In lieu of an abstract, here is a brief excerpt of the content:Notes and Discussions AGOSTINO NIFO'S EARLY VIEWS ON IMMORTALITY Various historians of Renaissance philosophy have taken some notice of the prolific author and important philosopher of the late 15th and early 16th centuries, Agostino Nifo (1470-1538), x but no one has yet studied his writings in a methodical and exhaustive fashion. 2 He not only published philosophical works in logic, physics, psychology and metaphysics, but he also authored treatises (...) on humanist topics? Recent scholars have tended to concentrate their attention on his psychological doctrines, no doubt because he was one of the major opponents of Pietro Pomponazzi (1462-1525) during the immortality controversy.4 Nifo published his De Immortalitate Animae in 1518 as a reply to the De lmmortalitate Ardmae, On the year of Nifo)s birth, see Bruno Nardi, Saggi sull'aristotelismo padovano dal secolo xav al xvl ('Florence, 1958), p. 284, n. 8. There is contemporary evidence that he died on January 18, 1538. See Bartolommeo Capasso, "Le cronache de li antiqui ri del regno di Napoli di D. Gaspare Fuscolill0," Archivio storico per le province napoletane, I (1876), p. 538. The standard bio-bibliography still remains Pasquale Tuozzi, "Agostino Nifo 9 le sue opere," Atti e memorie della R. Accademia di Scienze, Lettere ed Arti in Padova, Nuova scrie, XX (Padua, 1904), pp. 63-86. But see also Giuseppr Tommasino, Tra umanisti e filosoft (Maddaloni, 1921), Porte I, pp. 123-147; and Edward P. Mahoney, "A Note on Agostino Nifo," Philological Quarterly (forthcoming). z See Franeeseo Fiorentino, Pietro Pomponazzi; Studi storici su la scuola bolognese e padovana del secolo xvI (Florence, 1868); Carlo Giacon, La seconda scolastica: 1 grandi commentatori di San Tommaso (Milan, 1944); Etienne Gilson, "L'affaire de l'immortalit6 de l'fime ~t Venise at* d6but du xvIe si~ele," in Umanesirno europeo e uraanesimo veneziano, ed. Vittore Branea (Florence, 1963), pp. 31-61; Miehele Giorgiantonio, "Un nostro filosofo dimentieato dcl '400 (Luea Prassicio e Agostino Nifo)," Sophia, XVI (1948), pp. 212-214 and 303-312; Bruno Nardi, Saggi sulraristotelismo padovano dal secolo x]v al xvI (Florence, 1958); idem, Sigieri di Brabante nel pensiero del Rinascimento Italiano (Rome, 1945); Giovanni di NapoH, L'immortalitd delranima nel Rinascimento ('Turin, 1963); John Herman Randall, Jr., The School of Padua and the Emergence of Modern Science (Padua, 1961); Wilhelm Risse, Die Logik der Neuzeit, I (Stuttgart, 1964); Eugenio Garin, La cultura [ilosofica del Rinascimento Italiano (Florence, 1961); idem, Storia della filosofia italiana, II (Turin, 1966). See Nifo's De Armorum Literarumque Comparatione Commentariolus (Naples, 1526); De Pulchro et Amore (Rome, 1531); De Re Aulica (Naples, 1534); and Prima Pars Opusculorum (Venice, 1535). The second of these works has been studied by Jules Houdoy, La beaut~ des femmes dans la litt#rature et darts rart du xII" au xvIe si~cle; Analyse du livre de A. Niphus du Beau et de l'amour (Paris, 1876). 4 For recent discussion of the immortality controversy, see Etienne Gilson, "Autour de Pomponazzi, ProbMmatique de l'immortalit~ de l'~me en Italic au d~but du xvIe si~.cle," Archives d'histoire doctrinale et litt~raire du moyen dge, Ann6e 1961, pp. 163-179; Giovanni di Napoli, op. cit., especially pp. 227-338; Paul Oskar Kristeller, Eight Philosophers of the Italian Renaissance (Stanford, 1964), pp. 72-90; Bruno Nardi, Studi su Pietro Pomponazzi (Florence, 1965); Martin Pine, "Pomponazzi and the Problem of 'Double Truth'," Journal ot the History of Ideas, XXIX (1968), pp. 163-176; Harold Shulsky, "Paduan Epistemology and the Doctrine of the One Mind," lournal of the History of Philosophy, VI (1968), pp. 341-361. [451] 452 HISTORY OF PHILOSOPHY (1516) of Pomponazzi, who had argued that personal immortality cannot be philosophically demonstrated, s But while these scholars correctly point out that Nifo abandoned an Averroist interpretation of Aristotle concerning the unity of the intellect and the immortality of the soul for the position which they assume to be Thomistic, they are not precise as to just when Nile made the shift.6 They have not observed that in his first two printed works, namely, the commentary on Averroes' Destructio Destructionum (1497) and the early commentary on the De Anima (1503), Nifo explicitly accepts Averroes as the... (shrink)

This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice.

This new edition of the classic Contemporary Theories of Knowledge has been significantly updated to include analyses of the recent literature in epistemology.

Language, like other human traits, could only have evolved during one or more stages of development. We enlist the theoretical framework of human life history to account for certain aspects of linguistic evolution, with special reference to initial phases in the process. It is hypothesized that selection operated at several developmental stages, the earlier ones producing new behaviors that were reinforced by additional, and possibly more powerful, forms of selection during later stages, especially adolescence and early adulthood. Peer commentaries have (...) provided opportunities to explain human life history more comprehensively, and to add details to our account of spoken language. We made no attempt to explain syntax in the target article, but we propose here that selection for “vocal plumage” may have increased our species’ capacity for utterance complexity, a development that would have benefited all levels of language. (shrink)

This chapter traces the historical and conceptual development of the idea of the continuum and the allied concept of real number. Particular attention is paid to the idea of infinitesimal, which played a key role in the development of the calculus during the seventeenth and eighteenth centuries, and which has undergone a revival in the later twentieth century.

Van de Vliert embraces a model of human needs, underplaying a model whereby individuals, motivated by psychological needs, develop coping strategies that help them meet their personal goals and collectively exert an influence on social and economic systems. Undesirable climates may inflate the value of financial capital, but they also boost the value of social capital.

The usual meaning of the word continuous is “unbroken” or “uninterrupted”: thus a continuous entity —a continuum—has no “gaps.” We commonly suppose that space and time are continuous, and certain philosophers have maintained that all natural processes occur continuously: witness, for example, Leibniz's famous apothegm natura non facit saltus—“nature makes no jump.” In mathematics the word is used in the same general sense, but has had to be furnished with increasingly precise definitions. So, for instance, in the later 18th century (...) continuity of a function was taken to mean that infinitesimal changes in the value of the argument induced infinitesimal changes in the value of the function. With the abandonment of infinitesimals in the 19th century this definition came to be replaced by one employing the more precise concept of limit. (shrink)

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of (...) Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal. (shrink)

"The Third Edition of Philosophical Foundations of Adult Education presents seven theoretical approaches to adult education: liberal, progressive, behaviorist, humanist, radical/critical, analytic, and postmodem. The book gives the historical grounding as well as the basic principles for each approach. In this edition each chapter has been revised and brought up to date. The chapter on radical adult education incorporates recent developments in radical education, phenomenology, feminist educational theory, and critical social theory. The book contains an entirely new chapter on postmodem (...) adult education.". (shrink)

"A sequel to Pollock's How to Build a Person, this volume builds upon that theoretical groundwork for the implementation of rationality through artificial ...

This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory, an important form of type theory (...) based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined. (shrink)

In Volume Two of Ernest Fortin: Collected Essays, Fortin deals with the relationship between religion and civil society in a Christian context: that of an essentially nonpolitical but by no means entirely otherwordly religion, many of whose teachings were thought to be fundamentally at odds with the duties of citizenship. Sections focus upon Augustine and Aquinas, on Christianity and politics; natural law, natural rights, and social justice; and Leo Strauss and the revival of classical political philosophy. Fortin's treatment of these (...) and related themes betrays a keen awareness of one of the significant intellectual events of our time: the recovery of political philosophy as a legitimate academic discipline. (shrink)

Princeton University Press, 1974. This book is out of print, but can be downloaded as a pdf file (5 MB).

The principle of set theory known as the Axiom of Choice has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid's axiom of parallels which was introduced more than two thousand years ago” (Fraenkel, Bar-Hillel & Levy 1973, §II.4). The fulsomeness of this description might lead those unfamiliar with the axiom to expect it to be as startling as, say, the Principle of the Constancy of (...) the Velocity of Light or the Heisenberg Uncertainty Principle. But in fact the Axiom of Choice as it is usually stated appears humdrum, even self-evident. For it amounts to nothing more than the claim that, given any collection of mutually disjoint nonempty sets, it is possible to assemble a new set — a transversal or choice set — containing exactly one element from each member of the given collection. Nevertheless, this seemingly innocuous principle has far-reaching mathematical consequences — many indispensable, some startling — and has come to figure prominently in discussions on the foundations of mathematics. It (or its equivalents) have been employed in countless mathematical papers, and a number of monographs have been exclusively devoted to it. (shrink)

5.5. Every topos is linguistic: the equivalence theorem.

Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some (...) classical first-order logic and would like to learn about other logics important to their philosophical work. (shrink)

Hermann Weyl, one of the twentieth century's greatest mathematicians, was unusual in possessing acute literary and philosophical sensibilities—sensibilities to which he gave full expression in his writings. In this paper I use quotations from these writings to provide a sketch of Weyl's philosophical orientation, following which I attempt to elucidate his views on the mathematical continuum, bringing out the central role he assigned to intuition.

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

IN THEIR WELL-KNOWN PAPER, Kochen and Specker (1967) introduce the concept of partial Boolean algebra (pBa) and show that certain (finitely generated) partial Boolean algebras arising in quantum theory fail to possess morphisms to any Boolean algebra (we call such pBa's intractable in the sequel). In this note we begin by discussing partial..

In their writings on Africa and colonialism, John and Jean Comaroff have explored some of the fundamental questions of social science, delving into the nature of history and human agency, culture and consciousness, ritual and representation. How are human differences constructed and institutionalized, transformed and (sometimes) resisted? How do local cultures articulate with global forms? How is the power of some people over others built, sustained, eroded, and negated?These essays work toward an "imaginative sociology," demonstrating the techniques by which (...) social science may capture the contexts that human beings construct and inhabit. In the introduction the authors offer their most complete statement to date on historical anthropology. Standing apart from the traditional disciplines of social history and modernist social science, their work is dedicated to discovering how human worlds are made and signified, forgotten and remade. (shrink)

Traditionally, expressions in formal systems have been regarded as signifying finite inscriptions which are—at least in principle—capable of actually being written out in primitive notation. However, the fact that (first-order) formulas may be identified with natural numbers (via "Gödel numbering") and hence with finite sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas would be naturally identified as infinite sets . A "language" of this kind is called (...) an infinitary language : in this article I discuss those infinitary languages which can be obtained in a straightforward manner from first-order languages by allowing conjunctions, disjunctions and, possibly, quantifier sequences, to be of infinite length. In the course of the discussion it will be seen that, while the expressive power of such languages far exceeds that of their finitary (first-order) counterparts, very few of them possess the "attractive" features (e.g., compactness and completeness) of the latter. Accordingly, the infinitary languages that do in fact possess these features merit special attention. (shrink)

(1984). Weather foreasting and the development of meteorological theory at the Paris Observatory, 1853–1878. Annals of Science: Vol. 41, No. 4, pp. 359-382.

This essay is an attempt to sketch the evolution of type theory from its beginnings early in the last century to the present day. Central to the development of the type concept has been its close relationship with set theory to begin with and later its even more intimate relationship with category theory. Since it is effectively impossible to describe these relationships (especially in regard to the latter) with any pretensions to completeness within the space of a comparatively short article, (...) I have elected to offer detailed technical presentations of just a few important instances. (shrink)

We investigate Hilbert’s varepsilon -calculus in the context of intuitionistic type theories, that is, within certain systems of intuitionistic higher-order logic. We determine the additional deductive strength conferred on an intuitionistic type theory by the adjunction of closed varepsilon -terms. We extend the usual topos semantics for type theories to the varepsilon -operator and prove a completeness theorem. The paper also contains a discussion of the concept of “partially defined‘ varepsilon -term. MSC: 03B15, 03B20, 03G30.

The centrality of the whole/part relation in mathematics is demonstrated through the presentation and analysis of examples from algebra, geometry, functional analysis,logic, topology and category theory.

In this book Pollock deals with the subject of probabilistic reasoning, making general philosophical sense of objective probabilities and exploring their ...

Pollock describes an exciting theory of rationality and its partial implementation in OSCAR, a computer system whose descendants will literally be persons.