The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in (...) the famous Hilbert-Brouwer controversy in the 1920s. -/- The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics. (shrink)

According to the ‘fact-plus-value’ model of pathology propounded by K. W. M. Fulford, ‘disease’ is a value term that ought to reflect a ‘balance of values’ stemming from patients and doctors and other ‘stakeholders’ in medical nosology. In the present article I take issue with his linguistic-analytical arguments for why pathological status must be relative to such a kind of medico-ethical normativity. Fulford is right to point out that Boorse and other naturalists are compelled to utilize evaluative terminology when they (...) characterize the nature of diseases and biological dysfunctions. But the relevant ‘biofunctional judgements’ are no less factual and empirical for that. While it is indeed evaluative to say that biological dysfunctions involve failures to execute naturally selected functions, such judgments are not bound to entail anything about what is good or bad for us, and what should be treated or not. In the last part of the paper I ruminate briefly on the relationship between ‘biological evaluationism’, on my construal, and descriptions of ‘causal biology’. As I note in my conclusion, a strict bioevaluative concept of disease can be valid for every species on earth, and thus be of particular usefulness in general biological contexts. (shrink)

I develop a notion of nonlinear stochastic integrals for hyperfinite Lévy processes and use it to find exact formulas for expressions which are intuitively of the form $\sum_{s=0}^t\phi(\omega,dl_{s},s)$ and $\prod_{s=0}^t\psi(\omega,dl_{s},s)$ , where l is a Lévy process. These formulas are then applied to geometric Lévy processes, infinitesimal transformations of hyperfinite Lévy processes, and to minimal martingale measures. Some of the central concepts and results are closely related to those found in S. Cohen’s work on stochastic calculus for processes with jumps (...) on manifolds, and the paper may be regarded as a reworking of his ideas in a different setting and with totally different techniques. (shrink)

Critics of attention-deficit/hyperactivity disorder (ADHD) have repeatedly argued that there is no proof for the condition being symptomatic of an organic brain disease and that the current "ADHD epidemic" is an expression of medicalization. To this, the supporters of ADHD can retort that the condition is only defined as a mental disorder and not a physical disease. As such, ADHD needs only be a harmful mental dysfunction, which, like other genuine disorders, can have a complex and obscure etiology. This article (...) argues that such a line of argument fails to save ADHD as a valid diagnostic category. Given the general diagnostic logic of the DSM-IV and how ADHD has been defined in terms of everyday (male) child behaviors, there are compelling grounds to disbelieve that ADHD can be a true medical syndrome united by some type of harmful dysfunction. Indeed, strong logical and empirical reasons will be adduced to show that people may qualify for ADHD diagnosis without suffering from any type of underlying pathology. (shrink)

The third part, Cognition, concerns abstract questions about knowledge and truth as well as more concrete questions about the usefulness and tractability of various graphic representations of information. The book would be of special interest to Research Institutes in Computer Science, Researchers in Philosophical Logic, Deontic Logic, Applied Logic, Artificial Intelligence, and Cognitive Science.

A series of four lectures given in Athens during the author's tenure of a Fulbright Fellowship. The intention is to introduce Athenian public to three classical American philosophers, as well as to contemporary trends. The author sees interesting parallels between Emerson and the Byzantine Mystics and predicts that the interest of Americans in Ancient Greek philosophy will lead to closer studies of Byzantine philosophy. The chief defect of the book is its willingness to sacrifice content for coverage. Presentation is cursory (...) and often by terms which are misleading in themselves and particularly unfortunate when rendered into modern Greek.--. (shrink)

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...) today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

A series of four lectures given in Athens during the author's tenure of a Fulbright Fellowship. The intention is to introduce Athenian public to three classical American philosophers, as well as to contemporary trends. The author sees interesting parallels between Emerson and the Byzantine Mystics and predicts that the interest of Americans in Ancient Greek philosophy will lead to closer studies of Byzantine philosophy. The chief defect of the book is its willingness to sacrifice content for coverage. Presentation is cursory (...) and often by terms which are misleading in themselves and particularly unfortunate when rendered into modern Greek.--. (shrink)

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections (...) in the preservation process, and hope you enjoy this valuable book. (shrink)

Machine generated contents note: -- Preface -- Acknowledgements -- Notes on Contributors -- PART I: COMPLEXITY IN ANIMAL MINDS -- Introduction: M.McGonigle-Chalmers -- Relational and Absolute Discrimination Learning by Squirrel Monkeys: Establishing a Common Ground with Human Cognition; B.T.Jones -- Serial List Retention by Non-Human Primates: Complexity and Cognitive Continuity; F.R.Treichler -- The Use of Spatial Structure in Working Memory: A Comparative Standpoint; C.De Lillo -- The Emergence of Linear Sequencing in Children: A Continuity Account and a Formal Model; M.McGonigle-Chalmers&I.Kusel (...) -- Sensitivity to Quantity: What Counts Across Species?; S.T.Boysen&A.M.Yocom -- PART II: COMPLEXITY IN ROBOTS -- Editorial Introduction; D.McFarland -- Towards Cognitive Robotics: Robotics, Biology and Developmental Psychology; M.Lee, U.Nehmzow&M.Rodriguez -- Structuring Intelligence: The Role of Hierarchy, Modularity and Learning in Generating Intelligent Behaviour; J.J.Bryson -- Epistemology, Access, and Computational Models; G.Luger -- Reasoning About Representations in Autonomous Systems: What P´Olya and Lakatos Have To Say; A.Bundy -- PART III: LANGUAGE, EVOLUTION AND THE COMPLEX MIND -- Editorial Introduction; K.Stenning -- How to Qualify for a Cognitive Upgrade: Executive Control, Glass Ceilings, and the Limits of Simian Success; A.Clark -- Private Codes and Public Structures; C.Allen -- The Emergence of Complex Language; W.Hinzen -- Language Evolution: Enlarging the Picture; K.Stenning&M.Van Lambalgen -- Epilogue: Reminiscences of Brendan McGonigle -- Index. (shrink)

In 1981 I published an article called Early Supposition Theory. Then as now, the magisterial work on the subject was L.M. de Rijk’s Logica Modernorum and then as now any discussion of the topic would have to rely to a great extent on the texts published there. This means that many of the problems that existed then still remain, but a couple of important new studies and several new texts have been published in the meantime, so it may be time (...) to try to take stock of the situation. I will first look at the origin of the term suppositio and then at the chronology of our source texts. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Abaelards Logik by Wolfgang LenzenSten EbbesenWolfgang Lenzen. Abaelards Logik. Paderborn: Brill | mentis, 2021. Pp. 206. Hardback, €59.00.According to its author, this book aims at reconstructing key parts of Abelard's logic while denying him a role as a hero of connexive logic or more generally as one of history's greatest logicians. At the end of the preface, we are told that "Abaelard hat die Logik seiner Zeit nicht (...) revolutioniert; er hat keine Kalküle konstruiert; und er hat auch nicht die Logik seiner Zeit auf ein höheres Niveau gehoben" (xiv).The book is divided into twenty-three chapters with titles such as "'Destruierende' versus 'separierende' Negation," "Vollkommene und unvollkommne Folgerungen," and "'Leere' Begriffe." As the titles show, it ranges over a large field. The results of Lenzen's analyses of Abelard's argumentation are presented in modern logical notation. There are many fine analyses, and despite Lenzen's refusal to see Abelard as a genius, he, too, seems to have been quite impressed by the old logician. However, at the end of the day, I am not sure that I have become any wiser about Abelard's contribution to the history of logic.Lenzen is a newcomer to the study of twelfth-century logic, and the book is marked by this in several ways. Thus, he informs the reader that "Spätestens seit Prantls Publikation der 'Geschichte der Logik im Abendlande' steht fest, dass Abaelards Traktat 'De Sillogismis Ypoteticis' sich stark an das Werk 'De syllogismo hypothetico' von Boethius (470–524) anlehnt" (165). This is quite true, but anything else would have been very remarkable, so the reference to Prantl serves no purpose.Unsurprisingly, the main source texts used are Abelard's Dialectica and his Glosae super Peri hermeneias, a part of the series of commentaries on the Ars vetus that go under the common name of Logica ingredientibus. Lenzen displays a cavalier attitude to philology. He quotes the Dialectica from De Rijk's second edition (1970), but in the bibliography he mentions that there are two editions without stating explicitly which one he quotes. In the case of the Glosae, he uses the obsolete editio princeps by Bernhard Geyer from 1927, and he does not even mention its replacement, Klaus Jacobi and Christian Strub's much superior 2010 edition in the series Corpus Christianorum, Continuatio Mediaevalis. This is inexplicable, for in his preface Lenzen describes his book as the child of a research project he began several years after the publication of the new edition. Now, fortunately, the use of Geyer does not have disastrous consequences for Lenzen's interpretation of Abelard, but had he used Jacobi and Strub's edition, he would not have had to propose a textual emendation in one place (88n17), nor would he have needed to quote, in another place, a Latin text (which he does not translate) with a nonsensical significantem instead of figurative (94n1o).Lenzen sometimes proposes textual emendations, but not always in a perspicuous way, and they are not all felicitous. For example, a quotation of L. M. de Rijk's edition of Introductiones Montane Minores in Logica Modernorum (LM) II.2 (1967) contains the phrase aliquod opposit[or]um (127n2). An unsuspecting reader would think this means De Rijk had conjecturally emended oppositorum into oppositum, for this is what opposit[or]um would mean in LM II.2. In fact, De Rijk just prints oppositum, so Lenzen's opposit[or]um must mean that he wants to correct De Rijk's text by inserting 'or,' but he forgets to tell us that he does not [End Page 520] faithfully reproduce the text quoted and that his square brackets mean something different from what they do in De Rijk's edition. This issue aside, his conjecture is superfluous, as proven by a parallel passage in LM II.2: 118. Similarly, he quotes Abelard as saying "alterum istorum [est]: vel nox vel dies" (152). The "[est]" is Lenzen's own, again superfluous, contribution to the text. By contrast, elsewhere he proposes to insert a non at LM II.2: 64.2. This time, he explains what he is doing, and I think his conjecture... (shrink)

We give an elementary introduction to non-standard analysis and its applications to the theory of stochastic processes. This is based on a joint book with J. E. Fenstad, R. Høegh-Krohn and T. Lindstrøm. In particular we give a discussion of an hyperfinite theory of Dirichlet forms with applications to the study of the Hamiltonian for a quantum mechanical particle in the potential created by a polymer. We also discuss new results on the existence of attractive polymer measures in dimension d (...) ≤ 5, with applications to the (φ 1 2 φ 2 2 )d-mode1 of interacting quantum fields. (shrink)

In western philosophy and beyond, a tension between pluralism and monism has sparked many developments and debates. Pluralism of norms, of forms of knowledge, of aesthetic and moral values, of interests etc. has often been pitted against monism. Monism usually implies a hierarchical order of such norms etc. After having traced the origin of this tension between pluralism and monism in ancient tragedy and philosophy, I’m asking in this article whether a rejection of monism and embrace of pluralism necessarily raises (...) the specter of inconsistency and contradiction. The threat of inconsistency need not be associated with pluralism as even with regard to logic an argument can be made for a ‘multiplicity of logics’, as van Lambalgen and Stenning argue in several places. They refer to the varieties in reasoning that can be observed in humans and which are partly due to there being ‘dual systems’ of reasoning: System 1 processes information fast, automatized, and emotional, while System 2 is rather slow, more deliberative, and more rational. In contrast to a widely held view, the authors argue that System 1 processing is not without logic, even though it is a different form of logic from System 2. In addition, the multiplicity of logics they discuss is related to the multiple semantics required for distinct domains of reasoning. This perspective raises the subsequent question how this pluralism can be available while maintaining consistency, how should the available options be configured or related to each other? In the remainer of this chapter I’m addressing several such options for configurating pluralism like: non-foundational pluralism and foundational pluralism, moderate or temporary pluralism, antagonistic pluralism, incompatible pluralism, incommensurable pluralism, ‘Anything goes’ pluralism, complementary pluralism, integrative pluralism, and interactive pluralism. The discussion and examples of these options show that irrespective of its domain, the encounter with different configurations of pluralism shows how some forms of pluralism are likely to be productive, whereas others are less so - which is an important lesson given the prominent pluralism of pluralisms in philosophy and beyond. (shrink)

Temanummer om «etikkbølgen» i yrkesutdanning og -praksisHøstens utgave av Etikk i praksis er et temanummer om «etikkbølgen» innen yrkesutdanning og -praksis, altså tendensen til å gjøre etikk til et eksplisitt tema for fag, kurs, kodekser og retningslinjer innen ulike profesjoner og utdanningsløp. Den tematiske delen består av fire artikler som omhandler ulike yrkesgruppers møte med «etikkbølgen». I den åpne delen har vi to artikler: en som drøfter vårens store profesjonsetiske slag i norsk politikk, nemlig fastlegenes reservasjonsrett, og en som tar (...) for seg en ofte oversett side ved global rettferdighet, nemlig de fattige landenes forpliktelser. (shrink)

The Greek under the Latin and the Latin under the Greek -- Greek-Latin philosophical interaction -- The odyssey of semantics from the Stoa to Buridan -- The Chimera's diary -- Where were the stoics in the late Middle Ages? -- Theories of language in the Hellenistic age and in the twelfth and thirteenth centuries -- Late-ancient ancestors of medieval philosophical commentaries -- Boethius on Aristotle -- Boethius on the metaphysics of words -- Western and Byzantine approaches to logic -- Greek (...) and Latin medieval logic -- Philoponus, Alexander, and the origins of medieval logic -- Analyzing syllogisms or anonymus Aurelianensis III, the (presumably) earliest extant Latin commentary on the prior analytics, and its Greek model -- Fragments of Alexander's commentaries on Analytica posteriora and Sophistici elenchi. (shrink)

On Avicenna, 980-1037, a Muslim philosopher.