"With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics."--Carl B. Boyer, Brooklyn College. This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. Advanced (...) topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers. 1959 ed. 27 Figures. Index. (shrink)

Friedrich Waismann (1896–1959) was one of the most gifted students and collaborators of Moritz Schlick. Accepted as a discussion partner by Wittgenstein from 1927 on, he functioned as spokesman for the latter’s ideas in the Schlick Circle, until Wittgenstein’s contact with this most faithful interpreter was broken off in 1935 and not renewed when exile took Waismann to Cambridge. Nonetheless, at Oxford, where he went in 1939, and eventually became Reader in Philosophy of Mathematics (changing later to (...) Philosophy of Science), Waismann made important and independent contributions to analytic philosophy and philosophy of science (for example in relation to probability, causality and linguistic analysis). The full extent of these only became evident later when the larger (unpublished) part of his writings could be studied. His first posthumous work The Principles of Linguistic Philosophy (1965, 2nd edn.1997; German 1976) and his earlier Einführung in das mathematische Denken (1936) have recently proved of fresh interest to the scientific community. This late flowering and new understanding of Waismann’s position is connected with the fact that he somewhat unfairly fell under the shadow of Wittgenstein, his mentor and predecessor. Central to this book about a life and work familiar to few is unpublished and unknown works on causality and probability. These are commented on in this volume, which will also include a publication of new or previously scattered material and an overview of Waismann’s life. (shrink)

In this study Friedrich Waismann gives a systematic presentation of insights into philosophical problems which can be achieved by clarifying the language in which the problems are posed. Much of the material and the method itself derive from Wittgenstein's work in the early 30s. The book was originally envisaged as a lucid and well organized account of Wittgenstein's distinctive form of linguistic philosophy to enable the Vienna Circle to incorporate these valuable methods into their own programme of analysis. (...) The project evolved over many years into a wide-ranging survey of the dissolution of many philosophical problems and the construction of a systematic philosophical grammar. Waismann shows in detail how puzzlement can be removed by careful description of the uses of the terms employed in framing problems. At the same time, he sketches a general framework for analysis of language, including chapters on names, general terms, logical operators, propositions, questions, etc. This book is an authoritative presentation of Wittgenstein's influential philosophy of language in a format much easier to follow than his own intricate and elusive texts. Waismann exhibits clearly the merits of this method of philosophizing. This book should serve as an important and useful text for those who wish to understand the method and power of linguistic philosophy. It has no equal as an introduction to Wittgenstein's philosophy. (shrink)

The Voices of Wittgenstein brings for the first time, in both the original German and in English translation, over one hundred short essays in philosophical logic and the philosophy of mind. This text is of key historical importance to understanding Wittgenstein's philosophical thought and development in the 1930's. Transcribed from the papers of Friedrich Waismann and dating from 1932 to 1935, the majority are highly important dictations by Wittgenstein to Waismann. It also includes texts of redrafted material (...) by Waismann, closely based on these dictations. (shrink)

The author attempts to sketch a new picture of language: language is stratified into layers, each layer having a logic of its own and being separated from the others by gaps over which one may jump but which cannot be bridged by logical processes. Philosophers try to bridge the gaps and become entangled in pseudo-problems. Law statements exemplify one stratum, thing statements another, sense-datum statements another, ethical statements another, and so on. The different subject-matters are to be characterized by reference (...) to the different strata, rather than conversely; a sense impression is something that is describable in a language of such-and-such structure; a material object is something which can be described in such-and-such language; and so on. A consequence of the theory is said to be that logic loses its universal validity: logic can only be applied to statements that are homogeneous. However, relations between the layers do claim the attention of the logician. (shrink)

This work brings in both the original German and English translation of over one hundred short essays in philosophical logic and the philosophy of mind of historical importance to understanding Wittgenstein's philosophical thought and development in the 1930's. Transcribed from the papers of Friedrich Waismann and dating from 1932-35, the majority are highly important dictations by Wittgenstein to Waismann, but also includes texts of redrafted material by Waismann closely based on the dictations. Many of these texts (...) become the ultimate sources of material on philosophy of language that constitutes the bulk of Waismann's book Logic, Sprache, Philosophy. The transcriptions throw light on the development of Wittgenstein's thought in this period and some of the topics are not covered in any of the existing publications of his writings, in particular his detailed attention to causal theories of meaning. They also contain texts covering psychological concepts such as expecting, intending and experience; these have no counterparts in Waismann's publications. (shrink)

Bibliography of works by and about F. Waismann : p. [177]-184.

The year 1927 is a landmark in the evolution of physics—the year which saw the obsequies of the notion of causality. To avoid misconceptions, it should not be thought that the concept fell a victim to the unbridled antipathy of certain physicists or their indulgence in fancies. The truth is that men of science came, very reluctantly and almost against their will, to recognize the impossibility of giving a coherent causal description of the happenings on the atomic scale, though some (...) of them—curiously enough, amongst them Planck, Einstein, de Broglie, Schrödinger—could never bring themselves to accept wholeheartedly so drastic a renunciation of classical ideals. (shrink)

Schlicks philosophie is der bedeutendste Versuch, der je unternommen worden ist, über die Zersplitterung der philosophischen Systeme hinwegzukommen, zu einer Aufassung, die keiner Richtung angehört und doch für alle Richtungen bindend ist. Man hat bisher das Augenmerk fast immer den Antworten zugewandt, welche auf philosophische Fragen gegeben worden sind. Um diese Antworten, um ihre Wichtigkeit oder Falschheit, Ihre Begründung oder Widerlegung drehte sich bisher der Streit. Die neue Auffassung unterscheidet sich von den bisherigen darin, dass sie zunächst von den Antworten (...) ganz absieht und die Natur der Fragestellung selbst genau untersucht. Diese Einsicht führt zu einer vollkommen neue Lösung der philosophischen Fragen, freilich in einem anderen Sinne als man erwattet hatte. Man hatte nämlich Antworten erwartet, welche die gestellte Frage -- ob zum Beispiel die Aussenwelt wirklich existiert, ob der menschliche Wille frei ist.. -- in bejahendem oder in verneinendem Sinn entscheiden sollten. Statt dessen führt die tiefer dringende Analyse zu der Einsicht, dass die Form dieser Frage überhaupt auf einem Missverständnis beruht und erlöst uns, indem sie uns den Sinn unserer Worte und ihre Verknüpfungen so klar macht, dass wir von dem Zwang des Fragens befreit werden. Es ist eine Hinwendung zu einer objektiven, undogmatischen Philosophie, die keinen Gegner haben kann, weil sie nichts behauptet. In diesem Geiste philosophieren heisst gar nichts anderes, als mit Klarheit und Bewusstsein denken. Durch diese Methode wird die Situation der Philosophie von Grund auf geändert. Es zeigt sich vor allem, dass die sogenannten unlösbaren Probleme Scheinfragen sind. Ihre Unlösbarkeit war ja unsere eigene Schuld: denn wir haben die Worte in unzulässiger Weise zu einer Frage zusammengestellt und damit den Sinnbereich der Sprache verlassen. Jede Frage, die sinnvoll gestellt worden kann, ist auch im Prinzip einer Antwort fähig. Schlick war aber nicht nur der strenge, unerbittliche Denker; innerlich vielleicht noch näher standen ihm die grossen Lebensprobleme. Diese Geisteshaltung ist nur der Ausfluss von Schlicks Persönlichkeit. Ihr war auch ein dichterischer Zug zu eigen, der sogar in seinem Stil manchmal anklingt. Diesen Zug muss man sich wohl vor Augen halten, wenn man Schlick verstehen will. (shrink)

INTRODUCTION The present volume unites contributions by the leading figure of the Vienna Circle and by two of his closest assoCiates, contributions that deal with an area of thought represented, indeed, in this Collection but certainly not the central one in the common picture ofthe Circle's activities. It is no accident that an interest in ethics and the philosophy of action was particularly marked in what Neurath was apt to call the right wing of the Circle. For them, as for (...) Wittgenstein (the respected mentorofSchlickandWaismanninparticular),theadvancetobehoped for in philosophy consisted not solely in freeing natural science from a confused sense of dependence on speculative metaphysics but also in seeingthatotherareasoflanguageandaction hadto bethoughtaboutin theirownterms, whichwereneitherthoseofnaturalsciencenorthoseof philosophy as traditionally conceived. The scepticismofSchlick about theprogrammeofUnifiedSciencewaswellknown: EinheizwissenschaJt he called it, as it might be 'boozified science'. And in sober truth the programme sometimes masked a left-wing set of values taken (surely illogically) for granted, though the membersofthe Circle entertained a wide range ofpolitical views. Schlick's own contribution to the present volume is a section from thenotesforoneofhisfinal lectureseries,forsightofwhich wewarmly thanktheonlysurvivingcontributortoourvolume,DrJosephSchachter: Schlick'sgrandsonDra. M. H. vandeVeldehaskindlyconsentedtotheir publication. This section poses the problem we have outlined: there are questionsandaneedforclarificationinethics,butthesenomoredemand a metaphysical solution than does a similar situation in epistemology. Here, as in his earlier Problems of Ethics,l Schlick sets his face against thewholeprocess,mostobviousin Kant,ofmakingtheconceptofvalue absolute. One might say that for Schlick there is no unhypothetical imperative. (shrink)

It seems to make perfectly good sense to distinguish between what is expressed and the way in which it is expressed. There is little doubt that there are many different ways of saying the same thing open to us. If I denied this, I would certainly be wrong. And yet a word of caution may not be amiss. Among logicians a tendency has grown up to concentrate their attention on those properties of a statement which make it true or false, (...) what they call a “proposition”, and to neglect the form in which it is expressed. I think it is a dangerous tendency as it may lead to overlooking all sorts of differences which are due to the form. Let me give an example taken from F. P. Ramsey. (shrink)