Even though Husserl and Brouwer have never discussed each other's work, ideas from Husserl have been used to justify Brouwer's intuitionistic logic. I claim that a Husserlian reading of Brouwer can also serve to justify the existence of choice sequences as objects of pure mathematics. An outline of such a reading is given, and some objections are discussed.
Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But (...) other mathematicians and philosophers have been voicing objections to choice sequences from the start. This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl. (shrink)
Quine claims that holism (i.e., the Quine-Duhem thesis) prevents us from defining synonymy and analyticity (section 2). In Word and Object, he dismisses a notion of synonymy which works well even if holism is true. The notion goes back to a proposal from Grice and Strawson and runs thus: R and S are synonymous iff for all sentences T we have that the logical conjunction of R and T is stimulus-synonymous to that of S and T. Whereas Grice and Strawson (...) did not attempt to defend this definition, I try to show that it indeed gives us a satisfactory account of synonymy. Contrary to Quine, the notion is tighter than stimulus-synonymy – particularly when applied to sentences with less than critical semantic mass (section 3). Now according to Quine, analyticity could be defined in terms of synonymy, if synonymy were to make sense: A sentence is analytic iff synonymous to self-conditionals. This leads us to the following notion of analyticity: S is analytic iff, for all sentences T, the logical conjunction of S and T is stimulus-synonymous to T; an analytic sentence does not change the semantic mass of any theory to which it may be conjoined (section 4). This notion is tighter than Quine's stimulus-analyticity; unlike stimulus-analyticity, it does not apply to those sentences from the very center of our theories which can be assented to come what may, even though they are not synthetic in the intuitive sense (section 5). Conclusion: We can have well-defined notions of synonymy and analyticity even if we embrace Quine's holism, naturalism, behaviorism, and radical translation. Quine's meaning skepticism is to be repudiated on Quinean grounds. (shrink)
Marcin Lewinski: Internet Political Discussion Forums as an Argumentative Activity Type. A Pragma-dialectical Analysis of Online Forms of Strategic Manoeuvring in Reacting Critically Content Type Journal Article Pages 255-259 DOI 10.1007/s10503-011-9201-3 Authors Paul van den Hoven, Utrecht University, Utrecht, The Netherlands Journal Argumentation Online ISSN 1572-8374 Print ISSN 0920-427X Journal Volume Volume 25 Journal Issue Volume 25, Number 2.
Erratum to: Book Symposium on Peter Paul Verbeek’s Moralizing Technology: Understanding and Designing the Morality of Things . Chicago: University of Chicago Press, 2011 Content Type Journal Article Category Erratum Pages 1-27 DOI 10.1007/s13347-011-0058-z Authors Evan Selinger, Dept. Philosophy, Rochester Institute of Technology, Rochester, NY, USA Don Ihde, Dept. Philosophy, Stony Brook University, Stony Brook, NY, USA Ibo van de Poel, Delft University of Technology, Delft, the Netherlands Martin Peterson, Eindhoven University of Technology, Eindhoven, the Netherlands Peter-Paul Verbeek, (...) Dept. Philosophy, Twente University, Enschede, the Netherlands Journal Philosophy & Technology Online ISSN 2210-5441 Print ISSN 2210-5433. (shrink)
Jean Wagemans: Redelijkheid en overredingskracht van argumentatie. Een historisch-filosofische studie over de combinatie van het dialectische en het retorische perspectief op argumentatie in de pragma-dialectische argumentatietheorie (Reasonableness and Persuasiveness of Argumentation. An Historical-Philosophical Study on the Combination of the Dialectical and Rhetorical Perspective on Argumentation in the Pragma-Dialectical Argumentation Theory) Content Type Journal Article Pages 123-125 DOI 10.1007/s10503-010-9197-0 Authors Paul Gillaerts, Lessius University College, Antwerp, Belgium Journal Argumentation Online ISSN 1572-8374 Print ISSN 0920-427X Journal Volume Volume 25 Journal Issue (...) Volume 25, Number 1. (shrink)
In this paper, I argue against Peter van Inwagen’s claim (in “Free Will Remains a Mystery”), that agent-causal views of free will could do nothing to solve the problem of free will (specifically, the problem of chanciness). After explaining van Inwagen’s argument, I argue that he does not consider all possible manifestations of the agent-causal position. More importantly, I claim that, in any case, van Inwagen appears to have mischaracterized the problem in some crucial ways. Once we are clear on (...) the true nature of the problem of chanciness, agent-causal views do much to eradicate it. (shrink)
I. Introduction “We can and do see the truth about many things: ourselves, others, trees and animals, clouds and rivers—in the immediacy of experience.”1 Absent from Bas van Fraassen’s list of those things we see are paramecia and mitochondria. We do not see such things, van Fraassen has long maintained, because they are unobservable, that is, they are undetectable by means of the unaided senses.2 But notice that these two notions—what we can see in the “immediacy” of experience and what (...) is detectable by means of the unaided senses—are not the same. There is no incoherence in maintaining that the immediacy of experience is capable of disclosing to us truths concerning entities that are not detectable by the naked eye. And so, I claim, it does; science and technology provide us with the means to see things we have never seen before. Some of those things are van Fraassen’s unobservables. That suggestion is nothing new. Grover Maxwell long ago emphasized the continuity between seeing with and without instrumentation.3 Van Fraassen originally provided two responses to Maxwell’s arguments: some things that you can see with instruments you can also see without instruments (and those are the observables); and.. (shrink)
The anti-reductionist who wants to preserve the causal efficacy of mental phenomena faces several problems in regard to mental causation, i.e. mental events which cause other events, arising from her desire to accept the ontological primacy of the physical and at the same time save the special character of the mental. Psychology tries to persuade us of the former, appealing thereby to the results of experiments carried out in neurology; the latter is, however, deeply rooted in our everyday actions and (...) beliefs and despite the constant opposition of science still very much alive. Difficulties, however, arise from a combination of two claims that are widely accepted in philosophy of mind, namely, physical monism and mental realism, the acceptance of which leads us to the greatest problem of mental causation: the problem of causal exclusion. Since physical causes alone are always sufficient for physical effects mental properties are excluded from causal explanations of our behaviour, which makes them “epiphenomenal”. The article introduces Van Gulick’s solution to the exclusion problem which tries to prove that physical properties, in contrast to mental properties, do not have as much of a privileged status with respect to event causation as usually ascribed. Therefore, it makes no sense to say that physical properties are causally relevant whereas mental properties are not. This is followed by my objection to his argument for levelling mental and physical properties with respect to causation of events. I try to show that Van Gulick’s argument rests on a premise that no serious physicalist can accept. (shrink)
Van Heijenoort’s main contribution to history and philosophy of modern logic was his distinction between two basic views of logic, first, the absolutist, or universalist, view of the founding fathers, Frege, Peano, and Russell, which dominated the first, classical period of history of modern logic, and, second, the relativist, or model-theoretic, view, inherited from Boole, Schröder, and Löwenheim, which has dominated the second, contemporary period of that history. In my paper, I present the man Jean van Heijenoort (Sect. 1); then (...) I describe his way of arguing for the second view (Sect. 2); and finally I come down in favor of the first view (Sect. 3). There, I specify the version of universalism for which I am prepared to argue (Sect. 3, introduction). Choosing ZFC to play the part of universal, logical (in a nowadays forgotten sense) system, I show, through an example, how the usual model theory can be naturally given its proper place, from the universalist point of view, in the logical framework of ZFC; I outline another, not rival but complementary, semantics for admissible extensions of ZFC in the very same logical framework; I propose a way to get universalism out of the predicaments in which universalists themselves believed it to be (Sect. 3.1). Thus, if universalists of the classical period did not, in fact, construct these semantics, it was not that their universalism forbade them, in principle, to do so. The historical defeat of universalism was not technical in character. Neither was it philosophical. Indeed, it was hardly more than the victory of technicism over the very possibility of a philosophical dispute (Sect. 3.2). (shrink)
Søren Kierkegaard used his literary, philosophical, and theological voice to reintroduce Christianity to Christendom. In this effort, he repeatedly uses the Apostle Paul’s first letter to the church in Corinth. Though some have noted the importance of 1 Corinthians for Kierkegaard, they have not explained this importance nor this letter’s role in Kierkegaard’s corpus. This essay seeks to fill this gap in Kierkegaard scholarship by explaining the role this letter plays in Kierkegaard’s Climacean authorship. Paul’s battle with the (...) Corinthian view of wisdom and Kierkegaard’s battle with Hegelian philosophy, which seeks to go beyond faith through speculative thinking, share similarities that engender both their works. In their battles with their respective foes, both develop a Christocentric epistemology that displaces the import of human understanding and cognitive content with the person Jesus who inverts their opponents’ epistemic values by salvifically redefining wisdom and knowledge. This epistemology of a different kind is an offense, foolishness, and absurd to their opponents because it cannot be intellectually grasped by human understanding, but rather in and through the passion of faith, which places the individual in relation with Jesus. For both authors, this relation is the essential point for the Christian life. (shrink)
Van Heijenoort’s account of the historical development of modern logic was composed in 1974 and first published in 1992 with an introduction by his former student. What follows is a new edition with a revised and expanded introduction and additional notes.
The paper aims at drawing the main lines of a reflection about architectonic space, starting from the comparison between two hypothesis, as much as ever different: Theodor Lipps’ spatial aesthetics and Hans van der Laan’s elemental theory. The emphasis given by both authors to the intersection between directions and way, but also to the mutual subordination between thing and space, allows to rewrite the obituary of architecture as a spatial art, according to which the Modern Style has turned the spatiality (...) into its specular visibility, into the spaciousness, into the indefinite continuity of the Bigness. (shrink)
Since the first volume appeared in 2005, the collection Controversies has brought together pieces of work related to the field of argumentation, giving particular attention to those that are concerned with theoretical and practical problems connected with discursive controversy and confrontation. Authors such as P. Barrotta, M. Dascal, S. Frogel, H. Chang and D. Walton had already either edited or written previous editions to the present volume (volume six) of the collection. F. H. van Eemeren and B. Garssen (the former (...) has already, with P. Houtlosser, edited the second volume of this collection) are responsible for compiling and editing this collection. In this volume Van Eemeren and Garssen edit works they conceive as being akin to those elements which, in argumentation discourse, serve to resolve – or often to present – differences of opinion. However, it should be added that this is not a mere editing job, but rather the result of an intellectual collaboration between two international research groups dedicated to a common field – consisting, on the one hand, of controversies and, on the other, of argumentation. (shrink)
http://dx.doi.org/10.5007/1808-1711.2008v12n1p49 The aim of this article is to offer a rejoinder to an argument against scientific realism put forward by van Fraassen, based on theoretical considerations regarding microphysics. At a certain stage of his general attack to scientific realism, van Fraassen argues, in contrast to what realists typically hold, that empirical regularities should sometimes be regarded as “brute facts”, which do not ask for explanation in terms of deeper, unobservable mechanisms. The argument from microphysics formulated by van Fraassen is based (...) on the claim that in microphysics the demand for explanation leads to a demand for the so-called hidden-variable theories, which “runs contrary to at least one major school of thought in twentieth-century physics”. It is shown here that this argument does not represent an insurmountable obstacle to scientific realism, not even when a series of important theoretical and experimental results against hidden-variable theories — and not merely a conflict with a certain school of thought—is taken into account. (shrink)
http://dx.doi.org/10.5007/1808-1711.2008v12n2p121 O objetivo deste trabalho é discutir e desenvolver o diagnóstico que efetua van Fraassen (1987, p. 110) da lei de Hardy-Weinberg, de acordo coo qual esta: 1) não pode ser considerada uma lei a ser utilizada como un axioma da teoria genética de populações, pois é uma lei de equilíbrio que só vale sob certas condições especiais, 2) só determina uma subclasse de modelos, 3) sua generalização resulta vácua e 4) variantes complexas da lei podem ser deduzidas para pressupostos (...) mais realistas. A discussão e desenvolvimento deste diagnóstico será levada a cabo tomando como base noções propostas por outra das concepções semânticas afim daquela desenvolvida por van Fraassen, a saber: a concepção estruturalista das teorias, e uma reconstrução da genética clássica de populações no marco de uma tal metateoria, também apresentada neste trabalho. (shrink)
De acordo com a concepção dominante de causação, eventos espácio-temporalmente localizáveis que podem ser designados por termos singulares e descrições definidas são os únicos relata genuínos da relação causal. Isto dá apoio e é apoiado pela dicotomia aceita entre a explicação causal, concebida como uma relação intensional entre fatos ou verdades, e a relação natural e extensional da causação. O ensaio questiona este modo de ver e argumenta pela legitimidade da noção de causação por fatos: os relata de muitas relações (...) expressas pelo conector sentencial ‘(O fato) C causa (o fato) E’ podem ser causas e efeitos genuínos (I). Esta visão expandida da causação é então aplicada ao problema da causação mental. Assumindo a verdade do realizacionismo físico, o ensaio explora a conexão entre eficácia causal e relevância contrafactual de propriedades. Mostra-se que, pelo menos em muitos casos, as ligações contrafactuais corretas, requeridas pela causação, podem ser encontradas somente no nível dos fatos realizados, não no nível mais básico dos fatos realizadores (II). Finalmente, dadas as similaridades entre a defesa do fisicismo não-reducionista esboçada aqui e as tentativas menos modestas de justificação científica das pretensões do materialismo metafísico, justamente criticadas por van Fraassen como manifestações da ‘falsa consciência’, considera-se se e como a argumento principal do ensaio pode evitar o juízo crítico de van Fraassen (III). (shrink)
My review of Boghossian's book, Fear of Knowledge, is generally sympathetic toward his rejection of epistemic relativism and turns toward an examination of "constructivist" themes in light of an anti-nominalist perspective. In general terms, this is a fine little book, tightly argued, and well worth considerable attention--especially from the friends of relativism and those supporting versions of constructivism. (Constructivism + radical nominalism = relativism.).
This stimulating collection is devoted to the life and work of the most flamboyant of twentieth-century philosophers, Paul Feyerabend. Feyerabend's radical epistemological claims, and his stunning argument that there is no such thing as scientific method, were highly influential during his life and have only gained attention since his death in 1994. The essays that make up this volume, written by some of today's most respected philosophers of science, many of whom knew Feyerabend as students and colleagues, cover the (...) diverse themes in his extensive body of work and present a personal account of this fascinating thinker. (shrink)
Jean-Paul Sartre is one of the most famous philosophers of the twentieth century. The principal founder of existentialism, a political thinker and famous novelist and dramatist, his work has exerted enormous influence in philosophy, literature, politics and cultural studies. Jean-Paul Sartre: Basic Writings is the first collection of Sartre's key philosophical writings and provides an indispensable resource for readers of his work. Stephen Priest's clear and helpful introductions make the volume an ideal companion to those coming to Sartre's (...) writing for the first time. (shrink)
This collection of essays by philosophers and educationalists of international reputation, all published here for the first time, celebrates Paul Hirst's professional career. The introductory essay by Robin Barrow and Patricia White outlines Paul Hirst's career and maps the shifts in his thought about education, showing how his views on teacher education, the curriculum and educational aims are interrelated. Contributions from leading names in British and American philosophy of education cover themes ranging from the nature of good teaching (...) to Wittgensteinian aesthetics. The collection concludes with a paper in which Paul Hirst sets out his latest views on the nature of education and its aims. The book also includes a complete bibliography of works by Hirst and a substantial set of references to his writing. (shrink)
It is argued that, contrary to prevailing opinion, Bas van Fraassen nowhere uses the argument from underdetermination in his argument for constructive empiricism. It is explained that van Fraassen’s use of the notion of empirical equivalence in The Scientific Image has been widely misunderstood. A reconstruction of the main arguments for constructive empiricism is offered, showing how the passages that have been taken to be part of an appeal to the argument from underdetermination should actually be interpreted.
In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...) which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)
Over the last twenty years, Bas van Fraassen has developed a “new epistemology”: an attempt to sail between Bayesianism and traditional epistemology. He calls his own alternative “voluntarism”. A constant pillar of his thought is the thought that rationality involves permission rather than obligation. The present paper aims to offer an appraisal of van Fraassen’s conception of rationality. In section 2, I review the Bayesian structural conception of rationality and argue that it has been found wanting. In sections 3 and (...) 4, I analyse van Fraassen’s voluntarism. I raise some objections about van Fraassen’s reliance on prior opinion and argue that the content of a belief matters to its rationality. In section 5, I criticise van Fraassen’s view that inference to the best explanation is incoherent. Finally, in section 6, I take on van Fraassen’s conception of rationality and show that it is too thin to fully capture rational judgement. (shrink)
At his death in 1987, Paul W. Pruyser of the Menninger Foundation was widely recognized as one of America's foremost authorities on the psychology of religion. His book A Dynamic Psychology of Religion set the stage for creative dialogue on the subject. In this volume, two leading practitioners in the field present a compilation of Pruyser's seminal articles, providing an overview of the major themes in Pruyser's thought. Newton Malony and Bernard Spilka evaluate Pruyser's viewpoint and suggest (...) how his position continues to influence the psychology of religion. (shrink)
In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P , then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of (...) it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)
Projet En développant son « empirisme constructif », Bas Van Fraassen est devenu une référence incontournable pour la philosophie des sciences contemporaine. Après la vague de critiques qui, vers les années 1960, avait fait perdre à l'empirisme logique sa prédominance dans le champ des idées, le réalisme scientifique semblait s'être imposé comme le seul compte rendu acceptable du travail et des orientations de la recherche. Quine avait beau énoncer ce que pourrait être un empirisme affranchi de ses deux « dogmes (...) » (l'intangibilité de la distinction vérités analytiques / vérités synthétiques, et la réduction des constructions aux « faits »), le programme d'une philosophie des sciences empiriste renouvelée restait à l'état d'esquisse. Mais par trois ouvrages successifs, Scientific Image (1980), Laws and symmetry (1989), et Quantum mechanics an empiricist view (1991), Van Fraassen a posé les bases d'un empirisme viable, parce que capable de prendre en charge la plupart des spécificités dont se prévaut le réalisme contre l'empirisme classique ou logique, et de rendre raison des développements les plus actuels de la physique. Contre l'empirisme classique ou logique, les réalistes font d'abord valoir que la réduction de toute réalité et de tout acte de référence aux phénomènes, ne rend justice ni à la pratique du langage courant ni à celle des sciences. Lorsque quelqu'un procède à une dénomination, il ne cherche pas à désigner par là une tranche d'apparaître, ou quelque ensemble fini et répertorié d'apparitions; il pointe vers "quelque chose" dont les modalités de manifestation sans fin assignable sont pour partie anticipées et pour partie ouvertes. De même, quand un chercheur scientifique parle de l'objet de ses investigations, il ne limite pas son discours à un ensemble fini de résultats d'expérience obtenus sous des conditions instrumentales actuellement disponibles; il renvoie à une entité dont la variété des manifestations futures est prévue aussi complètement que possible (et avec un succès croissant) par des cadres conceptuels et théoriques révisables. Face à cette objection, Van Fraassen fait jouer un rôle capital aux modèles dans sa version de l'empirisme.. (shrink)
Paul Otlet (1868–1944) was a Belgian intellectual, a utopian internationalist and a visionary theorist of the field of information science. His work is a milestone in the history of information science since he launched the concept of "documentation," a field that evolved out of bibliography and developed into information science.1 Otlet defined documentation as the whole of the proper means of passing on, communicating, and distributing information. Otlet was a convinced apostle of the idea of universalism as the title (...) of one of his seminal books, Monde. Essai d'Universalisme, illustrates. This was the outcome of a course of fifteen lessons, entitled "L'universalisme, doctrine philosophique et économie mondiale," .. (shrink)
Considering Pragma-Dialectics honors the monumental contributions of one of the foremost international figures in current argumentation scholarship: Frans van Eemeren. The volume presents the research efforts of his colleagues and addresses how their work relates to the pragma-dialectical theory of argumentation with which van Eemeren’s name is so intimately connected. This tribute serves to highlight the varied approaches to the study of argumentation and is destined to inspire researchers to advance scholarship in the field far into the (...) future. Replete with contributions from highly-esteemed academics in argumentation study, chapters in this volume address such topics as: *Pragma-dialectic versus epistemic theories of arguing and arguments; *Pragma-dialectics and self-advocacy in physician-patient interactions; *The pragma-dialectical analysis of the ad hominem family; *Rhetoric, dialectic, and the functions of argument; and *The semantics of reasonableness. As an exceptional volume and a fitting tribute, this work will be of interest to all argumentation scholars considering the astute insights and scholarly legacy of Frans van Eemeren. (shrink)
The purpose of Pope John Paul''s encyclicalCentesimus Annus (CA) is to propound the foundations of a just economic order and to sketch its essential characteristics. As such he essentially provides an orientation or moral compass for the political economy rather than a precise road map. This article first reviews the principal components of CA and then analyzes and evaluates its central contentions on both cultural and economic grounds.
Analysis shows that statements of ability are disguised conditionals. More exactly, the correct analysis of 'X could have done A' is 'If X h decided (chosen, willed ...) to do A, X would have done A'. Therefore having acted freely--having been able to act otherwise than one fact did--is compatible with determinism (with the causal determination of one's acts).
Mijn wetenschappelijke bijdrage sluit aan bij het stuk van Jan Willem Klop in deze zelfde afscheidsbundel, dat ik van Jan Willem onder embargo te lezen heb gekregen. Je zult je herinneren dat Jan Willem in de CWI lezing ter gelegenheid van zijn eredoctoraat kort refereerde aan de Thue Morse reeks. Noem deze reeks M . Jan Willem gaf de versie die start met 1. Noem het resultaat van omwisselen van nullen en enen in de Thue Morse reeks M . De (...) reeks M is wat je krijgt als je het Thue Morse proces start met 0. (shrink)
This major volume assembles leading scholars to address and explain the significance of Paul Ricoeur's extraordinary body of work. Ricoeur's work is of seminal importance to the development of hermeneutics, phenomenology, and ideology critique in the human sciences. Opening with three key essays from Ricoeur himself--on Europe, fragility and responsibility, and love and justice--this fascinating volume offers a tour of his work ranging across topics such as the hermeneutics of action, narrative force, and the other and deconstruction, while discussing (...) his work in the context of such contemporary thinkers as Heidegger, Levinas, Arendt, and Gadamer. Offering a very useful overview of Paul Ricoeur's enormous contribution to modern thought, Paul Ricoeur will be invaluable for students and academics across the social and human sciences and philosophy. (shrink)
This volume is a collection of essays in appreciation, analysis and honor of Paul Ziff, one of the leading American philosophers of the post-World War II period. The essays address questions that loomed large in Ziff's own work. Essays by Zeno Vendler, Jay Rosenberg, and Tom Patton address topics in philosophy of language: understanding, misunderstanding, rules, regularities, and proper names. Michael Resnik examines the nature of numbers, Rita Nolan addresses `mutant predicates', and Peter Alexander discusses microscopes and corpuscles. Douglas (...) C. Long ruminates on Ziff's claim that machines can neither think nor feel. The essays of Dale Jamieson, Bill E. Lawson, Douglas Dempster, and Joseph Ullian address various questions in aesthetics: aesthetic appreciation and morality, expression, the scope of appreciation, and the aesthetics of sport. In the spirit of Ziff, Douglas Stalker criticizes some of the `mush' that looms large in our intellectual lives. The volume begins with a reminiscence by Paul Benacerraf, and ends with selections from an unpublished volume of plays by Paul Ziff. The volume should appeal to anyone whose work has been influenced by Ziff, or is interested in central philosophical problems concerning language, mind, and art. (shrink)
Gödel’s philosophical rationalism includes a program for “developing philosophy as an exact science.” Gödel believes that Husserl’s phenomenology is essential for the realization of this program. In this article, by analyzing Gödel’s philosophy of idealism, conceptual realism, and his concept of “abstract intuition,” based on clues from Gödel’s manuscripts, I try to investigate the reasons why Gödel is strongly interested in Husserl’s phenomenology and why his program for an exact philosophy is unfinished. One of the topics that has attracted much (...) attention recently is the development of Gödel’s philosophical thoughts and its connection with other philosophical ideas. For instance, some scholars are searching for the possible connections between Gödel’s philosophy and Husserl’s phenomenology and examining if there is any solid evidence of Husserl’s influence on Gödel from Gödel’s works (Tieszen, Bull Symbolic Logic 4(2):181–203, 1998; Huaser, Bull Symbolic Logic 12(4):529–588, 2006). Why is Gödel’ s interested in Husserl? How should this turn to Husserl be interpreted? Is it a dismissal of Leibnizian philosophy, or a different way to achieve similar goals? Way did Gödel turn specifically to Husserl’s transcendental idealism? (Van Atten and Kennedy, Bull Symbolic Logic 9(4):425–476, 2003) I believe, the reason is that Gödel has a valuable program for “developing philosophy as an exact science” and he believes that Husserl’s phenomenology is relevant to the realization of this program. So far there are no sufficient evidence to show that there is a direct inheritance relation between Gödel’s and Husserl’s thoughts. However, from the clues in Gödel’s idealistic philosophy, conceptual realism, and his concept of “abstract intuition,” we can perhaps explore some similarities between his thoughts and Husserl’s thoughts, and analyze the reason why Gödel is interested in Husserl’s phenomenology and why his program for an exact philosophy is unfinished. (shrink)
Brouwer and Weyl recognized that the intuitive continuum requires a mathematical analysis of a kind that set theory is not able to provide. As an alternative, Brouwer introduced choice sequences. We first describe the features of the intuitive continuum that prompted this development, focusing in particular on the flow of internal time as described in Husserl's phenomenology. Then we look at choice sequences and their logic. Finally, we investigate the differences between Brouwer and Weyl, and argue that Weyl's conception of (...) choice sequences is defective on several counts. (shrink)
Kant held that under the concept of √2 falls a geometrical magnitude, but not a number. In particular, he explicitly distinguished this root from potentially infinite converging sequences of rationals. Like Kant, Brouwer based his foundations of mathematics on the a priori intuition of time, but unlike Kant, Brouwer did identify this root with a potentially infinite sequence. In this paper I discuss the systematical reasons why in Kant's philosophy this identification is impossible.
Machine generated contents note: Part I. General: 1. The Gödel editorial project: a synopsis Solomon Feferman; 2. Future tasks for Gödel scholars John W. Dawson, Jr., and Cheryl A. Dawson; Part II. Proof Theory: 3. Kurt Gödel and the metamathematical tradition Jeremy Avigad; 4. Only two letters: the correspondence between Herbrand and Gödel Wilfried Sieg; 5. Gödel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counter-example interpretation W. W. Tait; 6. Gödel on intuition and on Hilbert's finitism W. W. (...) Tait; 7. The Gödel hierarchy and reverse mathematics Stephen G. Simpson; 8. On the outside looking in: a caution about conservativeness John P. Burgess; Part III. Set Theory: 9. Gödel and set theory Akihiro Kanamori; 10. Generalizations of Gödel's universe of constructible sets Sy-David Friedman; 11. On the question of absolute undecidability Peter Koellner; Part IV. Philosophy of Mathematics: 12. What did Gödel believe and when did he believe it? Martin Davis; 13. On Gödel's way in: the influence of Rudolf Carnap Warren Goldfarb; 14. Gödel and Carnap Steve Awodey and A. W. Carus; 15. On the philosophical development of Kurt Gödel Mark van Atten and Juliette Kennedy; 16. Platonism and mathematical intuition in Kurt Gödel's thought Charles Parsons; 17. Gödel's conceptual realism Donald A. Martin. (shrink)
Painting can only be thought in relation to the image. And yet, with (and within) painting what continues to endure is the image of painting. While this is staged explicitly in, for example, paintings of St. Luke by artists of the Northern Renaissance—e.g., Rogier van der Weyden, Jan Gossaert, and Simon Marmion—the same concerns are also at work within both the practices as well as the contemporaneous writings that define central aspects of the Italian Renaissance. The aim of this (...) paper is to begin an investigation into the process by which painting stages the activity of painting. This forms part of a project whose aim is an investigation of the way philosophy should respond to the essential historicity of art (where the latter is understood philosophically). (shrink)
Even though Husserl and Brouwer have never discussed each other's work, ideas from Husserl have been used to justify Brouwer's intuitionistic logic. I claim that a Husserlian reading of Brouwer can also serve to justify the existence of choice sequences as objects of pure mathematics. An outline of such a reading is given, and some objections are discussed.
Gödel always claimed that he did not know Skolem's Helsinki lecture when writing his dissertation. Some questions and doubts have been raised about this claim, in particular on the basis of a library slip showing that he had requested Skolem's paper in 1928. It is shown that this library slip does not constitute evidence against Gödel's claim, and that, on the contrary, the library slip and other archive material actually corroborate what Gödel said.
I argue that Brouwer''s general philosophy cannot accountfor itself, and, a fortiori, cannot lend justification tomathematical principles derived from it. Thus it cannot groundintuitionism, the jobBrouwer had intended it to do. The strategy is to ask whetherthat philosophy actually allows for the kind of knowledge thatsuch an account of itself would amount to.
Gödel, Tarski, Church, and the Liar , by György Serény, pages 3–25. From foundations to ludics , by Jean-Yves Girard, pages 131 -- 168. Symmetry and interactivity in programming , by P.-L. Curien, pages 169 -- 180. Two spaces looking for a geometer , by Giorgio Parisi, pages 181 -- 196. Model theory: Geometrical and set-theoretic aspects and prospects , by Angus Macintyre, pages 197 -- 212. Foundations and applications: axiomatization and education , by F. William Lawvere, pages 213 -- (...) 224. Differential calculus and nilpotent real numbers , by Anders Kock, pages 225 -- 230. The empty set, the singleton, and the ordered pair , by Akihiro Kanamori, pages 273 -- 298. Computable and continuous partial homomorphisms on metric partial algebras , by Viggo Stoltenberg-Hansen and John V. Tucker, pages 299 -- 334. Survey of the Steinhaus tiling problem , by Steve Jackson and R. Daniel Mauldin, pages 335 -- 361. A universal approach to self-referential paradoxes, incompleteness and fixed points , by Noson S. Yanofsky, pages 362 -- 386. On the philosophical development of Kurt Gödel , by Mark van Atten and Juliette Kennedy, pages 425 — 476. Identity of proofs based on normalization and generality , by Kosta Došen, pages 477 — 503. (shrink)