This two-volume work, first published in 1843, was John Stuart Mill's first major book. It reinvented the modern study of logic and laid the foundations for his later work in the areas of political economy, women's rights and representative government. In clear, systematic prose, Mill disentangles syllogistic logic from its origins in Aristotle and scholasticism and grounds it instead in processes of inductive reasoning. An important attempt at integrating empiricism within a more general theory of human knowledge, the work constitutes (...) essential reading for anyone seeking a full understanding of Mill's thought. Continuing the discussion of induction, Volume 2 concludes with Book VI, 'On the Logic of the Moral Sciences', in which Mill applies empirical reasoning to human behaviour. A crucial early formulation of his thinking regarding free will and necessity, this book establishes the centrality of 'the social science' to Mill's philosophy. (shrink)

1. Readers of Hume, even those who call attention to the depth and variety of his skeptical excursions, now happily admit that Hume is, in crucial respects, a “naturalist.” A naturalist is, broadly, someone who emphasizes the natural sources of our beliefs, attitudes, and practices; and Hume surely is at least this kind of naturalist. But understanding Hume’s naturalism to include only this general explanatory commitment obscures as much as it reveals, I will argue, about the text of Treatise I (...) iv, where Hume examines various skeptical “systems of philosophy.” To understand that part of the Treatise, we must, I will argue, understand Hume’s shifting allegiances to different kinds of naturalism. (shrink)

This lucid book is the first to be wholly dedicated to Hume's theory of personal identity, and presents a bold new interpretation which bears directly on ...

Color provides an instance of a general puzzle about how to reconcile the picture of the world given to us by our ordinary experience with the picture of the world given to us by our best theoretical accounts. The Red and the Real offers a new approach to such longstanding philosophical puzzles about what colors are and how they fit into nature. It is responsive to a broad range of constraints --- both the ordinary constraints of color experience and the (...) more theoretical constraints of color science, psychology, semantics, and ontology. (shrink)

The philosophy of mathematics has long been an important part of philosophy in the analytic tradition, ever since the pioneering works of Frege and Russell. Richard Dedekind was roughly Frege's contemporary, and his contributions to the foundations of mathematics are widely acknowledged as well. The philosophical aspects of those contributions have been received more critically, however. In the present essay, Dedekind's philosophical reception is reconsidered. At the essay’s core lies a comparison of Frege's and Dedekind's legacies, within and outside of (...) analytic philosophy. While the comparison proceeds historically, it is shaped by current philosophical concerns, especially by debates about neo-logicist and neo-structuralist views. In fact, philosophical and historical considerations are intertwined thoroughly, to the benefit of both. The underlying motivation is to rehabilitate Dedekind as a major philosopher of mathematics, in relation, but not necessarily in opposition, to Frege. (shrink)

Written for advanced undergraduates, physicists, and historians and philosophers of physics, this book tells the story of the development of our understanding of quantum phenomena through the extraordinary years of the first three decades of the twentieth century. Rather than following the standard axiomatic approach, this book adopts a historical perspective, explaining clearly and authoritatively how pioneers such as Heisenberg, Schrodinger, Pauli and Dirac developed the fundamentals of quantum mechanics and merged them into a coherent theory, and why the mathematical (...) infrastructure of quantum mechanics has to be as complex as it is. The author creates a compelling narrative, providing a remarkable example of how physics and mathematics work in practice. The book encourages an enhanced appreciation of the interaction between mathematics, theory and experiment, helping the reader gain a deeper understanding of the development and content of quantum mechanics than any other text at this level. (shrink)

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

Books reviewed: Piers Benn, Ethics Alexander Miller, Philosophy Of Language Michael Stanford, An Introduction to the Philosophy of History.

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)

In this paper, I assess recent claims in philosophy of science about scientific perspectivism being compatible with realism. I clarify the rationale for scientific perspectivism and the problems and challenges that perspectivism faces in delivering a form of realism. In particular, I concentrate my attention on truth, and on ways in which truth can be understood in perspectival terms. I offer a cost-benefit analysis of each of them and defend a version that in my view is most promising in living (...) up to realist expectations. (shrink)

A complete reappraisal of the philosophical meaning of Everett's interpretation of quantum mechanics is carried out, by analysing carefully the role of the concept of "observer" in physics. It is shown that Everett's interpretation is the limiting case of a series of conceptions of the measurement problem which leave less and less of the observer out of the quantum description of the measuring interaction. This limiting case, however, should not be considered as one wherein nothing is left outside the description. (...) Something is still needed besides this description: pure cognitive capacity, the subject, or, in a very abstract sense: "mind". The set of branches which arise, according to Everett, from a measuring interaction, gain a renewed signification. They do not refer to distinct "worlds", but to the points of view "mind" can identify itself to. This idea is compared and contrasted with Squires' "selection" of a branch by the mind (without quotation marks). Finally, the notion of indeterminism in quantum mechanics gains an unexpected and new light from a strict application of the previous ideas. (shrink)

Of all the major philosophical works, Kant's Critique of Pure Reason is one of the most rewarding, yet one of the most difficult. Norman Kemp Smith's Commentary elucidates not only textural questions and minor issues, but also the central problems which arise, he contends, from the conflicting tendencies of Kant's own thinking. Kemp Smith's Commentary continues to be in demand with Kant scholars, and it is being reissued here with a new introduction by Sebastian Gardner to set it in its (...) contemporary context. (shrink)

Buch 1. Geschichte des Materialismus bis auf Kant.--Buch 2. Geschichte des Materialismus seit Kant.

Dieses historische Buch kann zahlreiche Tippfehler und fehlende Textpassagen aufweisen. Kaufer konnen in der Regel eine kostenlose eingescannte Kopie des originalen Buches vom Verleger herunterladen (ohne Tippfehler). Ohne Indizes. Nicht dargestellt. 1910 edition. Auszug:...endliche als durch sie erzeugt; oder diese in jener involviert und aus ihr sich evolvierend. Der wahre Erzeuger der endlichen Grosse ist nicht die unendlichkleine" Grosse (das Unendlichkleine ware dem Grossenwert nach vielmehr Null), sondern es ist das Gesetz der Grosse (als Veranderlicher), das man sich nun wie (...) in einen Punkt zusammengezogen, d. h. fur den einzelnen Punkt ausgedruckt, oder an einer endlichen Erstreckung sich darstellend denken kann, das aber dem letzten Sachgehalt nach dasselbe ist fur den Punkt und die endliche Erstreckung, wenn es auch in Bezug auf beide verschiedene, im allgemeinen auseinander ableitbare Ausdrucke erhalten muss. Da aber die endliche Grosse uberhaupt von Punkt zu Punkt entstehend (d. h. veranderlich) gedacht wird, so ist insofern der punktuelle, d. h. infinitesimale Ausdruck der fundamentale, aus dem der extensionale gleichsam erst hervorwachst. Die Differenz entsteht eben von der Null an; nicht aus ihr; aus Null wird keine extensive Grosse; wohl aber von der Null, d. h. dem Nichtsein dessen, was werden soll, oder ganz schlicht1) vom Ausgangs wert an; woraus? Aus dem Gesetz; eine andere Antwort ist nicht zu geben und nicht zu verlangen. Durch dies Gesetz aber ist die Grosse als Eines, Identisches, im Unterschied von den sukzessiven Grossenwerten, also in ihrem Gattungsausdruck definiert. i) Vgl. oben S. 122. Fragt man also: wie soll aus der Null gewordenen, verschwundenen" Grosse die endliche Grosse wiederentstehen? so ist zu antworten: die Grosse zwar (yuantitas). (shrink)

The physiologist Johannes Müller’s doctrine of specific nerve energies had a decisive influence on neo-Kantian conceptions of the objectivity of knowledge in the 1850s - 1870s. In the first half of the nineteenth century, Müller amassed a body of experimental evidence to support his doctrine, according to which the character of our sensations is determined by the structures of our own sensory nerves, and not by the external objects that cause the sensations. Neo-Kantians such as Hermann von Helmholtz, F.A. Lange, (...) and Otto Liebmann took Müller’s doctrine to have far-reaching consequences for their epistemologies. Over the course of the 1850s - 1870s, these three neo-Kantians, each in his own way, argued that reflection on Müller’s doctrine ruled out a certain conception of the objectivity of knowledge. It ruled out the view that knowledge is objective in virtue of affording us information about objects in a mind-independent external world. -/- This paper traces how Helmholtz, Lange, and Liebmann developed their arguments for this view, and how each developed his own alternative conception of objectivity, according to which objectivity has nothing to do with a mind-independent world. Finally, the paper concludes by considering why these arguments modelled on Müller’s doctrine would have been so powerful against rival post-Hegelian conceptions of objectivity, especially those of scientific materialists like Ludwig Büchner. (shrink)

Both Frege's Grundgesetze, and Lagrange's treatises on analytical functions pursue a foundational purpose. Still, the former's program is not only crucially different from the latter's. It also depends on a different idea of what foundation of mathematics should be like . Despite this contrast, the notion of function plays similar roles in their respective programs. The purpose of my paper is emphasising this similarity. In doing it, I hope to contribute to a better understanding of Frege's logicism, especially in relation (...) to its crucial differences with a set-theoretic foundational perspective. This should also spread some light on a question arisen by J. Hintikka and G. Sandu in a widely discussed paper, namely whether Frege should or should not be credited with the notion of arbitrary function underlying our standard interpretation of second-order logic. In section 1, I account for Lagrange's notion of function. In section 2, I advance some remarks on connected historical matters. This will provide an appropriate framework for discussing the role played by the notion of function in Frege's Grundgesetze. Section 3 is devoted to this. Some concluding remarks will close the paper. (shrink)

This chapter recounts the rise, eminence, and rapid fall in the philosophical standing of Sir William Hamilton. It sets out the philosophical resources that Hamilton called upon to amend and sustain the ‘common sense’ philosophy of Thomas Reid, responding especially to the criticisms of Thomas Brown. It examines in detail the criticisms that were brought against his philosophy from both sympathizers and opponents. Special attention is given to books on Hamilton published in the nineteenth by Henry Calderwood, Hutchison Stirling, and (...) most notably J. S. Mill’s hugely influential ‘Examination’ of Hamilton. The chapter aims to explain both the high regard in which Hamilton was widely held and the reasons for his speedy relegation to the status of a minor philosopher. It also aims at a ‘Re-examination’ by assessing the cogency of Mill’s criticisms. (shrink)

Die Allgemeine Erkenntnislehre gilt als das Hauptwerk von Moritz Schlick. Hierin entwickelt Schlick in Auseinandersetzung mit zeitgenössischen Positionen seine einflussreichen Gedanken zum Wesen der Erkenntnis, zum Verhältnis zwischen Psychologie und Logik, zum Leib-Seele-Problem und zum erkenntnistheoretischen Realismusstreit. Der Text wurde während der frühen Rostocker Jahre Schlicks, von 1911 bis 1916, verfasst. Die Allgemeine Erkenntnislehre ist ein Meilenstein der wissenschaftlichen Philosophie und grundlegend für die spätere Entwicklung des Wiener Kreises des Logischen Empirismus.

"The Analysis of Matter" is one of the earliest and best philosophical studies of the new physics of relativity and quantum mechanics.

A key to modern studies of 18th century Western philosophy, the Treatise considers numerous classic philosophical issues, including causation, existence, freedom and necessity and morality. This abridged edition has an introduction which explain's Hume's thought and places it in the context of its times.

Histories of German philosophy in the nineteenth century typically focus on its first half--when Hegel, idealism, and Romanticism dominated. By contrast, the remainder of the century, after Hegel's death, has been relatively neglected because it has been seen as a period of stagnation and decline. But Frederick Beiser argues that the second half of the century was in fact one of the most revolutionary periods in modern philosophy because the nature of philosophy itself was up for grabs and the very (...) absence of certainty led to creativity and the start of a new era. In this innovative concise history of German philosophy from 1840 to 1900, Beiser focuses not on themes or individual thinkers but rather on the period's five great debates: the identity crisis of philosophy, the materialism controversy, the methods and limits of history, the pessimism controversy, and the Ignorabimusstreit. Schopenhauer and Wilhelm Dilthey play important roles in these controversies but so do many neglected figures, including Ludwig Büchner, Eugen Dühring, Eduard von Hartmann, Julius Fraunstaedt, Hermann Lotze, Adolf Trendelenburg, and two women, Agnes Taubert and Olga Pluemacher, who have been completely forgotten in histories of philosophy. The result is a wide-ranging, original, and surprising new account of German philosophy in the critical period between Hegel and the twentieth century. (shrink)

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such (...) later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism. (shrink)

This book offers a new interpretation of Hermann von Helmholtz's work on the epistemology of geometry. A detailed analysis of the philosophical arguments of Helmholtz's Erhaltung der Kraft shows that he took physical theories to be constrained by a regulative ideal. They must render nature "completely comprehensible", which implies that all physical magnitudes must be relations among empirically given phenomena. This conviction eventually forced Helmholtz to explain how geometry itself could be so construed. Hyder shows how Helmholtz answered this question (...) by drawing on the theory of magnitudes developed in his research on the colour-space. He argues against the dominant interpretation of Helmholtz's work by suggesting that for the latter, it is less the inductive character of geometry that makes it empirical, and rather the regulative requirement that the system of natural science be empirically closed. (shrink)

Is color real or illusory, mind independent or mind dependent? Does seeing in color give us a true picture of external reality? The metaphysical debate over color has gone on at least since the seventeenth century. In this book, M. Chirimuuta draws on contemporary perceptual science to address these questions. Her account integrates historical philosophical debates, contemporary work in the philosophy of color, and recent findings in neuroscience and vision science to propose a novel theory of the relationship between color (...) and physical reality. -/- Chirimuuta offers an overview of philosophy’s approach to the problem of color, finds the origins of much of the familiar conception of color in Aristotelian theories of perception, and describes the assumptions that have shaped contemporary philosophy of color. She then reviews recent work in perceptual science that challenges philosophers’ accounts of color experience. Finally, she offers a pragmatic alternative whereby perceptual states are understood primarily as action-guiding interactions between a perceiver and the environment. The fact that perceptual states are shaped in idiosyncratic ways by the needs and interests of the perceiver does not render the states illusory. Colors are perceiver-dependent properties, and yet our awareness of them does not mislead us about the world. Colors force us to reconsider what we mean by accurately presenting external reality, and, as this book demonstrates, thinking about color has important consequences for the philosophy of perception and, more generally, for the philosophy of mind. (shrink)

One of Hume's most well-known works and a masterpiece of philosophy, A Treatise of Human Nature is indubitably worth taking the time to read.

Hume's Treatise Book III appendix on personal identity is analyzed as concerned with a difficulty not with the Book I account of personal identity as such (the self as product of associational imagination) but a presupposition of that account: the succession of perceptions present to consciousness (which the imagination associates, thus giving to the fiction of an identity). It is then claimed that while Hume's theory of imagination offers no way out of quandary, Kantian imagination-based transcendental idealism does.

There has been considerable recent debate about whether Kant's account of intuitions implies that their content is conceptual. This debate, however, has failed to make significant progress because of the absence of discussion, let alone consensus, as to the meaning of ‘content’ in this context. Here I try to move things forward by focusing on the kind of content associated with Frege's notion of ‘sense ’, understood as a mode of presentation of some object or property. I argue, first, that (...) Kant takes intuitions to have a content in this sense, and, secondly, that Kant clearly takes the content of intuitions, so understood, to be distinct in kind from that possessed by concepts. I then show how my account can respond to the most serious objections to previous non-conceptualist interpretations.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.The Non-Conceptuality of the Content of Intuitions: A New ApproachVolume 18, Issue 1Clinton Tolley DOI: https://doi.org/10.1017/S1369415412000313Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. The Non-Conceptuality of the Content of Intuitions: A New ApproachVolume 18, Issue 1Clinton Tolley DOI: https://doi.org/10.1017/S1369415412000313Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. The Non-Conceptuality of the Content of Intuitions: A New ApproachVolume 18, Issue 1Clinton Tolley DOI: https://doi.org/10.1017/S1369415412000313Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation. (shrink)

Discussions of the applicability of mathematics in the natural sciences have been flawed by failure to realize that there are multiple senses in which mathematics can be ‘applied’ and, correspondingly, multiple problems that stem from the applicability of mathematics. I discuss semantic, metaphysical, descriptive, and and epistemological problems of mathematical applicability, dwelling on Frege's contribution to the solution of the first two types. As for the remaining problems, I discuss the contributions of Hartry Field and Eugene Wigner. Finally, I argue (...) that there are epistemological problems concerning the applicability of mathematics that nobody in the philosophical community has yet confronted, though the problems are well known to physicists. (shrink)

According to the ‘One Object’ reading of Kant's transcendental idealism, the distinction between the appearance and the thing in itself is not a distinction between two objects, but between two ways of considering one and the same object. On the ‘Metaphysical’ version of the One Object reading, it is a distinction between two kinds of properties possessed by one and the same object. Consequently, the Metaphysical One Object view holds that a given appearance, an empirical object, is numerically identical to (...) the thing in itself that appears as that object. I raise various indiscernibility arguments against that view; because an appearance has different spatiotemporal and modal properties than a thing in itself, no appearance can be identical to a thing in itself. I point out that these arguments are similar to arguments against Monism, the view that material objects are numerically identical to the matter of which they are made. I outline some strategies Monists have developed to respond to these indiscernibility arguments and then develop parallel responses on behalf of the Metaphysical One Object view. However, I then raise another indiscernibility argument, to which, I argue, the Metaphysical One Object view cannot respond, even using the resources I have developed thus far. I develop a modified version of the Metaphysical One Object view that can respond to this new indiscernibility argument, but, I argue, this modified version of the One Object view is only a terminological variant of the Two Object view. When the Metaphysical One Object view is fully thought through it becomes the Two Object view. I conclude that Kantian appearances are not numerically identical to the things in themselves that appear to us. (shrink)

1. Readers of Hume, even those who call attention to the depth and variety of his skeptical excursions, now happily admit that Hume is, in crucial respects, a “naturalist.” A naturalist is, broadly, someone who emphasizes the natural sources of our beliefs, attitudes, and practices; and Hume surely is at least this kind of naturalist. But understanding Hume’s naturalism to include only this general explanatory commitment obscures as much as it reveals, I will argue, about the text of Treatise I (...) iv, where Hume examines various skeptical “systems of philosophy.” To understand that part of the Treatise, we must, I will argue, understand Hume’s shifting allegiances to different kinds of naturalism. (shrink)

This paper uses neo-Fregean-style abstraction principles to develop the integers from the natural numbers (assuming Hume’s principle), the rational numbers from the integers, and the real numbers from the rationals. The first two are first-order abstractions that treat pairs of numbers: (DIF) INT(a,b)=INT(c,d) ≡ (a+d)=(b+c). (QUOT) Q(m,n)=Q(p,q) ≡ (n=0 & q=0) ∨ (n≠0 & q≠0 & m⋅q=n⋅p). The development of the real numbers is an adaption of the Dedekind program involving “cuts” of rational numbers. Let P be a property (of (...) rational numbers) and r a rational number. Say that r is an upper bound of P, written P≤r, if for any rational number s, if Ps then either s<r or s=r. In other words, P≤r if r is greater than or equal to any rational number that P applies to. Consider the Cut Abstraction Principle: (CP) ∀P∀Q(C(P)=C(Q) ≡ ∀r(P≤r ≡ Q≤r)). In other words, the cut of P is identical to the cut of Q if and only if P and Q share all of their upper bounds. The axioms of second-order real analysis can be derived from (CP), just as the axioms of second-order Peano arithmetic can be derived from Hume’s principle. The paper raises some of the philosophical issues connected with the neo-Fregean program, using the above abstraction principles as case studies. (shrink)

The paper investigates Ernst Cassirer’s structuralist account of geometrical knowledge developed in his Substanzbegriff und Funktionsbegriff. The aim here is twofold. First, to give a closer study of several developments in projective geometry that form the direct background for Cassirer’s philosophical remarks on geometrical concept formation. Specifically, the paper will survey different attempts to justify the principle of duality in projective geometry as well as Felix Klein’s generalization of the use of geometrical transformations in his Erlangen program. The second aim (...) is to analyze the specific character of Cassirer’s geometrical structuralism formulated in 1910 as well as in subsequent writings. As will be argued, his account of modern geometry is best described as a “methodological structuralism”, that is, as a view mainly concerned with the role of structural methods in modern mathematical practice. (shrink)

An appreciation of Hume’s psychology of object identity allows us to recognize certain tensions in his discussion of the origin of our belief in personal identity---tensions which have gone largely unnoticed in the secondary literature. This will serve to provide a new solution to the problem of explaining why Hume finds that discussion of personal identity so problematic when he famously disavows it in the Appendix to the Treatise. It turns out that the two psychological mechanisms which respectively generate the (...) ideas of object and of personal identity are mutually incompatible. It is this sort of conflict within Hume’s introspective or subjectivist psychology which is the source of his worry. (shrink)

This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of mathematics--the view that mathematics (...) is about things that really exist. (shrink)

Various contributors to recent philosophy of mathematics havetaken Richard Dedekind to be the founder of structuralismin mathematics. In this paper I examine whether Dedekind did, in fact, hold structuralist views and, insofar as that is the case, how they relate to the main contemporary variants. In addition, I argue that his writings contain philosophical insights that are worth reexamining and reviving. The discussion focusses on Dedekind''s classic essay Was sind und was sollen die Zahlen?, supplemented by evidence from Stetigkeit und (...) irrationale Zahlen, his scientific correspondence, and his Nachlaß. (shrink)