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)

Rae Langton offers a new interpretation and defense of Kant's doctrine of things in themselves. Kant distinguishes things in themselves from phenomena, and in so doing he makes a metaphysical distinction between intrinsic and relational properties of substances. Langton argues that his claim that we have no knowledge of things in themselves is not idealism, but epistemic humility: we have no knowledge of the intrinsic properties of substances. This interpretation vindicates Kant's scientific realism, and shows his primary/secondary quality distinction to (...) be superior even to modern-day competitors. And it answers the famous charge that Kant's tale of things in themselves is one that makes itself untellable. (shrink)

In a recent paper, Howard Stein makes a number of criticisms of an earlier paper of mine ('Are Probabilism and Special Relativity Incompatible?', Phil. Sci., 1985), which explored the question of whether the idea that the future is genuinely 'open' in a probabilistic universe is compatible with special relativity. I disagree with almost all of Stein's criticisms.

This is a study of the nature of time. In it, redeploying an argument first presented by McTaggart, the author argues that although time itself is real, tense is not. He accounts for the appearance of the reality of tense - our sense of the passage of time, and the fact that our experience occurs in the present - by showing how time is indispensable as a condition of action. Time itself is further analysed, and Dr Mellor gives answers to (...) most of the metaphysical questions it provokes, concerning the relation of time to space, the dissection of time, and its relation to change and causation. (shrink)

It has been repeatedly argued, most recently by Nicholas Maxwell, that the special theory of relativity is incompatible with the view that the future is in some degree undetermined; and Maxwell contends that this is a reason to reject that theory. In the present paper, an analysis is offered of the notion of indeterminateness (or "becoming") that is uniquely appropriate to the special theory of relativity, in the light of a set of natural conditions upon such a notion; and reasons (...) are given for regarding this conception as (not just formally consistent with relativity theory, but also) philosophically reasonable. The bearings upon Maxwell's program for quantum theory are briefly considered. (shrink)

First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method (...) of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge. (shrink)

It is by now well known that Gödel first advocated the philosophy of Leibniz and then, since 1959, that of Husserl. This raises three questions:1.How is this turn to Husserl to be interpreted? Is it a dismissal of the Leibnizian philosophy, or a different way to achieve similar goals?2.Why did Gödel turn specifically to the later Husserl's transcendental idealism?3.Is there any detectable influence from Husserl on Gödel's writings?Regarding the first question, Wang [96, p.165] reports that Gödel ‘[saw] in Husserl's work (...) a method of refining and consolidating Leibniz' monadology’. But what does this mean? In what for Gödel relevant sense is Husserl's work a refinement and consolidation of Leibniz' monadology?The second question is particularly pressing, given that Gödel was, by his own admission, a realist in mathematics since 1925. Wouldn't the uncompromising realism of the early Husserl's Logical investigations have been a more obvious choice for a Platonist like Gödel?The third question can only be approached when an answer to the second has been given, and we want to suggest that the answer to the first question follows from the answer to the second. We begin, therefore, with a closer look at the actual turn towards phenomenology.Some 30 years before his serious study of Husserl began, Gödel was well aware of the existence of phenomenology. Apart from its likely appearance in the philosophy courses that Gödel took, it reached him from various directions. (shrink)

Convinced that the classically undecidable problems of mathematics possess determinate truth values, Gödel issued a programmatic call to search for new axioms for their solution. The platonism underlying his belief in the determinateness of those questions in combination with his conception of intuition as a kind of perception have struck many of his readers as highly problematic. Following Gödel's own suggestion, this article explores ideas from phenomenology to specify a meaning for his mathematical realism that allows for a defensible epistemology.

Focusing on spacetime singularities, Earman engages with a host of foundational issues at the intersection of science and philosophy, ranging from the big bang to the possibility of time travel.

In this first extended treatment of his life and work, Hao Wang, who was in close contact with Godel in his last years, brings out the full subtlety of Godel's ideas and their connection with grand themes in the history of mathematics and ...

This is a book about the philosophy of time, and in particular the philosophy of the great logician Kurt Godel (1906-1978). It evaluates Godel's attempt to show that Einstein has not so much explained time as explained it away. Unlike recent more technical studies, it focuses on the reality of time. The book explores Godel's conception of time, existence, and truth with special reference to Plato, Aristotle, Kant, and Frege. In the light of this investigation an attempt is made to (...) shed light on such issues as the precise sense in which Godel believed in the possibility of time travel, the relationship of the reality of time to the objectivity of temporal becoming, and the significance of time for human existence.This is a book about the philosophy of time, and in particular the philosophy of the great logician Kurt Godel (1906-1978). It evaluates Godel's attempt to show that Einstein has not so much explained time as explained it away. Unlike recent more technical studies, it focuses on the reality of time. The book explores Godel's conception of time, existence, and truth with special reference to Plato, Aristotle, Kant, and Frege. In the light of this investigation an attempt is made to shed light on such issues as the precise sense in which Godel believed in the possibility of time travel, the relationship of the reality of time to the objectivity of temporal becoming, and the significance of time for human existence. (shrink)

This paper analyzes hegel's critique of kant's theoretical philosophy in terms of three specific objections to kant's transcendental deduction (concerning the representation of the i, The necessity of the categories, And the problem of a preliminary epistemology) and three specific objections to kant's transcendental idealism (concerning the thing in itself, The antinomies, And other specific problems of the transcendental dialectic).