In recent years, the so-calledindispensability argument has been given a lotof attention by philosophers of mathematics.This argument for the existence of mathematicalobjects makes use of the fact, neglected inclassical schools of philosophy of mathematics,that mathematics is part of our best scientifictheories, and therefore should receive similarsupport to these theories. However, thisobservation raises the question about the exactnature of the alleged connection betweenexperience and mathematics (for example: is itpossible to falsify empirically anymathematical theorems?). In my paper I (...) wouldlike to address this question by consideringthe explicit assumptions of different versionsof the indispensability argument. My primaryclaim is that there are at least three distinctversions of the indispensability argument (andit can be even suggested that a fourth,separate version should be formulated). I willmainly concentrate my discussion on thisvariant of the argument, which suggests thepossibility of empirical confirmation ofmathematical theories. A large portion of mypaper will focus on the recent discussion ofthis topic, starting from the paper by E.Sober, who in my opinion put reasonablerequirements on what is to be counted as anempirical confirmation of a mathematicaltheory. I will develop his model into threeseparate scenarios of possible empiricalconfirmation of mathematics. Using an exampleof Hilbert space in quantum mechanicaldescription I will show that the most promisingscenario of empirical verification ofmathematical theories has neverthelessuntenable consequences. It will be hypothesizedthat the source of this untenability lies in aspecific role which mathematical theories playin empirical science, and that what is subjectto empirical verification is not themathematics used, but the representabilityassumptions. Further I will undertake theproblem of how to reconcile the allegedempirical verification of mathematics withscientific practice. I will refer to thepolemics between P. Maddy and M. Resnik,pointing out certain ambiguities of theirarguments whose source is partly the failure todistinguish carefully between different sensesof the indispensability argument. For thatreason typical arguments used in the discussionare not decisive, yet if we take into accountsome metalogical properties of appliedmathematics, then the thesis that mathematicshas strong links with experience seems to behighly improbable. (shrink)

Imre Lakatos' views on the philosophy of mathematics are important and they have often been underappreciated. The most obvious lacuna in this respect is the lack of detailed discussion and analysis of his 1976a paper and its implications for the methodology of mathematics, particularly its implications with respect to argumentation and the matter of how truths are established in mathematics. The most important themes that run through his work on the philosophy of mathematics and which culminate (...) in the 1976a paper are (1) the (quasi-)empirical character of mathematics and (2) the rejection of axiomatic deductivism as the basis of mathematical knowledge. In this paper Lakatos' later views on the quasi-empirical nature of mathematical theories and methodology are examined and specific attention is paid to what this view implies about the nature of mathematical argumentation and its relation to the empirical sciences. (shrink)

This thesis presents and criticizes Hilary Putnam's argument that mathematics is as empirical as science, in particular the argument that the switch from Euclidean geometry to Riemannian geometry as the approporiate geometry for physical space constituted an instance of revising mathematics as a result of observation. The thesis explains Putnam's views on mathematics as following from his theory of meaning and reference for natural kind terms. It is argued that Putnam's account of reference is unsuitable for mathematical (...) terms and that an "if-thenist" approach to mathematical knowledge is more fruitful. (shrink)

Penelope Maddy's original solution to the dilemma posed by Benacerraf in his 'Mathematical Truth' was to reconcile mathematical empiricism with mathematical realism by arguing that we can perceive realistically construed sets. Though her hypothesis has attracted considerable critical attention, much of it, in my view, misses the point. In this paper I vigorously defend Maddy's account against published criticisms, not because I think it is true, but because these criticisms have functioned to obscure a more fundamental issue that is (...) well worth addressing: in general -- and not only in the mathematical domain -- empiricism and realism simply cannot be reconciled by means of an account of perception anything like Maddy's. But because Maddy's account of perception is so plausible, this conclusion raises the specter of the broader incompatibility of realism and empiricism, which contemporary philosophers are frequently at pains to forget. (shrink)

Husserl's contributions to the nature of mathematical knowledge are opposed to the naturalist, empiricist and pragmatist tendences that are nowadays dominant. It is claimed that mainstream tendences fail to distinguish the historical problem of the origin and evolution of mathematical knowledge from the epistemological problem of how is it that we have access to mathematical knowledge.

Any philosophy of science ought to have something to say about the nature of mathematics, especially an account like constructive empiricism in which mathematical concepts like model and isomorphism play a central role. This thesis is a contribution to the larger project of formulating a constructive empiricist account of mathematics. The philosophy of mathematics developed is fictionalist, with an anti-realist metaphysics. In the thesis, van Fraassen's constructive empiricism is defended and various accounts of mathematics (...) are considered and rejected. Constructive empiricism cannot be realist about abstract objects; it must reject even the realism advocated by otherwise ontologically restrained and epistemologically empiricist indispensability theorists. Indispensability arguments rely on the kind of inference to the best explanation the rejection of which is definitive of constructive empiricism. On the other hand, formalist and logicist anti-realist positions are also shown to be untenable. It is argued that a constructive empiricist philosophy of mathematics must be fictionalist. Borrowing and developing elements from both Philip Kitcher's constructive naturalism and Kendall Walton's theory of fiction, the account of mathematics advanced treats mathematics as a collection of stories told about an ideal agent and mathematical objects as fictions. The account explains what true portions of mathematics are about and why mathematics is useful, even while it is a story about an ideal agent operating in an ideal world; it connects theory and practice in mathematics with human experience of the phenomenal world. At the same time, the make-believe and game-playing aspects of the theory show how we can make sense of mathematics as fiction, as stories, without either undermining that explanation or being forced to accept abstract mathematical objects into our ontology. All of this occurs within the framework that constructive empiricism itself provides the epistemological limitations it mandates, the semantic view of theories, and an emphasis on the pragmatic dimension of our theories, our explanations, and of our relation to the language we use. (shrink)

Rudolf Carnap’s formative years as a philosopher were his time in Jena where he studied mathematics, physics, and philosophy, among others, with Gottlob Frege, the neo-Kantian Bruno Bauch, and Herman Nohl, a pupil of Wilhelm Dilthey.2 Whereas both the influence of Frege and of the neo-Kantians is quite well known,3 the importance of the Dilthey school for Carnap’s intellectual development was recently highlighted by scholars, such as Gottfried Gabriel and Hans-Joachim Dahms.4 Although Carnap himself was interested mainly in the (...) problems of logic and the philosophy of the natural sciences, the community in which he worked until he went to Vienna in 1926 was neither a community of neo-Kantian philosophers nor of logicians or philosophers of the natural sciences but a community of members of the Dilthey school that were interested in history of philosophy,5 pedagogic,6 aesthetics,7 and sociology.8 Carnap and his friends were all members of the so-called Seracircle, a group of young people that met frequently in Jena and, between 1919 and 1926, also in Carnap’s home in Buchenbach near Freiburg.9 The first version of the Aufbau was written in close connection with this group of young people that were interested in a reform of the whole society, including arts, politics, sciences, and everyday life. In Carnap’s Werkstatt in Buchenbach, the Aufbau and at least two more manifestos of a more or less philosophical nature were written: Franz Roh’s “Nach-Expressionismus” and Wilhelm Flitner’s “Laienbildung.”10 Given these historical facts, we must conclude that the Aufbau is the product of an intellectual enterprise that developed in close connection with the Dilthey school, but in which Frege and the neo-Kantians seem to have played only a small role. (shrink)

Rudolf Carnap’s formative years as a philosopher were his time in Jena where he studied mathematics, physics, and philosophy, among others, with Gottlob Frege, the neo-Kantian Bruno Bauch, and Herman Nohl, a pupil of Wilhelm Dilthey.2 Whereas both the influence of Frege and of the neo-Kantians is quite well known,3 the importance of the Dilthey school for Carnap’s intellectual development was recently highlighted by scholars, such as Gottfried Gabriel and Hans-Joachim Dahms.4 Although Carnap himself was interested mainly in the (...) problems of logic and the philosophy of the natural sciences, the community in which he worked until he went to Vienna in 1926 was neither a community of neo-Kantian philosophers nor of logicians or philosophers of the natural sciences but a community of members of the Dilthey school that were interested in history of philosophy ,5 pedagogic ,6 aesthetics ,7 and sociology .8 Carnap and his friends were all members of the so-called Seracircle, a group of young people that met frequently in Jena and, between 1919 and 1926, also in Carnap’s home in Buchenbach near Freiburg.9 The first version of the Aufbau was written in close connection with this group of young people that were interested in a reform of the whole society, including arts, politics, sciences, and everyday life. In Carnap’s Werkstatt in Buchenbach, the Aufbau and at least two more manifestos of a more or less philosophical nature were written: Franz Roh’s “Nach-Expressionismus” and Wilhelm Flitner’s “Laienbildung.”10 Given these historical facts, we must conclude that the Aufbau is the product of an intellectual enterprise that developed in close connection with the Dilthey school, but in which Frege and the neo-Kantians seem to have played only a small role. (shrink)

The aim of this paper is to provide a unified account of scientific and mathematical change in a thoroughly empiricist setting. After providing a formal modelling in terms of embedding, and criticising it for being too restrictive, a second modelling is advanced. It generalises the first, providing a more open-ended pattern of theory development, and is articulated in terms of da Costa and French's partial structures approach. The crucial component of scientific and mathematical change is spelled out in terms of (...) partial embeddings. Finally, an application of this second pattern is made, with the examination of the early formulation of set theory. (shrink)

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This `foundational debate' in computer science, mathematics and physics was already fully developed in (...) 1930 in the Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics. (shrink)

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This `foundational debate' in computer science, mathematics and physics was already fully developed in (...) 1930 in the Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics. (shrink)

Wittgenstein’s ‘ethnological approach’ to the philosophy of mathematics, in particular his discussion of calculation as an experiment and the limits of empiricism in mathematics, is presented against three interrelated backdrops: (1) James’ critique of Spencer’s evolutionary empiricism, specifically regarding necessary truths; (2) the Cambridge Anthropological Expedition to Torres Straits, led by Haddon and Rivers, whose Reports implicitly confuted Spencer; and (3) the subsequent work of Malinowski, especially his supplement to Ogden and Richards’ The Meaning of Meaning, (...) a book sent to Wittgenstein upon its publication in 1923. String figures as mathematics is a main illustrative example. (shrink)

David Hume is the most influential precursor of modern empiri cism. By modern empiricism, I intend a belief that all cognitive conflicts can be resolved, in principle, by either appeal to matters offact, via scientific procedure, or by appeal to some sets of natural or conventional standards, whether linguistic, mathematical, aes thetic or political. This belief itself is a consequent of an old appre hension that all synthetic knowledge is based on experience, and that the rest can be reduced (...) to a set of self-evident truths. In this broad sense, Modern Empiricism encompasses classes, such as Logi cal Empiricism, Logical Atomism and Philosophical Analysis, and unique individuals such as Russell and Moore. It excludes, thereby, the present day continental philosophies, such as Thomism, Exist entialism, and Dialectical Materialism. Modern empiricists, to be sure, are influenced by many other phi losophers. Locke, Berkeley, and Mill, among the classical empiri cists, and Leibniz and Kant, among the rationalists (the former especially on the logico-mathematical side) in one way or other are responsible for the appearance of empiricism in its new form. But none of them were as influential as Hume. This, by itself is not news. Weinberg, in his well-known book, An Examination of Logical Positivism, observes that: Many, if not all, of the principal doctrines of contemporary positivism derive from Hume. (shrink)

The work of Jacques Derrida is often characterized as anti-scientific, and his philosophy of language taken to mean we are sealed off from empirical reality, confined to our metaphysical prison. This position is reinforced by the fact that his forerunners, Heidegger and Nietzsche, did diminish the importance of the sciences, and argued that we are enclosed within the limits of language. Today, philosophy continues to deconstruct the nature/culture distinction, and challenge the meaning of materialism, but in recent decades has realized (...) that this work requires, in addition to a critique of the modern concept of science, a rehabilitation of the sciences outside their metaphysical definition. The fact that Derrida continues to be understood as an anti-science thinker has led to the exclusion of his work from this project. In this paper, I show that Derrida, while deconstruction the metaphysical concepts of science, nature and empiricism, in fact takes the mathematical sciences as an important force of deconstructing, and develops an interpretation of empiricism that points to a non-metaphysical understanding of it. From this perspective, Derrida's work is useful for thinking through the relation of the human to language and nature in the age of globalization and anthropogenic climate change. (shrink)

Contemporary philosophy often chants the mantra, ‘Philosophy is continuous with science.’ Now Shepanski gives it a clear sense, by extracting from W. V. Quine’s writings an explicit normative epistemology – i.e. an explicit set of norms for theorizing – that applies to philosophy and science alike. It is recognizably a version of empiricism, yet it permits the kind of philosophical theorizing that Quine practised all his life. Indeed, it is that practice, more than any overt avowals, that justifies attributing (...) this set of norms to Quine. -/- The Quinean epistemology is supported by a metaphilosophy that judges epistemologies by the tenability of their consequences. Shepanski explores the Quinean epistemology’s consequences for inductive and abductive inference, for mathematical entities, for science and for common sense. Moreover, he finds that it continues to be fruitful, as illustrated by a case study in which Quinean methods lead to a new formal treatment of the propositional attitudes. Finally, there is critical discussion of popular alternative views, including foundationalism, the centrality of knowledge, and Quine’s own epistemological naturalism. -/- By focusing on Quine’s normative epistemology, Shepanski illuminates a part of Quine’s thought that has hitherto been insufficiently discussed, and provides a tractable starting point for readers who are new to Quine. Most importantly, he isolates the part of Quine’s thought that has the greatest potential impact outside epistemology, outside philosophy of language, and even outside philosophy. (shrink)

The aim of this paper is to take Galileo's mathematization of nature as a springboard for contrasting the time-honoured empiricist conception of phenomena, exemplified by Pierre Duhem's analysis in To Save the Phenomena , with Immanuel Kant's. Hence the purpose of this paper is twofold. I) On the philosophical side, I want to draw attention to Kant's more robust conception of phenomena compared to the one we have inherited from Duhem and contemporary empiricism. II) On the historical side, I (...) want to show what particular aspects of Galileo's mathematization of nature find a counterpart in Kant's conception of phenomena.------------------------------------------------------------------------------------------ ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- --------------------------------------------------. (shrink)

This paper attempts to explain the emergence of the logical empiricist philosophy of space and time as a collision of mathematical traditions. The historical development of the ``Riemannian'' and ``Helmholtzian'' traditions in 19th century mathematics is investigated. Whereas Helmholtz's insistence on rigid bodies in geometry was developed group theoretically by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag triggered Christoffel's and Lipschitz's work on quadratic differential forms, paving the way to Ricci's absolute differential calculus. The transition from special to general (...) relativity is briefly sketched as a process of escaping from the Helmholtzian tradition and entering the Riemannian one. Early logical empiricist conventionalism, it is argued, emerges as the failed attempt to interpret Einstein's reflections on rods and clocks in general relativity through the conceptual resources of the Helmholtzian tradition. Einstein's epistemology of geometry should, in spite of his rhetorical appeal to Helmholtz and Poincaré, be understood in the wake the Riemannian tradition and of its aftermath in the work of Levi-Civita, Weyl, Eddington, and others. (shrink)

Steve Awodey and A. W. Carus. The Turning Point and the Revolution: Philosophy of Mathematics in Logical Empiricism from Tractatus on Logical Syllogism.

This abridged and revised edition of the original book (Springer-Verlag Vienna, 2001) offers the only comprehensive history and documentation of the Vienna Circle based on new sources with an innovative historiographical approach to the study of science. With reference to previously unpublished archival material and more recent literature, it refutes a number of widespread clichés about "neo-positivism" or "logical positivism". Following some insights on the relation between the history of science and the philosophy of science, the book offers an accessible (...) introduction to the complex subject of "the rise of scientific philosophy" in its socio-cultural background and European philosophical networks till the forced migration in the Anglo-Saxon world. The first part of the book focuses on the origins of Logical Empiricism before World War I and the development of the Vienna Circle in "Red Vienna" (with the "Verein Ernst Mach"), its fate during Austro-Fascism (Schlick's murder 1936) and its final expulsion by National-Socialism beginning with the "Anschluss" in 1938. It analyses the dynamics of the Schlick-Circle in the intellectual context of "late enlightenment" including the minutes of the meetings from 1930 on for the first time published and presents an extensive description of the meetings and international Unity of Science conferences between 1929 and 1941. The chapters introduce the leading philosophers of the Schlick Circle (e.g., Hans Hahn, Otto Neurath, Rudolf Carnap, Philipp Frank, Felix Kaufmann, Edgar Zilsel) and describe the conflicting interaction between Moritz Schlick and Otto Neurath, the long term communication between Moritz Schlick, Friedrich Waismann and Ludwig Wittgenstein, as well as between the Vienna Circle with Heinrich Gomperz and Karl Popper. In addition, Karl Menger's "Mathematical Colloquium" with Kurt Gödel is presented as a parallel movement. The final chapter of this section describes the demise of the Vienna Circle and the forced exodus of scientists and intellectuals from Austria.The second part of the book includes a bio-bibliographical documentation of the Vienna Circle members and for the first time of the assassination of Moritz Schlick in 1936, followed by an appendix comprising an extensive list of sources and literature. (shrink)

At once a distinguished mathematician and an important figure in the Vienna Circle, Hans Hahn conducted a seminar in 1924-25 on the Principia Mathematica to "a very large audience" of mathematicians and philosophers. Translated from the German and edited by Brian McGuinness, with a biographical introduction by Karl Menger, the present volume consists largely of papers in the philosophy of mathematics covering the years 1929-34. "Our adoption of Russell’s position," writes Hahn, "may cause some surprise in Germany where all (...) ears are tuned, to the controversy between... Hilbert and Brouwer." It turns out, however, that Wittgenstein has made the decisive move: mathematics consists of tautologies, Russell having "shown" how to get by without sets. (shrink)

The present paper deals with the ontological status of numbers and considers Frege ́s proposal in Grundlagen upon the background of the Post-Kantian semantic turn in analytical philosophy. Through a more systematic study of his philosophical premises, it comes to unearth a first level paradox that would unset earlier still than it was exposed by Russell. It then studies an alternative path, that departin1g from Frege’s initial premises, drives to a conception of numbers as synthetic a priori in a more (...) Kantian sense. On this basis, it tentatively explores a possible derivation of basic logical rules on their behalf, suggesting a more rudimentary basis to inferential thinking, which supports reconsidering the difference between logical thinking and AI. Finally, it reflects upon the contributions of this approach to the problem of the a priori. (shrink)

In _Aristotle’s Empiricism_, Jean De Groot argues that an important part of Aristotle’s natural philosophy has remained largely unexplored and shows that much of Aristotle’s analysis of natural movement is influenced by the logic and concepts of mathematical mechanics that emerged from late Pythagorean thought. De Groot draws upon the pseudo-Aristotelian_ Physical Problems_ XVI to reconstruct the context of mechanics in Aristotle’s time and to trace the development of kinematic thinking from Archytas to the Aristotelian _Mechanics_. She shows the influence (...) of kinematic thinking on Aristotle’s concept of power or potentiality, which she sees as having a physicalistic meaning originating in the problem of movement. De Groot identifies the source of early mechanical knowledge in kinesthetic awareness of mechanical advantage, showing the relation of Aristotle’s empiricism to more ancient experience. The book sheds light on the classical Greek understanding of imitation and device, as it questions both the claim that Aristotle’s natural philosophy codifies opinions held by convention and the view that the cogency of his scientific ideas depends on metaphysics. (shrink)

This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal (...) science, mathematical ontology: what does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is. The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies. (shrink)

In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, (...) there was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level. (shrink)

Introduction: mathematization and the language of nature -- Realists and nominalists : language and mathematics before the scientific revolution -- Ontology recapitulates epistemology : Gassendi, epicurean atomism, and nominalism -- British empiricism, nominalism, and constructivism -- Three mathematicians : constructivist epistemology and the new mathematical methods -- Conclusion: mathematization and the nature of language.

Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. We also show (...) that some of what mathematicians take to be deductive knowledge is in fact non-deductive. 1 Introduction2 Why It Might Matter3 Two Further Examples and Preliminaries4 An Exclusive Epistemic Virtue of Proof?5 Analyses of Knowledge6 The Inductive Basis of Deduction7 Physical to Mathematical Linkages8 Conclusion. (shrink)

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

Computational methods such as computer simulations, Monte Carlo methods, and agent-based modeling have become the dominant techniques in many areas of science. Extending Ourselves contains the first systematic philosophical account of these new methods, and how they require a different approach to scientific method. Paul Humphreys draws a parallel between the ways in which such computational methods have enhanced our abilities to mathematically model the world, and the more familiar ways in which scientific instruments have expanded our access to the (...) empirical world. This expansion forms the basis for a new kind of empiricism, better suited to the needs of science than the older anthropocentric forms of empiricism. Human abilities are no longer the ultimate standard of epistemological correctness.Humphreys also includes arguments for the primacy of properties rather than objects, the need to consider technological constraints when appraising scientific methods, and a detailed account of how the path from computational template to scientific application is constructed. This last feature allows us to hold a form of selective realism in which anti-realist arguments based on formal reconstructions of theories can be avoided. One important consequence of the rise of computational methods is that the traditional organization of the sciences is being replaced by an organization founded on computational templates.Extending Ourselves will be of interest to philosophers of science, epistemologists, and to anyone interested in the role played by computers in modern science. (shrink)

"Understanding Empiricism" is an introduction to empiricism and the empiricist tradition in philosophy. The book presents empiricism as a philosophical outlook that unites several philosophers and discusses the most important philosophical issues bearing on the subject, while maintaining enough distance from, say, the intricacies of Locke, Berkeley, Hume scholarship to allow students to gain a clear overview of empiricism without being lost in the details of the exegetical disputes surrounding particular philosophers. Written for students the book (...) can serve both as an introduction to current problems in the theory of knowledge as well as a comprehensive survey of the history of empiricist ideas. The book begins by distinguishing between the epistemological and psychological/causal versions of empiricism, showing that it is the former that is of primary interest to philosophers. The next three chapters, on Locke, Berkeley, Hume respectively, provide an introduction to the main protagonists in the British empiricist tradition from this perspective. The book then examines more contemporary material including the ideas of Sellars, foundations and coherence theories, the rejection of the a priori by Mill, Peirce and Quine, scepticism and, finally, the status of religious belief within empiricism. Particular attention is paid to criticisms of empiricism, such as Leibniz's criticisms of Locke on innatism and Frege's objections to Mill on mathematics. The discussions are kept at an introductory level throughout to help students to locate the principles of empiricism in relation to modern philosophy. (shrink)

"Understanding Empiricism" is an introduction to empiricism and the empiricist tradition in philosophy. The book presents empiricism as a philosophical outlook that unites several philosophers and discusses the most important philosophical issues bearing on the subject, while maintaining enough distance from, say, the intricacies of Locke, Berkeley, Hume scholarship to allow students to gain a clear overview of empiricism without being lost in the details of the exegetical disputes surrounding particular philosophers. Written for students the book (...) can serve both as an introduction to current problems in the theory of knowledge as well as a comprehensive survey of the history of empiricist ideas. The book begins by distinguishing between the epistemological and psychological/causal versions of empiricism, showing that it is the former that is of primary interest to philosophers. The next three chapters, on Locke, Berkeley, Hume respectively, provide an introduction to the main protagonists in the British empiricist tradition from this perspective. The book then examines more contemporary material including the ideas of Sellars, foundations and coherence theories, the rejection of the a priori by Mill, Peirce and Quine, scepticism and, finally, the status of religious belief within empiricism. Particular attention is paid to criticisms of empiricism, such as Leibniz's criticisms of Locke on innatism and Frege's objections to Mill on mathematics. The discussions are kept at an introductory level throughout to help students to locate the principles of empiricism in relation to modern philosophy. (shrink)

Kant contends that necessity is a criterion of the a priori—that is, that all knowledge of necessary propositions is a priori. This contention, together with two others that Kant took to be evident—we know some mathematical propositions and such propositions are necessary—leads directly to the conclusion that some knowledge is a priori. Although many contemporary philosophers endorse Kant’s criterion, supporting arguments are hard to come by. Gordon Barnes provides one of the few examples. My purpose in this chapter is to (...) articulate and examine his argument. I have two goals in doing so. The first is to uncover several significant gaps in the argument. The second is to show that it suffers from a common defect in rationalist arguments. If the argument were successful against empiricist accounts of modal knowledge, it would apply with equal force to extant rationalist accounts of such knowledge. Hence, the cost of refuting modal empiricism is modal scepticism. (shrink)

The central idea of Lakatos’ quasi-empiricism view of the philosophy of mathematics is that truth values are transmitted bottom-up, but only falsity can be transmitted from basic statements. As it is falsity but not truth that flows bottom-up, Lakatos emphasizes that observation and induction play no role in both conjecturing and proving phases in mathematics. In this paper, I argue that Lakatos’ view that one cannot obtain primitive conjectures by induction contradicts the history of mathematics, and (...) therefore undermines his quasi-empiricism theory. I argue that his misconception of induction causes this view of Lakatos. Finally, I propose that Wittgenstein’s view that “mathematics does have a grammatical nature, but it is also rooted in empirical regularities” suggests the possibility to improve Lakatos’ view by maintaining his quasi-empiricism while accepting the role induction plays in the conjecturing phase. (shrink)

Empiricism in philosophy is either a method or a theory. The two are separable: one might hold that all knowledge is empirical but that philosophy does something other than add to our knowledge, e.g., that it clarifies concepts; or one might hold that philosophy’s method is empirical and that one of the things known in that way is that not all knowledge is empirical, e.g., mathematics. And what is the empirical? If it is knowledge based on observation, then (...) what is it that can be observed? If philosophy is in method empirical, the range of the observable must be broad, perhaps including mental processes, human history, social institutions such as language, and even the difference between good and evil.In Peirce’s... (shrink)

Empiricism has traditionally been concerned with two questions: What is the source of our concepts and ideas? and How should claims to empirical knowledge be judged? The empiricist answer to the first question is ‘From observation or experience.’ The concern in the second question is not to ground science in pure observation or in direct experience, but rather to ensure that claims to scientific knowledge are judged against the natural phenomena themselves. Questions about nature must be settled by nature (...) — not by faith, nor metaphysics, nor mathematics, and not by convention or convenience either. From Francis Bacon to Karl Popper empiricists have wanted to police the methods of scientific enquiry. (shrink)

David Hume is the most influential precursor of modern empiri cism. By modern empiricism, I intend a belief that all cognitive conflicts can be resolved, in principle, by either appeal to matters off act, via scientific procedure, or by appeal to some sets of natural or conventional standards, whether linguistic, mathematical, aes thetic or political. This belief itself is a consequent of an old appre hension that all synthetic knowledge is based on experience, and that the rest can be (...) reduced to a set of self-evident truths. In this broad sense, Modern Empiricism encompasses classes, such as Logi cal Empiricism, Logical Atomism and Philosophical Analysis, and unique individuals such as Russell and Moore. It excludes, thereby, the present day continental philosophies, such as Thomism, Exist entialism, and Dialectical Materialism. Modem empiricists, to be sure, are influenced by many other phi losophers. Locke, Berkeley, and Mill, among the classical empiri cists, and Leibniz and Kant, among the rationalists (the former especially on the logico-mathematical side) in one way or other are responsible for the appearance of empiricism in its new form. But none of them were as influential as Hume. This, by itself is not news. Weinberg, in his well-known book, An Examination of Logical Positivism, observes that: Many, if not all, of the principal doctrines of contemporary positivism derive from Hume. (shrink)

This paper is in two parts. The first presents an analysis of the epistemology underlying the practice of classical Indian mathematical astronomy, as presented in three works of Nīlakaṇṭha Somayāji (1444–1545 CE). It is argued that the underlying concepts put great value on careful observation and skill in development of algorithms and use of computation. This is reflected in the technical terminology used to describe scientific method. The keywords in this enterprise include parīkṣā, anumāna, gaṇita, yukti, nyāya, siddhānta, tarka and (...) anveṣaṇa. The concepts that underlie these terms are analysed and compared with such ideas as theory, model, computation, positivism, empiricism etc. In a short second part, it is proposed that the primacy awarded to number and computation in classical Indian science led to an artificial language that did include equations but emphasized displays that facilitated calculation, as in the Bakshali manuscript (800 CE?). It is further argued that echoes of these concepts can be recognized in current science, where computation is once again playing a greater role triggered by spectacular developments in computer technology. (shrink)