In den letzten Jahrzehntel! hat sich das Interesse an der Grund­ legung der Mathematik immer gesteigert. Fanden frtiher die wenigen Forscher, die sich emsthaft mit dieser 'Frage beschaftigten, wenig Be­ achtung, heute ist die Teilnahme sowohl von mathematischer wie von philosophischer Seite fast allgemein. Zu diesem Umschwung hat sieher die CANToRSche Mengenlehre, die gleich nach ihrem Entstehen lebhafte Erorterungen tiber ihre Berechtigung hervorrief, den AnstoB gegeben, und besonders die bei riicksichtsloser Durchfiihrung ihrer Grundgedanken auftretenden Widerspriiche zogen die allgemeine Aufmerksamkeit auf (...) sich. Doch ist die bisweUen noch geauBerte Behauptung, der Zweck -der Grundlagenforschung liege in der Beseitigung der Widersprtiche, verfehlt. In philosophischer und in mathematischer Richtung geht diese weit tiber eine solche Zielsetzung hinaus. Philosophisch untersucht man -das Wesen der mathematischen Erkenntnis, ihre Voraussetzungen und Endziele, ihr Verhaltnis zu anderen Wissensgebieten, insbesondere der Physik, und ihre Abgrenzung gegen diese dem lnhalt und der Methode nacho An diese philosophischen Erorterungen schlieBen sich umfangreiche mathematische Untersuchungen tiber den Aufbau der Mathematik aus den philosophisch gegebenen Voraussetzungen und tiber die Struktur der mathematischen Beweisftihrungen. Einzelne Teilgebiete dieser Unter­ suchungen entwickeln sich schon zu selbstandigen Disziplinen, die sich in ihren Methoden und Problemstellungen von der eigentlichen Grund­ lagenforschung unabhangig machen; ein Beispiel eines solchen neuen Zweiges der Mathematik, der sein Entstehen der Grundlagenforschung verdankt, ist die mathematischp. Logik. Allmahlich haben sich drei J. auptrichtungen gebildet, die je einer eigenen Auffassung tiber das Wesen der Mathematik entsprechen undo je zu verschieden gearteten mathematischen Untersuchungen geftihrt haben. (shrink)

In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-L f. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, (...) with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples. (shrink)

From the reviews: "A good textbook can improve a lecture course enormously, especially when the material of the lecture includes many technical details. Van Dalen's book, the success and popularity of which may be suspected from this steady interest in it, contains a thorough introduction to elementary classical logic in a relaxed way, suitable for mathematics students who just want to get to know logic. The presentation always points out the connections of logic to other parts of mathematics. The reader (...) immediately see the logic is "just another branch of mathematics" and not something more sacred." Acta Scientiarum Mathematicarum, Hungary. (shrink)

The second, corrected edition of the first and only complete English translation of Kant’s highly influential introduction to philosophy, presenting both the terminological and structural basis for his philosophical system, and offering an invaluable key to his main works, particularly the three Critiques. Extensive editiorial apparatus.

To begin with the obvious, both philosophers and empirical scientists in various fields are interested in learning about the mind and mental states. That the philosophical task is different from the scientific task was once taken for granted. It has become increasingly more common, however, to hear philosophers of mind suggesting some sort of "partnership" between philosophy and cognitive science. There is no bright line separating philosophy and science, the argument goes. Each field, it is said, can learn from the (...) other. These suggested partnerships have always struck me as shaky at best—bewildering at worst. In this paper I want to defend the traditional separation of philosophical and empirical questions. I want to urge that we render unto cognitive science its empirical investigation, while we render unto philosophy the fundamental epistemological and ontological questions that empirical science never will and never could answer. (shrink)

In this paper I will argue that a profile of the pseudo-sciences can be gained from the scientific pretensions of the pseudo-scientist. These pretensions provide two yardsticks which together take care of the charge of scientific prejudice that any suggested demarcation of pseudo-science has to face. To demonstrate that my analysis has teeth I will apply it to Freud and modern-day Bach-kabbalists. Against Laudan I will argue that the problem of demarcation is not a pseudo-problem, though the discussion will bear (...) out that Laudan's replacement question, namely the question whether someone's theory is well-confirmed, is not, as Lugg claimed, independent of the question as to whether that person is a pseudo-scientist. I further argue that my prototype pseudo-scientists do not have the shortcomings highlighted in Thagard's recent analysis of pseudo-science. (shrink)

Does perception provide us with direct and unmediated access to the world around us? The so-called 'argument from illusion ' has traditionally been supposed to show otherwise: from the subject's point of view, perceptual illusions are often indistinguishable from veridical perceptions; hence, perceptual experience, as such, cannot provide us with knowledge of the world, but only with knowledge of how things appear to us. Disjunctive accounts of perceptual experience, first proposed by John McDowell and Paul Snowdon in the early 1980s (...) and at the centre of current debates in the philosophy of perception, have been proposed to block this argument. According to the traditional view, a case of perception and a subjectively indistinguishable illusion or hallucination can exemplify what is fundamentally the same kind of mental state even though they differ in how they relate to the non-mental environment. In contrast, according to the disjunctive account, the concept of perceptual experience should be seen as essentially disjunctive, encompassing (at least) two distinct kinds of mental states, namely genuinely world-involving perceptions and mere appearances. This book presents seven recent essays on disjunctivism first published in two special issues of Philosophical Explorations: An International Journal for the Philosophy of Mind and Action. (shrink)

Two chief problems of the theory of knowledge are the question of meaning and the question of verification. The first question asks under what conditions a sentence has meaning, in the sense of cognitive, factual meaning. The second one asks how we get to know something, how we can find out whether a given sentence is true or false. The second question presupposes the first one. Obviously we must understand a sentence, i.e. we must know its meaning, before we can (...) try to find out whether it is true or not. But, from the point of view of empiricism, there is a still closer connection between the two problems. In a certain sense, there is only one answer to the two questions. If we knew what it would be for a given sentence to be found true then we would know what its meaning is. And if for two sentences the conditions under which we would have to take them as true are the same, then they have the same meaning. Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. (shrink)

Kant was centrally concerned with issues in the philosophy of natural science throughout his career. The Metaphysical Foundations of Natural Science presents his most mature reflections on these themes in the context of both his 'critical' philosophy, presented in the Critique of Pure Reason, and the natural science of his time. This volume presents a new translation, by Michael Friedman, which is especially clear and accurate. There are explanatory notes indicating some of the main connections between the argument of the (...) Metaphysical Foundations and the first Critique - as well as parallel connections to Newton's Principia. The volume is completed by an historical and philosophical introduction and a guide to further reading. (shrink)

What is mind? This book attempts to give a philosophical answer to that question in language accessible to the layperson, but with a rigor acceptable to the specialist. Published on the centenary of the birth of Wittgenstein and the 40th anniversary of the publication of Gilbert Ryle 's classic The Concept of Mind, this work testifies to the influence of those thinkers on Kenny's own work in the philosophy of mind, and assembles Kenny's ideas on philosophical psychology into a systematic (...) whole. (shrink)

Provability, Computability and Reflection.

This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.

Hegel's system of philosophy was not only the leading form of metaphysics during his lifetime, but it has taken on increasing significance in our own time. The main element in this compact collection of Hegel's thought is an eagerly awaited new translation of one of the most influential works of thought ever written, the "Encyclopedia of the Philosophical Sciences in Outline." Also included is "Preface to the System of Philosophy" and "Solger's Posthumous Writings and Correspondence." (For other texts in German (...) Philosophy, see vols. 5, 13, 23, 27, 40, 48, and 78). (shrink)

This famous book, first published in 1929 was considerably revised and enlarged in its fourth edition, which is being reprinted now.

Pain is the most prominent member of a class of sensations known as bodily sensations, which includes itches, tickles, tingles, orgasms, and so on. Bodily sensations are typically attributed to bodily locations and appear to have features such as volume, intensity, duration, and so on, that are ordinarily attributed to physical objects or quantities. Yet these sensations are often thought to be logically private, subjective, self-intimating, and the source of incorrigible knowledge for those who have them. Hence there appear to (...) be reasons both for thinking that pains (along with other similar bodily sensations) are physical objects or conditions that we perceive in body parts, and for thinking that they are not. This apparent paradox is one of the main reasons why philosophers are especially interested in pain. One increasingly popular but still controversial way to deal with this apparent paradox is to defend a perceptual or representational view of pain, according to which feeling pain is in principle no different from undergoing other standard perceptual processes like seeing, hearing, touching, etc. But there are many who think that pains are not amenable to such a treatment. Although it was the treatment of pain as a sensory-discriminative experience that had dominated the philosophical discussions throughout most of the twentieth century, attention to pains’ affective-motivational dimension has gained prominence in recent years. (shrink)

In demarcating science from pseudo-science and non-science, traditional suggestions make verifiability or falsifiability the decisive criteria. it is in the context of questioning and problem-stating that the activities of verifying and falsifying really receive their significance. the purpose of the work is to demarcate science by proposing criteria for scientific problem-stating. logic of discovery can supply the criteria (cf. bolzano, cf. also traditional problem lists).

It was about half a century ago that the mind–body problem, which like much else in serious metaphysics had been moribund for several decades, was resurrected as a mainstream philosophical problem. The first impetus came from Gilbert Ryle's The Concept of Mind , published in 1948, and Wittgenstein's well-known, if not well-understood, reflections on the nature of mentality and mental language, especially in his Philosophical Investigations which appeared in 1953. The primary concerns of Ryle and Wittgenstein, however, focused on the (...) logic of mental discourse rather than the metaphysical issue of how our mentality is related to our bodily nature. In fact, Ryle and Wittgenstein would have regarded, each for different reasons, the metaphysical problem of the mind-body relation as arising out of deplorable linguistic confusions and not amenable to intelligible discussion. There was C. D. Broad's earlier and much neglected classic, The Mind and Its Place in Nature , which appeared in 1925, but this work, although robustly metaphysical, failed to connect with, and shape, the mind–body debate in the second half of this century. (shrink)