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

One of the most important philosophical topics in the early twentieth century and a topic that was seminal in the emergence of analytic philosophy was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of (...) logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant. (shrink)

Benacerraf has presented two problems for the philosophy of mathematics. These are the problem of identification and the problem of representation. This paper aims to reconstruct the latter problem and to unpack its undermining bearing on the version of Ontic Structural Realism that frames scientific representations in terms of abstract structures. I argue that the dichotomy between mathematical structures and physical ones cannot be used to address the Benacerraf problem but strengthens it. I conclude by arguing that versions of OSR (...) that do not rely on mathematical frameworks for representational purposes need not be vulnerable to Benacerraf’s second problem. (shrink)

Michael Friedman’s Dynamics of Reason is a welcome contribution to the ongoing articulation of philosophical perspectives for understanding the sciences in the context of post-positivist philosophy of science. Two perspectives that have gained advocacy since the demise of the “received view” are Quinean naturalism and Kuhnian relativism. In his 1999 Stanford lectures, Friedman articulates and defends a neo-Kantian perspective for philosophy of science that opposes both of these perspectives. His proffered neo-Kantian perspective is presented within the context of the problem (...) of theory change or “scientific revolutions,” and its main feature is a conception of scientific knowledge that requires “relativized constitutive a priori principles.” The lectures make up the first part of the book; the second part of the book, “Fruits of Discussion,” is a further elaboration and defence of the ideas advanced in the lectures. The resulting book serves as a useful sequel to Friedman’s impressive historical studies in Foundations of Space-Time Theories, Kant and the Exact Sciences, and Reconsidering Logical Positivism. In the preface, Friedman tells us that this book represents the philosophical viewpoint that he has arrived at as a result of completing these works. As such, it is not surprising that the prominent themes of the book are ones that have occupied Friedman’s attention in the past, viz., the importance of a priori principles in the exact sciences, the conventionalism of the logical positivists, and, more generally, an articulation of what remains defensible in neo-Kantian philosophy of science. (shrink)

I present an argument for an interpretation of Kant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations of Kant's views on cognitive content, which ascribes to Kant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading of Kant put forward by McDowell and others, according to which Kant embraces a version of Russellianism, I argue that Kant's views on this topic (...) are of a much more Fregean bent than has traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp of Kant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non-conceptual content. (shrink)

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)

This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...) dominance principle. (shrink)

This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the formal sciences. (...) We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines. Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis. In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later. (shrink)

This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ (...) in his theory of axiomatics is presented. Specifically, it is shown that Carnap’s early model theory is based on a convention to simulate domain variation that is not identical but logically comparable to the modern account. (shrink)

In Untersuchungen zur allgemeinen Axiomatik and Abriss der Logistik, Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability. These attempts were largely unsuccessful, also in his own considered judgment. A detailed assessment of Carnap’s attempt shows, nevertheless, that his approach is much less confused and hopeless than it has often been made out to (...) be. By providing such a reassessment, the paper contributes to a reevaluation of Carnap’s contributions to the development of modern logic. (shrink)

This article aims to give an overview of Carnap's 1928 book Logical Structure of the World or Aufbau and the most influential interpretations of its significance. After giving an outline of the book in Section 2 , I turn to the first sustained interpretations of the book offered by Goodman and Quine in Section 3 . Section 4 explains how this empirical reductionist interpretation was largely displaced by its main competitor. This is the line of interpretation offered by Friedman and (...) Richardson which focuses on issues of objectivity. In Section 5 , I turn to two more recent interpretations that can be thought of as emphasizing Carnap's concern with rational reconstruction. Finally, the article concludes by noting some current work by Leitgeb that aims to develop and update some aspects of the Aufbau project for contemporary epistemology. (shrink)

The perennial question – What is meaning? – receives many answers. In this paper I present and discuss inferentialism – a recent approach to semantics based on the thesis that to have ( such and such ) a meaning is to be governed by ( such and such ) a cluster of inferential rules . I point out that this thesis presupposes that looking for meaning requires seeing language as a social institution (rather than, say, a psychological reality). I also (...) indicate that this approach may be seen as a new embodiment of the old ideas of structuralism. (shrink)

On the basis of historical and textual evidence, this paper claims that after his Tractatus, Wittgenstein was actually influenced by Einstein's theory of relativity and, the similarity of Einstein's relativity theory helps to illuminate some aspects of Wittgenstein's work. These claims find support in remarkable quotations where Wittgenstein speaks approvingly of Einstein's relativity theory and in the way these quotations are embedded in Wittgenstein's texts. The profound connection between Wittgenstein and relativity theory concerns not only Wittgenstein's “verificationist” phase , but (...) also Wittgenstein's later philosophy centred on the theme of rule‐following. (shrink)

German supporters of the Kantian philosophy in the late 19th century took one of two forks in the road: the fork leading to Baden, and the Southwest School of neo-Kantian philosophy, and the fork leading to Marburg, and the Marburg School, founded by Hermann Cohen. Between 1876, when Cohen came to Marburg, and 1918, the year of Cohen's death, Cohen, with his Marburg School, had a profound influence on German academia.

Hans Reichenbach’s position in the debate over scientific realism is remarkable. On the one hand, he endorsed the programmatic premises of logical empiricism; on the other, he explicitly employed a realist approach to conceptions such as reference, causality, and inference to the best explanation. How could that work out? It will be shown in the present paper that in Reichenbach’s view scientific realism is not, as frequently assumed, opposed to logical empiricism but rather to logical positivism. A distinction without a (...) difference? Not at all, at least for Reichenbach. As is well known, his particular—probabilistic—variant of logical empiricism was intended to circumvent what he considered the shortcomings of the Vienna Circle’s verificationist approach to the language of science. In Experience and Prediction, Reichenbach became most explicit in this regard. However, I shall argue that his position remained notoriously unstable in the end. It oscillated between a full-fledged scientific realist reading and an eminently pragmatist reading. Nevertheless, Reichenbach’s contribution proved instrumental in preparing subsequent efforts at reconciling logical empiricism and scientific realism. (shrink)

Helmholtz's theory of space had significant impact on Schlick's early ?critical realist? point of view. However, it will be argued in this paper that Schlick's appropriation of Helmholtz's ideas eventually lead to a rather radical transformation of the original Helmholtzian position.

We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind,and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our (...) main thesis is that Marburg neo-Kantian philosophy formulated a sophisticated position towards the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals, nor whiggishly subscribed to the new orthodoxy of the “great triumvirate” of Cantor, Dedekind, and Weierstrass that declared infinitesimals conceptus nongrati in mathematical discourse. Rather, following Cohen’s lead, the Marburg philosophers sought to clarify Leibniz’s principle of continuity, and to exploit it in making sense of infinitesimals and related concepts. (shrink)

In the course of the last few decades, Bolzano has emerged as an important player in accounts of the history of philosophy. This should be no surprise. Few authors stand at a more central junction in the development of modern thought. Bolzano's contributions to logic and the theory of knowledge alone straddle three of the most important philosophical traditions of the 19th and 20th centuries: the Kantian school, the early phenomenological movement and what has come to be known as analytical (...) philosophy. This paper identifies three Bolzanian theoretical innovations that warrant his inclusion in the analytical tradition: the commitment to ‘logical realism’, the adoption of a substitutional procedure for the purpose of defining logical properties and a new theory of a priori cognition that presents itself as an alternative to Kant's. All three innovations concur to deliver what counts as the most important development of logic and its philosophy between Aristotle and Frege. In the final part of the paper, I defend Bolzano against a common objection and explain that these theoretical innovations are also supported by views on syntax, which though marginal are both workable and philosophically interesting. (shrink)

The Laboratory of the Mindwas written with two purposes in mind. The first was to contribute to the growing literature on thought experiments with a selection of the most interesting examples of the genre. The second and much more ambitious purpose was to serve as a “first attempt at a rationalist interpretation of science”.

The paper argues that the theory of Implicit Definition cannot give an account of knowledge of logical principles. According to this theory, the meanings of certain expressions are determined such that they make certain principles containing them true; this is supposed to explain our knowledge of the principles as derived from our knowledge of what the expressions mean. The paper argues that this explanation succeeds only if Implicit Definition can account for our understanding of the logical constants, and that fully (...) understanding a logical constant in turn requires the ability to apply it correctly in particular cases. It is shown, however, that Implicit Definition cannot account for this ability, even if it draws on introduction rules for the logical constants. In particular, Implicit Definition cannot account for our ability to apply negation in particular cases. Owing to constraints relating to the unique characterisation of logical constants, invoking the notion of rejection does not remedy the situation. Given its failure to explain knowledge of logic, the prospects of Implicit Definition to explain other kinds of a priori knowledge are even worse. (shrink)

Electronic computers form an integral part of modern mathematical practice. Several high-profile results have been proven with techniques where computer calculations form an essential part of the proof. In the traditional philosophical literature, such proofs have been taken to constitute a posteriori knowledge. However, this traditional stance has recently been challenged by Mark McEvoy, who claims that computer calculations can constitute a priori mathematical proofs, even in cases where the calculations made by the computer are too numerous to be surveyed (...) by human agents. In this article we point out the deficits of the traditional literature that has called for McEvoy’s correction. We also explain why McEvoy’s defence of mathematical apriorism fails and we discuss how the debate over the epistemological status of computer-assisted mathematics contains several unfortunate conceptual reductions. (shrink)

This paper examines popular‘conventionalist’explanations of why philosophers need not back up their claims about how‘we’use our words with empirical studies of actual usage. It argues that such explanations are incompatible with a number of currently popular and plausible assumptions about language's ‘social’character. Alternate explanations of the philosopher's purported entitlement to make a priori claims about‘our’usage are then suggested. While these alternate explanations would, unlike the conventionalist ones, be compatible with the more social picture of language, they are each shown to (...) face serious problems of their own. (shrink)

According to Alberto Coffa in The Semantic Tradition from Kant to Carnap, Kant’s account of mathematical judgment is built on a ‘semantic swamp’. Kant’s primitive semantics led him to appeal to pure intuition in an attempt to explain mathematical necessity. The appeal to pure intuition was, on Coffa’s line, a blunder from which philosophy was forced to spend the next 150 years trying to recover. This dismal assessment of Kant’s contributions to the evolution of accounts of mathematical necessity is fundamentally (...) backward-looking. Coffa’s account of how semantic theories of the a priori evolved out of Kant’s doctrine of pure intuition rightly emphasizes those developments, both scientific and philosophical, that collectively served to undermine the plausibility of Kant’s account. What is missing from Coffa’s story, apart from any recognition of Kant’s semantic innovations, is an attempt to appreciate Kant’s philosophical context and the distinctive perspective from which Kant viewed issues in the philosophy of mathematics. When Kant’s perspective and context are brought out, he can not only be seen to have made a genuinely progressive contribution to the development of accounts of mathematical necessity, but also to be relevant to contemporary issues in the philosophy of mathematics in underappreciated ways. (shrink)

According to Alberto Coffa in The Semantic Tradition from Kant to Carnap, Kant’s account of mathematical judgment is built on a ‘semantic swamp’. Kant’s primitive semantics led him to appeal to pure intuition in an attempt to explain mathematical necessity. The appeal to pure intuition was, on Coffa’s line, a blunder from which philosophy was forced to spend the next 150 years trying to recover. This dismal assessment of Kant’s contributions to the evolution of accounts of mathematical necessity is fundamentally (...) backward-looking. Coffa’s account of how semantic theories of the a priori evolved out of Kant’s doctrine of pure intuition rightly emphasizes those developments, both scientific and philosophical, that collectively served to undermine the plausibility of Kant’s account. What is missing from Coffa’s story, apart from any recognition of Kant’s semantic innovations, is an attempt to appreciate Kant’s philosophical context and the distinctive perspective from which Kant viewed issues in the philosophy of mathematics. When Kant’s perspective and context are brought out, he can not only be seen to have made a genuinely progressive contribution to the development of accounts of mathematical necessity, but also to be relevant to contemporary issues in the philosophy of mathematics in underappreciated ways. (shrink)

Reichenbach emphasizes the central importance of prediction, which is—for him—the principal aim of science. This paper offers a critical reconstruction of his concept of prediction, taking into account the different periods of his thought. First, prediction is studied as a key factor in rejecting the positivism of the Vienna Circle. This part of the discussion concentres on the general features of prediction before Experience and Prediction (EP) (section 1). Second, prediction is considered in the context of Reichenbach's disagreements with his (...) contemporaries—Carnap and Popper—(section 2). Pointing out these differences gives an additional basis for understanding how Reichenbach saw “prediction” in the period when EP was written. Third, Reichenbach's theoretical framework of prediction is analysed following EP. This analysis studies the semantical, logical, epistemological and methodological bases of his concept of prediction (section 3). Fourth, Reichenbach's conception of prediction, based on an objectivist interpretation of probabilities, is compared with the perspective on prediction of subjective Bayesians (the present personalists). This comparison (section 4) illustrates Reichenbach's views regarding the links of prediction with probability. Fifth, innovations and elements of continuity after EP are noted which give a more complete picture of Reichenbach's thought on prediction (section 5). This contributes to a comprehensive characterization of his concept of prediction. Finally, there is an assessment of his whole view of the matter and a presentation of the ingredients for a satisfactory alternative (section 6). (shrink)

Frege’s account, according to which the problem of how thoughts are apprehended should be a part of psychology, has led scholars to the idea that every consideration regarding subjectivity is absent in this author. From the latter follows a certain way of conceiving the relation between Frege and Husserl which establishes an absolute chasm between both authors regarding the topic mentioned. In the present contribution an extremely different view is defended, namely, that Frege plays an intermediate role between 19th century (...) Platonism and husserlian phenomenology. The main focus of the argument is the commitment between naturalism and idealism which characterizes Platonism before Frege and the beginning of its overcoming carried out by him. (shrink)

The paper surveys different notions of implicit definition. In particular, we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such “structural definitions” can be semantically understood in two different ways, namely as specifications of the meaning of the primitive terms of a theory and as definitions of higher-order mathematical concepts or structures. We analyze these (...) two conceptions of structural definition both in the history of modern axiomatics and in contemporary philosophical debates. Based on that, we give a systematic assessment of the underlying semantics of these two ways of understanding the definiens of such definitions, by considering alternative model-theoretic and inferential accounts of meaning. (shrink)

This paper attempts to show how the logical empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as the initiator of a 19th century geometrical tradition, whose main protagonists were Helmholtz and Poincaré, the logical empiricists neglected the fact that Riemann’s revolutionary insight flourished instead in a non-geometrical tradition dominated by the works of Christoffel and Ricci-Curbastro roughly in the same years. I will argue that, in the attempt to interpret (...) general relativity as the last link of the chain Riemann–Helmholtz–Poincaré–Einstein, logical empiricists were led to argue that Einstein’s theory of gravitation mainly raised a problem of mathematical under-determination, i.e. the discovery that there are physical differences that cannot be expressed in the relevant mathematical structure of the theory. However, a historical reconstruction of the alternative Riemann–Christoffel–Ricci–Einstein line of evolution shows on the contrary that the main philosophical issue raised by Einstein’s theory was instead that of mathematical over-determination, i.e. the recognition of the presence of redundant mathematical differences that do not have any correspondence in physical reality. (shrink)

This paper compares the claims about our knowledge of the external world presented by Rudolf Carnap, in the book known as the Aufbau, to those of Clarence Irving Lewis, in Mind and the World-Order. This comparison is made in terms of the opposition to Kantian epistemology that both books establish; the Aufbau is regarded as the peak of the logicist tradition and Mind and the World-Order is taken in continuity with pragmatism. It is found that both books present knowledge of (...) the external world as a consequence of a structural organization of human experience. However, there is an important point of divergence: the concept of verification each author adopts is different, such a concept was even a matter of discussion between Lewis and the Vienna Circle. This paper shows this disagreement but also shows how Carnap changed his point of view in the decade after the Aufbau was published, towards a standpoint which is much closer to Lewis’s ideas. In that process, nevertheless, Carnap changed his focus and did not deal with the problem of the external world anymore. This paper also seeks to draw attention to some features of the relation between Carnap and the pragmatist tradition which have only recently started to attract interest. (shrink)

This paper discusses the neo-logicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neo-logicist school, present a generic form (...) of the Bad Company objection and introduce an epistemic issue connected to this general problem that will be the focus of the rest of the paper. In the third section, we present an alternative approach within philosophy of mathematics, a view that emerges from Hilbert's Grundlagen der Geometrie (1899, Leipzig: Teubner; Foundations of geometry (trans.: Townsend, E.). La Salle, Illinois: Open Court, 1959.). We will argue that Bad Company-style worries, and our concomitant epistemic issue, also affects this conception and other foundationalist approaches. In the following sections, we then offer various ways to address our epistemic concern, arguing, in the end, that none resolves the issue. The final section offers our own resolution which, however, runs against the foundationalist spirit of the Scottish neo-logicist program. (shrink)

This paper considers Kant's understanding of conceptual representation in light of his view of geometry.

Abstract: This article contends that the relation of early logical empiricism to Kant was more complex than is often assumed. It argues that Reichenbach's early work on Kant and Einstein, entitled The Theory of Relativity and A Priori Knowledge (1920) aimed to transform rather than to oppose Kant's Critique of Pure Reason. One the one hand, I argue that Reichenbach's conception of coordinating principles, derived from Kant's conception of synthetic a priori principles, offers a valuable way of accounting for the (...) historicity of scientific paradigms. On the other hand, I show that even Reichenbach, in line with Neo-Kantianism, associated Kant's view of synthetic a priori principles too closely with Newtonian physics and, consequently, overestimated the difference between Kant's philosophy and his own. This is even more so, I point out, in the retrospective account logical empiricism presented of its own history. Whereas contemporary reconstructions of this history, including Michael Friedman's, tend to endorse this account, I offer an interpretation of Kant's conception of a priori principles that contrasts with the one put forward by both Neo-Kantianism and logical empiricism. On this basis, I re-examine the early Reichenbach's effort to accommodate these principles to the paradigm forged by Einstein. (shrink)

My discussion addresses the differences between analytic and continental philosophy concerning the use of logic and exact reasoning in philosophical practice. These differences are mainly examined in the light of the controversial dominance of Hegel's concept of logic in twentieth-century continental philosophy. The inquiry is developed in two parts. In the first, I indicate some aspects of the analytic -continental divide, pointing to the role that the topic 'logic and philosophy' plays in it. In the second part, I give a (...) short account of the views of logic which are typical of the three main trends of continental philosophy. I also suggest how, with the aid of some typical analytical devices, some continental 'anti-logical' attitudes may be corrected, on their own terms. (shrink)

Alberto Coffa used the phrase "the Copernican turn in semantics" to denote a revolutionary transformation of philosophical views about the connection between the meanings of words and the acceptability of sentences and arguments containing those words. According to the new conception resulting from the Copernican turn, here called "the Copernican view", rules of use are constitutive of the meanings of words. This view has been linked with two doctrines: (A) the instances of meaning-constitutive rules are analytically and a priori true (...) or valid; (B) to grasp a meaning is to accept its rules. The pros and cons of different versions of the Copernican view, ascribable to Wittgenstein, Carnap, Gentzen, Dummett, Prawitz, Boghossian and other authors, will be weighed. A new version will be proposed, which implies neither (A) nor (B). (shrink)

The main focus of this paper ison ways in which Kantian philosophy can informproponents and opponents of constructivismalike. Kant was primarily concerned withreconciling natural and moral law. His approachto this general problematic was to limit andseparate what we can know about things(phenomena) from things as they are inthemselves (noumena), and to identify moralagency with the latter. Revisiting the Kantianproblematic helps to address and resolve longstanding epistemological concerns regardingconstructivism as an educational philosophy inrelation to issues of objectivity andsubjectivity, the limits of (...) theoretical andpractical reason, and the relation betweenhuman experience and the world. It also servesto address ethical concerns regardingliberation from limited self-interests andcontexts conditioned by localised beliefs andinclinations. In light of revisiting theKantian problematic, both Glasersfeld's radicalview of constructivism and Jardine's socialcritique of constructivism are found wanting.Beyond constructivism, Kant's distinctionbetween phenomena and noumena and the limits ofreason that follow from it are brieflyconsidered in terms of Merleau-Ponty's noveldouble-embodied notion of flesh as anontological primitive – as a matter of beingboth in, and of, the world – with an aim tomore intimate connections between epistemologyand ethics. (shrink)

Four Basic Logical Issues: The paper addresses what we see as the four major issues in logic. The overriding issue is that of the choice of logic. We start with some discussion of the preliminary issue of whether there is such a 'one true logic,' but we reserve the main discussion for the first issue of 'classical logic versus nonclassical logic.' Here, we discuss the role of meaning and truth, the relation between classical logic and classical negation, and whether and, (...) if so, how classical logic should reside at the base world. Given the argument in favor of an overall use of nonclassical logic, the second issue is that of the choice of nonclassical logic. Brady's logic MC of meaning containment is argued for, with some comparison made with other relevant logics. For the remaining two issues, we make a case for relevant deduction, in comparison with classical deduction, and we explore possibilities for the appropriate metalogic, comparing classical and nonclassical approaches. (shrink)

The relationship between Carnap’s Logical Syntax of Language and Wittgenstein’s Tractatus Logico-Philosophicus has been interpreted in several ways during past decades. One of the interpretations has gained keen advocates among Carnap scholars. It was originally provoked by what Caranp said in LSL, and it consists of two parts. First, it indicates that in TLP the possibility of speaking about the logical form of a language within the same language had been foresworn by Wittgenstein, but Carnap proved him wrong by producing (...) a book written exactly in the manner which had been proscribed by Wittgenstein. This is the debate about the possibility of speaking about logical form. Second, Wittgenstein’s dogmatism with regard to the existence of a unique correct grammar at the foundation of the language has been contrasted with Carnap’s open-mindedness in conceiving a boundless ocean of possibilities for constructing logical systems. Interestingly enough, Wittgenstein rambled with rage in reaction to Carnap’s view about the LSL-TLP relationship. But unlike Carnap’s view, which led to a dominant interpretation of the relationship, Wittgenstein’s testimony about the case has been strangely ignored in the history of analytic philosophy. In this paper, I try to make an inquiry about the grounds for Wittgenstein’s dissatisfaction with the Carnapian reading of the LSL-TLP relationship. I will show that Wittgenstein was not totally unfair in his judgment, and that some salient aspects of LSL could be best understood in the light, or rather the gloom, of TLP, and bear a significant resemblance to it. This, however, does not need to diminish the logical and historical significance of LSL. (shrink)

The ArgumentIn this paper I argue that Kuhn's and Hanson's notion of incommensurable paradigms is rooted in the rhetoric of finality of the Copenhagen dogma — the orthodox philosophical interpretation of quantum physics. I also argue that arguments for holism of a paradigm, on which the notion of the impossibility of its gradual modification is based, misinterpret the Duhem-Quine thesis. The history of science (Copernican, Chemical, and Quantum Revolutions) demonstrates fruitful selective appropriation of ideas from seemingly “incommensurable” paradigms (rather than (...) the impossibility of communication between their representatives). I argue in conclusion that such openness underlies scientific creativity, and that dialogue between different alternatives is indispensable for the growth of knowledge. (shrink)

In 1929 Carnap gave a paper in Prague on Investigations in General Axiomatics; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnap''s publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing (...) that it provides important insights intoCarnap''s development during this critical period, thetransition from Aufbau to Syntax,especially regarding the nature and motivation ofCarnap''s logicism. Moreover, we show how theAxiomatics influenced Carnap''s student Gödel inreaching the fundamental logical results that soonafterwards undermined Carnap''s project. (shrink)

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

This book proposes to identify three long-term structures in causal reasoning - in particular, in terms of the relationship between cause and identity - that appear to be of value in categorizing and organizing various trends in philosophical thought.<br>Such conceptual schemes involve a host of philosophical dilemmas (such as the problem of relativism), which are examined in the first chapter. A number of naturalistic and transcendental approaches to this problem are also analysed.<br>In particular, the book attempts to construct a theoretical (...) basis for Foucault's tripartite classification of epistemological structures in European thought.<br>The final chapter attempts to buttress the above schema by extending the analysis from cause and identity to growth, change, and stability, critiquing certain ideas of Foucault and Heidegger, as well as examining the contemporary thought of process philosophy and complexity theory.<br><br>Contents<br><br>Contents: Plurality and Causality - What is a Paradigm? - Paradigms and Causal Structure - Universality and Mathesis Universalis - Temporality and Visibility - Classical and Modern Probability Theory - The Environment and Non-Monotonicity - The Marburg School and the Limit Concept; Foucault's concept of 'Man' - Nineteenth Century Philosophy of Science - A Dynamic Model - Foucault and the Birth of the Clinic - Process, Growth and Complexity - Time and History. (shrink)

I raise a problem about the possibility of metaphysics originally raised by Kant: what explains the fact that the terms in our metaphysical theories (e.g. “property”) refer to entities and structures (e.g. properties) in the world? I distinguish a meta-metaphysical view that can easily answer such questions (“deflationism”) from a meta-metaphysical view for which this explanatory task is more difficult (which I call the “substantive” view of metaphysics). I then canvass responses that the substantive metaphysician can give to this Kantian (...) demand for an explanation of reference in metaphysics. I argue that these responses are either inadequate, or depend, implicitly or explicitly, on the idea of “joint carving”: carving at the joints is part of the explanation of reference-facts quite generally and our metaphysical terms in particular refer because they carve at the joints. I examine Ted Sider’s recent work on joint carving and structure and argue that it cannot fill the explanatory gap. I conclude that this is reason ceterus paribus to reject the substantive view of metaphysics. Kant’s critique, far from being obsolete, applies to the most cutting-edge of contemporary meta-metaphysical views. (shrink)