An animal confronts numerous challenges when constructing an optimal navigational route. Spatial representations used for path optimization are likely constrained by critical environmental factors that dictate which neural systems control navigation. Multiple coding schemes depend upon their ecological relevance for a particular species, particularly when dealing with the third, or vertical, dimension of space.

On the basis of evidence drawn from the Waste book, Westfall and Nicholas have argued that Newton arrived at his second law of motion by reflecting on the implications of the first law. I analyze another argument in the Waste book which reveals that Newton also arrived at the second law by another very different route. On this route, it is the consideration of the third law and the principle of conservation of motion—and not the first law—that prompts Newton to (...) formulate the second law. The existence of these two routes is significant because each employs a distinct kind of reasoning about forces. Whereas the Nicholas–Westfall route via the principle of inertia bears the mark of Descartes’s influence, the alternative route proceeds from the action–reaction principle, which is widely regarded as an original Newtonian contribution to mechanics. In the course of exploring this alternate route to the second law, the origins and justification of the third law are examined.Keywords: Issac Newton; Waste book; Third law of motion; Second law of motion; Richard Westfall; John Nicholas. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Multiculturalist theories of recognition consist of explanatory-descriptive social theoretical accounts of the position of the minorities whose predicaments the theories seek to address, together with normative principles generating political implications. Although theories of recognition are often based on illiberal principles or couched in illiberal-sounding language, it is possible to combine proper liberal principles with the kind of social theoretical accounts of minority groups highlighted in multiculturalism. The importance of ‘the social bases of self-respect’ in Rawls’s political liberalism is used to (...) illustrate how a liberal theory of recognition might be constructed, and it is argued that such a theory can capture some, though not all, of the concerns of multiculturalism, even though the resulting ‘politics of recognition’ is neither a ‘politics of difference’ nor a kind of ‘identity politics’. (shrink)

The story of the end of the Philosophical Society of Edinburgh in 1783, is linked with that of the founding of the Society of Antiquaries of Scotland and the Royal Society of Edinburgh , both of which were given Royal Charters sealed on 6 May 1783. It is a story which has been admirably told by Steven Shapin. He persuasively argued that the P.S.E. was a casualty of bitter quarrels rooted in local Edinburgh politics, in personal animosities and in disputes (...) about the control of cultural property and intellectual leadership. In all this he was surely correct just as he was in finding the principal actors in this controversy to be: David Erskine, 11th Earl of Buchan; the Reverend Dr John Walker, Professor of Natural History in Edinburgh University; Dr William Cullen, Professor of the Theory and Practice of Medicine and Vice-President of the P.S.E.; Mr William Smellie, Printer to the Society of Antiquaries; Henry Home, Lord Kames, S.C.J. and President of the P.S.E.; Sir George Clerk-Maxwell, Vice-President of the P.S.E.; John Robison, Professor of Natural Philosophy and Secretary to the P.S.E.; Edinburgh University's Principal, William Robertson; the Curators of the Advocates Library: Ilay Campbell, Robert Blair, Alexander Abercromby, Alexander Fraser Tytler, Professor of Public Law; Henry Dundas, Lord Advocate and M.P. for Midlothian. In a peripheral way, the Royal Colleges of Physicians and Surgeons were probably also involved; so too were Lord Buchan's brothers, Henry and Thomas Erskine, Foxite Whigs who opposed Dundas politically. Henry Erskine displaced Dundas as Lord Advocate in August 1783. After the change of ministry on 18 December 1783 he was ousted, but became Dean of the Faculty of Advocates in 1785. National as well as burgh politics touched these disputes and gave the parties of the Erskines and Dundas and his friends some leverage in London. (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 ...

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

Pollock argues that theories of ideal rationality are largely irrelevant to the decision making of real agents. Thinking about Acting aims to provide a theory of "real rationality.".

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

Princeton University Press, 984. This book is out of print, but can be downloaded as a pdf file (3.9 MB).

Princeton University Press, 1982. This book is out of print, but can be downloaded as a pdf file (5 MB).

This exceptionally successful survey text introduces the teachings and practice of Islam from its earliest origins up to its contemporary practice. John L. Esposito, an internationally renowned expert on Islam, traces the development of Islam and its impact on world history and politics.Lucidly written and expansive in scope, Islam: The Straight Path, Updated Fifth Edition, provides keen insight into one of the world's least understood religions. It is ideally suited for use in courses on Islam, world religions, comparative religions, (...) and Middle East history and culture.A FREE 6-month subscription to Oxford Islamic Studies Online, edited by John L. Esposito, is included with the purchase of every new copy of this text. (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)

Imagine yourself sitting on your front porch, sipping your morning coffee and admiring the scene before you. You see trees, houses, people, automobiles; you see a cat running across the road, and a bee buzzing among the flowers. You see that the flowers are yellow, and blowing in the wind. You see that the people are moving about, many of them on bicycles. You see that the houses are painted different colors, mostly earth tones, and most are one-story but a (...) few are two-story. It is a beautiful morning. Thus the world interfaces with your mind through your senses. There is a strong intuition that we are not disconnected from the world. We and the other things we see around us are part of a continuous whole, and we have direct access to them through vision, touch, etc. However, the philosophical tradition tries to drive a wedge between us and the world by insisting that the information we get from perception is the result of inference from indirect evidence that is about how things look and feel to us. The philosophical problem of perception is then to explain what justifies these inferences. We will focus on visual perception. Figure one presents a crude diagram of the cognitive system of an agent capable of forming beliefs on the basis of visual perception. Cognition begins with the stimulation of the rods and cones on the retina. From that physical input, some kind of visual processing produces an introspectible visual image. In response to the production of the visual image, the cognizer forms beliefs about his or her surroundings. Some beliefs the perceptual beliefs are formed as direct responses to the visual input, and other beliefs are inferred from the perceptual beliefs. The perceptual beliefs are, at the very least, caused or causally influenced by having the image. This is signified by the dashed arrow marked with a large question mark. We will refer to this as the mystery link. Figure one makes it apparent that in order to fully understand how knowledge is based on perception, we need three different theories.. (shrink)

An argument is self-defeating when it contains defeaters for some of its own defeasible lines. It is shown that the obvious rules for defeat among arguments do not handle self-defeating arguments correctly. It turns out that they constitute a pervasive phenomenon that threatens to cripple defeasible reasoning, leading to almost all defeasible reasoning being defeated by unexpected interactions with self-defeating arguments. This leads to some important changes in the general theory of defeasible reasoning.

Counterexamples are constructed for the theory of rational choice that results from a direct application of classical decision theory to ordinary actions. These counterexamples turn on the fact that an agent may be unable to perform an action, and may even be unable to try to perform an action. An alternative theory of rational choice is proposed that evaluates actions using a more complex measure, and then it is shown that this is equivalent to applying classical decision theory to "conditional (...) policies" rather than ordinary actions. (shrink)

"There is no attempt here to lay down as inviolable or to legislate certain ways of looking at things or ways of proceeding for philosophers of religion, only proposals for how to deal with a range of basic issues-proposals that I hope will ignite much fruitful discussion and which, in any case, I shall take as a basis for my own ongoing work in the field."-from the Preface Providing an original and systematic treatment of foundational issues in philosophy of religion, (...) J. L. Schellenberg's new book addresses the structure of religious and irreligious belief, the varieties of religious skepticism, and the nature of religion itself. From the author's searching analysis of faith emerges a novel understanding of propositional faith as requiring the absence of belief. Schellenberg asks what the aims of the field should be, setting out a series of principles for carrying out some of the most important of these aims. His account of justification considers not only belief but also other responses to religious claims and distinguishes the justification of responses, propositions, and persons. Throughout Prolegomena to a Philosophy of Religion, Schellenberg is laying the groundwork for an elaboration of his own vision while at the same time suggesting how philosophers might rethink assumptions guiding most of today's work in analytic philosophy of religion. (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.

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.

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.

What kind of turn is the turn to ethics? A Right turn? A Left turn? A wrong turn? A U-turn? Ethics is back in literary studies, philosophy, and political theory. Where critiques of universal man and the autonomous human subject had, in recent years, produced a resistance to ethics in many fields of scholarship, today these critiques have generated a crossover among disciplines and led to theories and practices that see and do ethics otherwise. The decentering of the subject, the (...) contributors to this volume suggest, has brought about a recentering of the ethical. The philosophers, political theorists, literary critics and physician whose essays are collected here bring the particularities of their disciplines and training to a vital complex of questions. Many of these authors express concerns that the turn to ethics is a turn away from politics towards moralism. All ultimately conclude, however, that such concerns, rather than leading away from ethics, have helped to reinvigorate the intellectual field in the present moment. Contributors: Judith Butler, Homi K. Bhabha, Lawrence Buell, Nancy Fraser, John Guillory, Beatrice Hanssen, Barbara Johnson, Perri Klass, Chantal Mouffe, Doris Sommer, Rebecca Walkowitz. (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.

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)

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)

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

Hastings Center Report, Volume 52, Issue 2, Page 14-20, March‐April 2022.

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)

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

As his editor John L. Stanley points out, Georges Sorel was "that fascinating polymath." This volume, the third in his selected works in the English language published by Transaction, emphasizes Sorel's extraordinary writings in the philosophy of science, religion, culture, and art. For those who know Sorel only as author of Reflections on Violence, the present volume will come as a forceful reminder of the range and depth of Sorelian efforts to construct a world view. Sorel is throughout concerned (...) with the moral development of human beings. In this sense, his writings on politics are of a piece with his writings on religion, "facticity" of human history and society. Sorel's earliest writings were on religion, and key portions of that period are reflected in selections here. And he went on from there to study the sociology of science, the ways in which science fits into the cultural history of civilization and present day social relationships of industrial society. Stanley provides a profound framework based on two decades of close study and translation of Sorel's texts. He helps to explain how the partial theories of Sorel lead to holistic intellectual consequences, how the psychological method does not foreclose political activism, and how historical limits can be transformed against a background of aesthetics or considerations of taste. He shows that Sorel comes as a close as Manheim and Simmel and Durkheim to the creation of a modern social science--albeit he lacks the overall philosophical theorems of people like Marx and Weber. In Sorel we have a first-class mind at work. And in Stanley, we have a first-class analyst at work. Together, the volume adds up to something special for the political scientist, sociologist, art historian, theologian--in short for those to whom the ideal of a human science endures. John L. Stanley is professor of political science at the University of California at Riverside. He is the author of The Sociology of Virtue: The Political and Social Theories of Georges Sorel. He has written many articles and reviews on the history of European political theory. With his wife, Charlotte Stanley, he has been long engaged in the translation of the works of Georges Sorel. (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.

Perkins, John L With his regular programmes on radio and television, newspaper columns and commentary, Waleed Aly has become Australia's favourite Muslim celebrity. He is intelligent, articulate and provides incisive analysis of political and social issues. Given this, it might have been expected that he could have applied the same quality of analysis in his book, People Like Us: How Arrogance is Dividing Islam and the West (2007); however this is not the case.

then E has a subset which is the domain of a model of Peano's axioms for the natural numbers. (This result is proved explicitly, using classical reasoning, in section 3 of [1].) My purpose in this note is to strengthen this result in two directions: first, the premise will be weakened so as to require only that the map ν be defined on the family of (Kuratowski) finite subsets of the set E, and secondly, the argument will be constructive, i.e., (...) will involve no use of the law of excluded middle. To be precise, we will prove, in constructive (or intuitionistic) set theory3, the following.. (shrink)

Counterexamples are constructed for classical decision theory, turning on the fact that actions must often be chosen in groups rather than individually, i.e., the objects of rational choice are plans. It is argued that there is no way to define optimality for plans that makes the finding of optimal plans the desideratum of rational decision-making. An alternative called “locally global planning” is proposed as a replacement for classical decision theory. Decision-making becomes a non-terminating process without a precise target rather than (...) a terminating search for an optimal solution. (shrink)

Two seemingly complementary trends stand out currently in school science education in the United States: one is the increased emphasis on inquiry activities in classrooms, and the other is the high level of attention given to student understanding of the nature of science. This essay looks at the range of activities that fall within the first trend, noting, in particular, the growing popularity of inquiry activities that engage students in engineering-type tasks. The potential for public disengagement from science and technology (...) issues is described as a result of the continued juxtaposition of these sorts of inquiry activities with our current, idealized portrayals of the nature of science—the emphasis of the second trend. Drawing on Dewey's instrumental theory of knowledge, an alternative way of thinking about science is offered that would not only provide for a more authentic understanding of science, but also invite much needed public participation in the broad governance of science in modern-day democratic societies. (shrink)

is a presentation of mathematics in terms of the fundamental concepts of transformation, and composition of transformations. While the importance of these concepts had long been recognized in algebra (for example, by Galois through the idea of a group of permutations) and in geometry (for example, by Klein in his Erlanger Programm), the truly universal role they play in mathematics did not really begin to be appreciated until the rise of abstract algebra in the 1930s. In abstract algebra the idea (...) of transformation of structure (homomorphism) was central from the beginning, and it soon became apparent to algebraists that its most important concepts and constructions were in fact formulable in terms of that idea alone. Thus emerged the view that the essence of a mathematical structure is to be sought not in its internal constitution, but rather in the nature of its relationships with other structures of the same kind, as manifested through the network of transformations. This idea has achieved its fullest expression in category theory, an axiomatic framework within which the notions of transformation (as morphism or arrow) and composition (and also structure, as object) are fundamental, that is, are not defined in terms of anything else. (shrink)

It is shown by Parsons [2] that the first-order fragment of Frege's logical system in the Grundgesetze der Arithmetic is consistent. In this note we formulate and prove a stronger version of this result for arbitrary first-order theories. We also show that a natural attempt to further strengthen our result runs afoul of Tarski's theorem on the undefinability of truth.

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.