegedly more advanced science (say psychology) but its non?reductive replacement by new theories (of the same or of another field) that do not incorporate the older ones. As a ?global? alternative to the reduction of sociology to psychology, the frontier?crossing direct application of psychological theories to sociological phenomena is proposed. A plea is made for a pluralistic science without reduction, based on intra? and interscientific criticism as the proper method for the advancement of knowledge. (shrink)

It is argued that the theories of the modern cognitive psychology of perception and recognition show, under rigorous logical analysis, the same problems which arise in the philosophical theories of knowledge of Descartes and Locke and lead to relativistic and solipsistic consequences. Through examination of the approachs of D. Sanders, E. B. Goldstein and J. Fodor it is shown that the perceptible world in these theories dissolves in internal representations so that despite its realistic starting-point modern cognitive psychology runs into (...) epistemological idealism or solipsism. (shrink)

In this note the claim is defended that Frege was a realist in the sense that he attributed causal efficacy to certain abstract objects. The arguments of Dummett and Sluga (cf. Inquiry, Vols. 18, 19, and 20 [1975–77]) to the contrary are criticized.

Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably construed, in accordance with an abundant (...) or deflationary conception, Quine’s charge can be resisted. This interpretation need not be seen as precluding the use of model-theoretic semantics for second-order languages; but it will preclude the use of the standard semantics, along with the more general Henkin semantics, of which it is a special case. To that extent, the approach I recommend has revisionary implications which some may find unpalatable; it is, however, compatible with the quite different special case in which the second-order variables are taken to range over definable subsets of the first-order domain, and with respect to such a semantics, some important metalogical results obtainable under the standard semantics may still be obtained. In my final section, I discuss the relations between second-order logic, interpreted as I recommend, and a strong version of schematic ancestral logic promoted in recent work by Richard Heck. I argue that while there is an interpretation on which Heck’s logic can be contrasted with second-order logic as standardly interpreted, when it is so interpreted, its differences from the more modest form of second-order logic I advocate are much less substantial, and may be largely presentational. (shrink)

This paper aims to shed light on the broader significance of Frege’s logicism against the background of discussing and comparing Wittgenstein’s ‘showing/saying’-distinction with Brandom’s idiom of logic as the enterprise of making the implicit rules of our linguistic practices explicit. The main thesis of this paper is that the problem of Frege’s logicism lies deeper than in its inconsistency : it lies in the basic idea that in arithmetic one can, and should, express everything that is implicitly presupposed so that (...) nothing is left unsaid. This, in fact, is the target of Wittgenstein’s critique. Rather than the Tractatus, with its claim that logicism attempts to say something that can only be shown, it is the Philosophical Investigations, with its argument by regress against the thesis that every rule which one can follow must be of an explicit nature, that is of real significance here. (shrink)

This essay consists of two parts. In the first part, I focus my attention on the remarks that Frege makes on consistency when he sets about criticizing the method of creating new numbers through definition or abstraction. This gives me the opportunity to comment also a little on H. Hankel, J. Thomae—Frege’s main targets when he comes to criticize “formal theories of arithmetic” in Die Grundlagen der Arithmetik (1884) and the second volume of Grundgesetze der Arithmetik (1903)—G. Cantor, L. E. (...) J. Brouwer and D. Hilbert (1899). Part 2 is mainly devoted to Hilbert’s proof theory of the 1920s (1922–1931). I begin with an account of his early attempt to prove directly, and thus not by reduction or by constructing a model, the consistency of (a fragment of) arithmetic. In subsequent sections, I give a kind of overview of Hilbert’s metamathematics of the 1920s and try to shed light on a number of difficulties to which it gives rise. One serious difficulty that I discuss is the fact, widely ignored in the pertinent literature on Hilbert’s programme, that his language of finitist metamathematics fails to supply the conceptual resources for formulating a consistency statement qua unbounded quantification. Along the way, I shall comment on W. W. Tait’s objection to an interpretation of Hilbert’s finitism by Niebergall and Schirn, on G. Gentzen’s allegedly finitist consistency proof for Peano Arithmetic as well as his ideas on the provability and unprovability of initial cases of transfinite induction in pure number theory. Another topic I deal with is what has come to be known as partial realizations of Hilbert’s programme, chiefly advocated by S. G. Simpson. Towards the end of this essay, I take a critical look at Wittgenstein’s views about (in)consistency and consistency proofs in the period 1929–1933. I argue that both his insouciant attitude towards the emergence of a contradiction in a calculus and his outright repudiation of metamathematical consistency proofs are unwarranted. In particular, I argue that Wittgenstein falls short of making a convincing case against Hilbert’s programme. I conclude with some philosophical remarks on consistency proofs and soundness and raise a question concerning the consistency of analysis. (shrink)

The main purpose of this paper is to characterize and compare two forms any relativist thesis can take: indexical relativism and genuine relativism. Indexical relativists claim that the implicit indexicality of certain sentences is the only source of relativity. Genuine relativists, by contrast, claim that there is relativity not just at the level of sentences, but also at propositional level. After characterizing each of the two forms and discussing their difficulties, I argue that the difference between the two is significant.

The authors believe that the questions raised at the beginning of Frege’s On Sense and Reference – ‘Is [identity] a relation? A relation between objects, or between names or signs of objects?’ – set the course for a long-lasting but not at all satisfying discussion. For the disputants tend to advocate, either a ‘name-view’ of identity in a straightforward but rudimentary and logically untenable form, or else a version of an ‘object-view’ that makes all too light of the analysandum–analysans distinction (...) and hence is damned to analytical barrenness. In contrast, by unfolding the underlying idea of the original ‘name-view’, the authors offer three alternative and mutually compatible interpretations of identity that may best be characterized as the ‘name-based’, the ‘hybrid’ and the ‘sense-based’ variant of a ‘concept-view of identity’. At the same time, however, these interpretations may well be considered variants of a non-barren ‘object-view’. (shrink)

The unique relation between logic and truth is crucial for understanding Fregean conception of logic. Frege has an insight that the nature of logic resides in the “truth“, which he finally locates in the assertoric-force of a sentence. Though Frege admits that assertoric-force is ineffable in ordinary language, he coins in his conceptual notation for such a force a much-disputed sign, i.e., judgment-stroke. In this paper, I will try to demonstrate that judgment-stroke is not adequate for the task its inventor (...) has assigned to it. Accordingly, it is misconceived and inconducive to clarify Frege’s vague insight into the protorelation. The mistake of judgment-stroke for the sign of assertoric-force has its root in Frege’s ignorance of the significant difference between “judgment” and assertion”, which will be elucidated at length in the light of Husserl’s theory of “doxic-modification“. In the end, based on a further elucidation of the activity of assertion, I will advance a tentative interpretation of the vague insight Frege has concerning the protorelation. (shrink)

It has been noted before in the history of logic that some of Frege's logical and semantic views were anticipated in Stoicism. In particular, there seems to be a parallel between Frege's Gedanke (thought) and Stoic lekton; and the distinction between complete and incomplete lekta has an equivalent in Frege's logic. However, nobody has so far claimed that Frege was actually influenced by Stoic logic; and there has until now been no indication of such a causal connection. In this essay, (...) we attempt, for the first time, to provide detailed evidence for the existence of this connection. In the course of our argumentation, further analogies between the positions of Frege and the Stoics will be revealed. The classical philologist Rudolf Hirzel will be brought into play as the one who links Frege with Stoicism. The renowned expert on Stoic philosophy was Frege's tenant and lived in the same house as the logician for many years. In der Geschichte der Logik ist häufig bemerkt worden, dass einige der logischen und semantischen Auffassungen Freges in der Stoa antizipiert worden sind. Genannt wurden insbesondere die Parallelen zwischen dem Fregeschen Gedanken und dem stoischen Lekton sowie die Unterscheidung zwischen vollständigen und unvollständigen Lekta, die bei Frege ihre Entsprechung hat. Ein Wirkungszusammenhang ist allerdings nicht behauptet worden. Dazu gab es bislang auch keinen Anlass. Der vorliegende Beitrag versucht erstmalig, einen detaillierten Indizienbeweis für das Bestehen eines solchen Zusammenhangs vorzulegen. Dabei werden weitere charakteristische Übereinstimmungen zwischen Frege und der Stoa aufgewiesen. Als Mittelsmann wird der Altphilologe Rudolf Hirzel vorgestellt. Er wohnte lange Jahre als Mieter zusammen mit Frege im selben Haus und war ein anerkannter Experte der stoischen Philosophie. (shrink)

I attempt to explain Frege's handling of the Julius Caesar issue in terms of his more general philosophical commitments. These only became fully explicit in his middle-period writings, but his earlier moves are best explained, I suggest, if we suppose them to be implicit in his earlier thinking. These commitments conditionally justify Frege in rejecting Hume's Principle as either a definition or axiom but in accepting Axiom V. However, the general epistemological picture they constitute has serious problems in accounting for (...) how knowledge is possible at all of such propositions as that Julius Caesar is not a number. (shrink)

Michael Dummett has shown that the fragment ‘17 Kernsätze zur Logik’ is evidence that Frege knew Lotze's Logik Dummett’s dating of this fragment prior to 1879, however, must be rejected.The present paper shows that there are other articles of Frege’s which bear clear traces of Lotze's LogikFirst of all, the expressions Vorstellungsverlauf from ‘Über die wissenschaftliche Berechtigung einer Begriffsschrift’, and veranlassenden Ursachen, from ‘Logik’, certainly are borrowed from Lotze.Second, there are links between ‘Booles rechnende Logik und die Begriffsschrift’ and Lotze's (...) Logik. Furthermore, it is shown that Frege’s ‘Kernsätze’, the ‘Dialog mit Pünjer über Existenz’, and his ‘Logik’ are intimately connected.All of this indicates that these texts were written in roughly the same period, namely the early 1880s.Conclusive evidence for this is that the terms Vorstellung and Vorstellungsverbindung are used indiscriminately in both a psychological and a logical sense in the ‘Begriffsschrift’, a fact which contradicts the ‘Kernsätze’. (shrink)

Un trait du langage qui menace de saper la sûreté de la pensée est sa tendance à former des noms propres auxquels aucun objet ne correspond. [...] Un exemple particulièrement remarquable de cela est la formation d’un nom propre selon le schéma «l’extension du concept a», par exemple «l’extension du concept étoile». À cause de l’article défini, cette expression semble désigner un objet; mais il n’y a aucun objet pour lequel cette expression pour-rait être une désignation appropriée. De là les (...) paradoxes de la théorie des ensembles, qui ont porté un coup mortel à la théorie des ensembles elle-même. J’étais moi-même sous cette illusion quand afin de fournir une fondation logique aux nombres, j’ai tenté de construire les nombres comme des ensembles. (shrink)

There is a lot of misunderstanding and ignorance about Husserl’s philosophy among analytic philosophers. The present paper attempts to help correct that situation. It begins with some quotations of Husserl written around 1890, which clearly establish that he arrived at the distinction between sense and reference with independence from Frege. Then follows a brief survey of the most important themes of Husserl’s Logical Investigations, emphazising those that are of special interest to analytic philosophers. The paper concludes by mentioning other interesting (...) issues treated in later Husserlian writings, including his valuable conferences on ancient and modern logic from 1908-1909.Existen muchos malentendidos y mucha ignorancia acerca de la filosofía de Husserl entre los filósofos analíticos. El presente artículo intenta contribuir a corregir esa situacion. Él comienza con algunas citas de Husserl de aproximadamente 1890, que claramente establecen que Husserl obtuvo la distinción entre sentido y referente con independenica de Frege. Luego sigue un breve recuento de los más importantes temas de las Investigaciones Lógicas de Husserl, destacando aquéllos que son de particular interés para los filósofos analíticos. El artículo concluye haciendo référencia a otros temas tratados en escritos posteriores de Husserl, incluyendo sus valiosas conferencias acerca de lógica antigua y moderna de 1908-1909. (shrink)