Gödel's relation to the work of Plato, Leibniz, Kant, and Husserl is examined, and a new type of platonic rationalism that requires rational intuition, called ...

Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel's texts on foundations with materials from Gödel's Nachlass and from Hao Wang's discussions with Gödel. He provides discussions of Gödel's views, and develops a new (...) type of platonic rationalism that requires rational intuition, called 'constituted platonism'. (shrink)

Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and (...) Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincaré and Frege. (shrink)

"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as (...) if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book. (shrink)

The thesis is a study of the notion of intuition in the foundations of mathematics which focuses on the case of natural numbers and hereditarily finite sets. Phenomenological considerations are brought to bear on some of the main objections that have been raised to this notion. ;Suppose that a person P knows that S only if S is true, P believes that S, and P's belief that S is produced by a process that gives evidence for it. On a phenomenological (...) view the relevant evidence is provided by intuition , and this should be the case in either ordinary perceptual knowledge or in mathematical knowledge. Intuition is to be understood in terms of fulfillments of intentions. Knowledge is a product of intuition and intention. In the case of mathematical knowledge it is said that there is a construction for a mathematical statement S if and only if the intention expressed by S is fulfilled . Constructions are thus viewed as intuition processes that could actually or possibly be carried out. In elementary parts of mathematics they might be characterized in terms of certain classes of recursive functions. This view is discussed in the case where S is taken to be a singular statement about natural numbers or finite sets, and also where S is taken to be a general statement about such objects. The distinction between intuition of and intuition that is also investigated in this context. ;It is pointed out how on a phenomenological view a number of central problems about mathematical intuition can be avoided: problems about the analogousness of perceptual and mathematical intuition, about causal accounts of knowledge in mathematics, and about structuralism in mathematics. The bearing of the account on issues concerning constructivism and platonism is also discussed. (shrink)

New Atheists, such as Richard Dawkins and Sam Harris, energetically say, No! Many others, including some believers, insist that faith is utterly beyond reasoned ...

"This book explores the religious underpinnings of psychoanalysis and examines how the tenets of Judaism and Christianity specifically influenced the theories and practices of Freud and Jung, respectively. It demonstrates that secular psychoanalysis is in large measure a revision of religious principles contained within the Judeo-Christian ethic and questions whether Freud's and Jung's approaches may best be suited to the psychological configurations of their fellow religionists." -- Back cover.

Theories of Truth provides a clear, critical introduction to one of the most difficult areas of philosophy. It surveys all of the major philosophical theories of truth, presenting the crux of the issues involved at a level accessible to nonexperts yet in a manner sufficiently detailed and original to be of value to professional scholars. Kirkham's systematic treatment and meticulous explanations of terminology ensure that readers will come away from this book with a comprehensive general understanding of one of philosophy's (...) thorniest set of topics. -/- Included are discussions of the correspondence, coherence, pragmatic, semantic, performative, redundancy, appraisal, and truth-as-justification theories. There are also chapters or sections of chapters on the liar paradox, three-valued logic, Field's critique of Tarski, Davidson's program, Dummett's theory of linguistic competence, satisfaction, recursion, the extension/intension distinction, and an explanation of how theories of justification, properly understood, differ from theories of truth. -/- A persistent theme is that philosophers have too often failed to recognize that not all theories of truth are intended to answer the same question. When the various questions are made distinct, it is apparent that many of the "debates" in this field are really cases of philosophers talking past one another. There is much less disagreement within the field than has commonly been thought. (shrink)

We propose a framework for including information‐processing bounds in rational analyses. It is an application of bounded optimality (Russell & Subramanian, 1995) to the challenges of developing theories of mechanism and behavior. The framework is based on the idea that behaviors are generated by cognitive mechanisms that are adapted to the structure of not only the environment but also the mind and brain itself. We call the framework computational rationality to emphasize the incorporation of computational mechanism into the definition of (...) rational action. Theories are specified as optimal program problems, defined by an adaptation environment, a bounded machine, and a utility function. Such theories yield different classes of explanation, depending on the extent to which they emphasize adaptation to bounds, and adaptation to some ecology that differs from the immediate local environment. We illustrate this variation with examples from three domains: visual attention in a linguistic task, manual response ordering, and reasoning. We explore the relation of this framework to existing “levels” approaches to explanation, and to other optimality‐based modeling approaches. (shrink)

The purpose of this paper is to examine the distinction between "negative" and "positive" duties. Special attention will be given to certain criticism raised against this distinction by Michael Tooley.

I defend mereological nihilism, the view that there are no composite objects, against a challenge from ontological emergence, the view that some things have properties that are ‘something over and above’ the properties of their parts. As the nihilist does not believe in composite wholes, there is nothing in the nihilist's ontology to instantiate emergent properties – or so the challenge goes. However, I argue that some simples can collectively instantiate an emergent property, so the nihilist's ontology can in fact (...) accommodate emergent properties. Furthermore, I show that employing plural instantiation does not bloat the nihilist's ontology or ideology. (shrink)

This book draws upon philosophical arguments, criminological evidence, and legal literature on prisoners' rights and sentencing to explore the restrictions and deprivations that can be legitimately imposed on serious offenders in the name of punishment.

2. But even to the common understanding it soon becomes evident that such knowledge, pursued even to its ultimate perfection, is nevertheless inadequate to many of the modest demands which confront that understanding. For immediately upon the achievement of even slight knowledge of the essence, existence or causes of any finite thing there comes an awareness that this thing could have been other than as it is, could have been produced by other or different causes, could have failed to come (...) into existence at all--is, in other words, radically contingent. Nor does this awareness seem merely a function of the partiality, the incompleteness and finitude of human experience; if it were, we could expect it to diminish directly in proportion to the increasing scope and depth of our experience; this it does not do, but rather grows and increases as experience grows, reaching at last such a state that many, under the spell of its conviction, are led to assert either that such an awareness is a necessary part or aspect of all experience or that its object must be a necessary, analytically discoverable part or aspect of all the objects of experience. No such assertions are necessary here; it suffices to re-affirm our faith in, and faithfulness to, the data of experience; one of the most pervasive and fundamental of all such data, then, we may honestly declare to be the radical contingency of the finite objects of our awareness. The most pervasive is existence. (shrink)

The first of my preliminary arguments which Mr. Wild feels to be erroneous is that in which possibility is held to involve both being and non-being. In defending this thesis I return to the original problem to which it attempted a preliminary solution. The pervasiveness of contingency and change in human experience was first asserted, together with the demand that metaphysics explain, as best it might, all such data; with this much I understand Mr. Wild to agree in the opening (...) paragraph of his critique. Further it was affirmed that through awareness of contingency and change, the understanding comes to possess the concepts of being and nonbeing, and can see that both contingency and change must involve these two concepts. With Mr. Wild I agree that "There is a gulf between being and non-being." To bridge this gulf, then, to mediate these terms, is the very function of possibility. It was this gulf that demanded an intermediate conception, and the characteristics attributed to this mediator were, at the outset, simply those which its function seemed to require. My whole preliminary account of the possible, then, was constructed strictly with this function in mind. Upon careful re-consideration of the matter, I find myself still holding that the bridging of this chasm between the simple non-being of an entity and the simple being of that same entity requires intermediation of precisely the sort that I first offered. How else can we proceed, either in thought or existence, from the non-being of X to the being of X, except by means of that which exceeds but has its basis in the former, and tends toward but falls short of the latter? (shrink)

Although any generalization in matters of such scope is risky, the central issue involved would seem to be this: Can man achieve, and know that he has achieved, a true and adequate philosophy? The Jesuit tendency is to stress the developmental aspects of philosophy and theology, identifying them more closely with the natural sciences. The Dominicans, on the other hand, see in this tendency great dangers, with theological pluralism as perhaps the gravest, short of outright skepticism.

This book presents modern logic as the formalization of reasoning that needs and deserves a semantic foundation. Chapters on propositional logic; parsing propositions; and meaning, truth and reference give the reader a basis for establishing criteria that can be used to judge formalizations of ordinary language arguments. Over 120 worked examples illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, and functions. The chapter on second-order logic shows how different conceptions of predicates (...) and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things. Notable for its clarity of presentation and supplemented by many exercises, this volume will be invaluable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formal reasoning. (shrink)

This analysis of Frege's views on language and metaphysics in On Sense and Reference, arguably one of the most important philosophical essays of the past hundred years, provides a thorough introduction to the function/argument analysis and applies Frege's technique to the central notions of predication, identity, existence and truth. Of particular interest is the analysis of the Paradox of Identity and a discussion of three solutions: the little-known Begriffsschrift solution, the sense/reference solution, and Russell's 'On Denoting' solution. Russell's views wend (...) their way through the work, serving as a foil to Frege. Appendices give the proofs of the first 68 propositions of Begriffsschrift in modern notation. This book will be of interest to students and professionals in philosophy and linguistics. (shrink)

In a number of essays published over the last decade or so, W. V. Quine has made some interesting suggestions concerning the ontology of theories. If I understand him correctly, one of his principal objects has been to formulate a criterion by means of which one can correctly decide what are the ontological commitments of any given theory. My aim in this paper is to reveal what I think are inadequacies in Quine's criterion and to indicate the direction in which (...) a proper formulation lies. (shrink)

In _Freedom and the End of Reason_, Richard L. Velkley offers an influential interpretation of the central issue of Kant’s philosophy and an evaluation of its position within modern philosophy’s larger history. He persuasively argues that the whole of Kantianism—not merely the Second Critique—focuses on a “critique of practical reason” and is a response to a problem that Kant saw as intrinsic to reason itself: the teleological problem of its goodness. Reconstructing the influence of Rousseau on Kant’s thought, Velkley (...) demonstrates that the relationship between speculative philosophy and practical philosophy in Kant is far more intimate than generally has been perceived. By stressing a Rousseau-inspired notion of reason as a provider of practical ends, he is able to offer an unusually complete account of Kant’s idea of moral culture. (shrink)

It is well documented that the effects of legal punishment tend to drift to the family members, friends, and larger communities of convicted offenders. Instead of conceiving of punishment drift as incidental to legal punishment, or as merely foreseen but not intended by state authorities and thus permissible, I argue that efforts ought to be undertaken to limit or ameliorate it. Failure to confine punishment drift comes perilously close to punishment of the innocent and is at odds with other legal (...) doctrines and broader penal practices that hold offenders, and offenders alone, responsible for their crimes. Numerous arguments urging tolerance of punishment drift, or more assertively defending it, are examined and found wanting. (shrink)