Notes taken by these last four are the basis for the thirty-one lectures in this book.

From his return to Cambridge in 1929 to his death in 1951, Wittgenstein influenced philosophy almost exclusively through teaching and discussion. These lecture notes indicate what he considered to be salient features of his thinking in this period of his life.

Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

This five-volume German-English edition presents, for the first time, new translations of all of Wittgenstein's mature 1937-1944 writings on mathematics and logic. The first (1956) and third (1978) editions of Wittgenstein's Remarks on the Foundations of Mathematics omitted, unsystematically, more than half of Wittgenstein's later writings on mathematics; for that reason, the reader will here read some entire manuscripts for the first time, and other manuscripts for the first time as unabridged, sustained pieces of writing. Philosophers (...) and other interested readers will gain fresh insight into Wittgenstein's perspectives on a wide range of topics, from Gödelian propositions and the Cantorian conception of real numbers to the nature of mathematical propositions and the diversity of proof techniques. Other subjects covered include: mathematical sense; axioms and self-evidence; prudish proofs; the functionality of extra-mathematical application; undecided mathematical conjectures; rule-governed unwinding; and G. H. Hardy's conceptions and claim. (shrink)

Purpose. The paper is aimed at analyzing in a comparative way the philosophical conceptions of the human, proposed by Ludwig Wittgenstein and Martin Heidegger as the main representatives of the analytic and continental tradition of philosophizing in the XXth century. The theoretical basis of the study is determined by Wittgenstein’s legacy in the field of logical and linguistic analysis, as well as Heidegger’s existential, hermeneutical, and phenomenological ideas. Originality. Based on the analysis of the philosophical works of (...) class='Hi'>Wittgenstein and Heidegger, the initial principles of their anthropological concepts in the unity of transcendental preconditions, essential foundations, and correlations to the world in the technosphere are reconstructed. It is demonstrated that, despite the difference in the explanation of the peculiarities in the interpretation of the realm of the transcendental and basic characteristic of the inner world of human, both philosophers emphasized the understanding of the human being through the prism of language and the need for anthropologization of science and technology. Conclusions. Wittgenstein and Heidegger developed their own original considerations on the nature of human being, which fully conform to the basic theoretico-methodological principles of their philosophical conceptions. The former focused on how language reflects a human’s world and serves as a means of expressing their knowledge and aspirations. The latter, on the contrary, interpreted the world as a reflection of language that expresses itself through human. As a supporter of analytic methodology and, accordingly, of accuracy in formulations, Wittgenstein came to the concept of the unspeakable in the process of reflection on the being of human over the language. But in Heidegger’s existential discourse, which is full of metaphors and neologisms, being of human is limited by the concept of Nothing. As a consequence, it is noted that the ontological status of values is transcendental to the world according to Wittgenstein, but it is immanent to the world, according to Heidegger. It is argued that the Austrian thinker developed a linguo-psychological approach to the study of human through the prism of the mental, but the German philosopher comprehended the human on the basis of the concept of self in the ontological sphere. It has been demonstrated that both thinkers have pointed to the challenges faced by humans in the development of science and technology while emphasizing the importance of substantiating their anthropological foundations. (shrink)

Problem: A dualistic position faces considerable problems as Mitterer, inter alia, clearly pointed out. Mitterer not only wants to name these problems, but to provide a genuine alternative with his non-dualism. However, this non-dualistic alternative also contains severe problems. Thus this text suggests preferring Wittgenstein's concept of a pragmatic investigation of language-games to Mitterer's non-dualism in order to tackle the problems of dualism. Solution: With recourse to Wittgenstein's pragmatic investigation of language-games, a fundamental problem of dualism can be (...) solved. With the concept of certainty, Wittgenstein succeeds in avoiding an ontological grounding in an independent world -- or, as Mitterer would put it, the assumption of a "beyond of discourse." At the same time, the assumption of an independent world as a concept that provides a basis for our language-games is maintained on an epistemological level. This assumption, however, is not maintained as a phenomenon that requires to be substantiated but as a certainty that is constitutive for language-games and does not need to be substantiated. Such a concept is suitable for preventing epistemological operations such as knowledge, doubt, giving reasons, etc., from being made void, without having to provide an ontological basis for them. Implications: Wittgenstein's point of view therefore provides an attractive alternative to Mitterer's non-dualism. By getting rid of the "beyond of discourse," Mitterer's non-dualism faces the problem of not being able to explain how we can manage to understand epistemological operations within our language-games without referring to a "beyond of discourse." From this point of view arises the consequence that it would make sense to analyze language-games from a pragmatic standpoint rather than to keep on honing non-dualistic vocabulary. (shrink)

The primary purpose of this book is to probe the "deep common sources" of Wittgenstein’s Investigations and Remarks on the Foundation of Mathematics in his later philosophy of language. The question is whether Wittgenstein’s thought about mathematics can be presented sympathetically, and so defended from charges of superficiality or eccentricity which have often been levelled against it. There are other strands in this complex, simultaneously gripping and maddening work, including confrontations of varying extent with relevant doctrines of Dummett, (...) Davidson, and Quine, to cite the main cases. The character of Wittgenstein’s own thought was far from systematic, yet this does not seem to justify the virtual lack of systematic presentation of his defense by Wright. We can, nevertheless, pick out the main thrust of Wright’s case. The author takes his bearings by the quarrel within twentieth century philosophy of mathematics between platonism and intuitionism. Platonism may be briefly described as the view that, if p is a mathematical proposition, we know what would be the case if p were true, even if we can't show that p is true. For intuitionism, on the other hand, to know what would be the case if p were true, is impossible unless we can show that p is indeed true. (shrink)

Open peer commentary on the article “What Can the Global Observer Know?” by Diana Gasparyan. Upshot: While I agree with Gasparyan’s incisive critique of the concept of the “general observer,” her use of the concept of “event” is somewhat ambiguous. On the one hand, she equates “events” to Wittgenstein’s and “configurations of objects” or “states of affairs” and she consider the world as a collection of such states of affairs. On the other hand, she cites Badiou’s work in support (...) of her criticism of the “general observer.” Yet Badiou’s conception of events is very different from Wittgenstein’s: they are locally produced by historically situated agents in their concrete inter-subjective activities. I argue that a resolution of the target article’s ambiguity in favour of Badiou’s conception of events would allow constructivism to escape a narrow epistemological reading of its basic thesis in favor of a broader interpretation. (shrink)

Pole neatly characterizes Wittgenstein's philosophical method in the Investigations and Remarks on the Foundations of Mathematics, and, in an epilogue, Wisdom's procedure in Other Minds and Philosophy and Psycho-Analysis. Although he criticizes both for their emphasis on ordinary usage to the exclusion of creative philosophizing, his work is sympathetic and will be useful both to those who know Wittgenstein's works well and to those who do not.--E. S.

The aim of this chapter is to open the question of this pervasiveness of the moral by arguing for the impossibility of delimiting the moral in one specific case, that of psychological self-ascription. The first part presents two views of the relationship between nature and morality found in forms of scientific and relaxed naturalism. In the main part, I argue, first, that psychological self-ascriptions are in most cases not to be understood on the standard model of observation and descriptions, but (...) rather as expressions of thoughts and feelings already present for us. And in the second, I contend that psychological self-ascriptions therefore always involve elements of endorsement and responsibility, which means that they are ways of situating ourselves morally in relations to others. (shrink)

_Wittgenstein's Remarks on the Foundations of AI_ is a valuable contribution to the study of Wittgenstein's theories and his controversial attack on artifical intelligence, which successfully crosses a number of disciplines, including philosophy, psychology, logic, artificial intelligence and cognitive science, to provide a stimulating and searching analysis.

_Wittgenstein's Remarks on the Foundations of AI_ is a valuable contribution to the study of Wittgenstein's theories and his controversial attack on artifical intelligence, which successfully crosses a number of disciplines, including philosophy, psychology, logic, artificial intelligence and cognitive science, to provide a stimulating and searching analysis.

In the preface to the Tractatus Wittgenstein acknowledged ‘Frege's great works’ as one of the two primary stimulations for his thoughts. Throughout his life he admired Frege both as a great thinker and as a great stylist. This much is indisputable. What is disputable is how he viewed his own philosophical work in relation to Frege's and, equally, how we should view his work in this respect. Some followers of Frege are inclined to think that Wittgenstein's work builds (...) on or complements that of Frege. If that were true it would be plausible to suppose that the joint legacy of these two great philosophers can provide a coherent foundation for our own endeavours. But it is debatable whether their fundamental ideas can be synthesized thus. The philosophy of Wittgenstein, both early and late, is propounded to a very large extent in opposition to Frege's. They can no more be mixed than oil and water – or so I shall argue. (shrink)

For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. (...) Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary. (shrink)

For Wittgenstein's supposed private language is one which it is logically impossible to teach another and similarly impossible for anyone else to understand. The global purpose of Wittgenstein's discussion of private knowledge of experience, private ownership of experience and private ostensive definition (which might be called the private language argument in a narrow sense) is not to establish that language is essentially social. Of course, human languages are shared, and are learned in social contexts from parents, elders and (...) siblings. That is an anthropological and psychological truth. What is distinctive about early modern philosophy was its unquestioned adoption of the concepts of ideas and impressions as the primary tools for explanation of the sources, nature and limits of knowledge and understanding, and as the foundations of language. What Wittgenstein aimed to show is not that sensation‐language, like the rest of language, is essentially shared, but that it is essentially shareable. (shrink)

Wittgenstein's anti‐psychologism had induced him not to investigate the concepts that informed the psychological presuppositions of the Tractatus; only the essence of any possible symbolism seemed relevant to his concerns. The private language arguments have shown the incoherence of the idea that the foundations of language lie in private mental objects that constitute, or explain, the meanings of primitive indefinables of language. For language is 'alive' for one only in so far as one thinks or understands the senses (...) attached to sentences. Thinking is a psychological process of coming into intellectual contact with, grasping, these lexical souls. One deep root of our troubles lies in a supposition which Wittgenstein criticized in the context of his discussion of the name/object model as misapplied to the concept of pain and its relation to pain‐behaviour. We must remind ourselves how specialized is the language‐game of saying what we think, of communicating our thoughts, of telling them to others. (shrink)

Wicker's concern is to build a philosophical and justificational foundation for a "Christian radicalism" which can serve to synthesize the two modern secular themes of self-determination and communalism. He explores particular secular theories of perception, language, and society and rejects them as irrelevant to modern realities. He then constructs in their place three sacred theories, where "sacred" is to be understood not as a sheltered corner of our experience but rather as the basis of the more general intersubjectivity which defines (...) man-in-society. He draws on Merleau-Ponty for a theory of perception, Wittgenstein for a theory of language, and Marx for a theory of society. All three theories find man in a closer participating relation with his world environment than do their rejected alternatives. These three theories suggest three modes of being-in-the-world: the bodily, the linguistic, and the economic, all of which are expressive—the latter in the sense that it involves the transformation of environment into expressiveness. The conjunction of the three modes, then, defines our community life. Wicker uses George Eliot, Dickens, Orwell, and William Golding to show how various human attitudes toward environment are manifest in literature. These attitudes are classifiable into the secular—environment as passive context for human life—and the sacred—environment as fraught with primordial significance which man shares and of which he is part. Wicker further justifies his vision of Christianity with the aid of Levy-Bruhl, van der Leeuw, and Eliade whose studies in primitive religions fructify Wicker's notion of the sacred. The book ends with a theological formulation of its main themes involving new translations of old doctrines. The book is a brave effort to revitalize with secular insights a moribund Christianity and to point it to its own roots in the foundations of man.—S. O. H. (shrink)

This chapter contains sections titled: Setting the stage Leitmotifs External guidelines Necessary propositions and norms of representation Concerning the truth and falsehood of necessary propositions What necessary truths are about Illusions of correspondence: ideal objects, kinds of reality and ultra‐physics The psychology and epistemology of the a priori Propositions of logic and laws of thought Alternative forms of representation The arbitrariness of grammar A kinship to the non‐arbitrary Proof in mathematics Conventionalism.

The pivotal thesis of Cunningham’s critical discussion is that Husserl failed to realize that consciousness is essentially "language-using consciousness." The spread of argumentation throughout her analysis is designed to show that this failure on Husserl’s part resulted in a number of unhappy consequences. It occluded the primacy of the social context; it misconstrued what is at issue in the phenomenological transcendental and eidetic reductions; and it led to unwarranted claims for an apodictic foundation of science and metaphysics. The launching-pad for (...) Cunningham’s critique is Husserl’s Cartesian Meditations, of which she offers, in her own words, "a somewhat oblique commentary." This work by Husserl is selected because it illustrates most clearly the conflict between linguistic performance and the quest for certainty. Cunningham works out from this conflict, from time to time calling upon the later Wittgenstein to help her demonstrate the untenability of Husserl’s separation of language from intentional consciousness. After correcting this mistake by Husserl she then goes on to show how attentiveness to the language-using posture of consciousness is able to bridge the chasms between essence and existence, the transcendental and the transcendent, the ideal and the real—chasms which remained unbridged throughout Husserl’s intellectual development. (shrink)

Our online interaction with information-systems may well provide the largest arena of formal logical reasoning in the world today. Presented here is a critique of the foundations of Logic, in which the metaphysical assumptions of such 'closed world' reasoning are contrasted with those of traditional logic. Closed worlds mostly employ a syntactic alternative to formal language namely, recording data in files. Whilst this may be unfamiliar as logical syntax, it is argued here that propositions are expressed by data stored (...) in files which are essentially non-linguistic and so cannot be expressed by simple formulae F(a), with the inference-rules normally used in Logic. Hence, the syntax of data may be said to define a fundamentally new kind of logical form for simple propositions. In this way, the logic of closed systems is shown to be non-classical, differing from traditional logic in its truth-conditions, inferences and metaphysics. This paper will be concerned mainly with how the reference and certain inferences in such a closed system differ metaphysically from classical logic. (shrink)

The numbering in the new edition of Wittgenstein's Remarks does not in general correspond to the part and section numbers of the 1956 edition. The following concordance is useful for making cross references between the two editions.

The conception of first‐person knowledge of thought and experience was present in antiquity. It played a major role in Western philosophy in the early modern era as an integral part of the Cartesian and Lockean conceptions of the mind. If inner sense is a form of introspective self‐observation yielding knowledge, as it seemed to be, then awareness of the contents of the mind appears to be analogous to what we take to be awareness or consciousness of objects by the exercise (...) of a perceptual faculty. Descartes thought that the impossibility of doubt implied the presence of complete certainty. Consequently, he cast what he called 'thoughts' in the role of the certain foundations of empirical knowledge. Both Locke and Descartes supposed that one is conscious of what passes in the mind, and that what one is conscious of one knows to exist or obtain. (shrink)

This chapter contains sections titled: The continuation of the Early Draft into philosophy of mathematics Hidden isomorphism A common methodology The flatness of philosophical grammar.

The debate on the foundations of knowledge and meaning has gained particular attention in recent philosophical discourse. A number of commentators, including Richard Rorty, have categorized leading contemporary philosophers such as Wittgenstein as being 'anti-foundationalist". In this comprehensive analysis of Wittgenstein's concept of the form of life and its implications, Professor Conway takes issue with this characterization of Wittgenstein. Instead, the author interprets Wittgenstein as continuing the discussion of foundations, while radically transforming the very (...) understanding of foundations. (shrink)

This book collects 13 papers that explore Wittgenstein's philosophy throughout the different stages of his career. The author writes from the viewpoint of critical rationalism. The tone of his analysis is friendly and appreciative yet critical. Of these papers, seven are on the background to the philosophy of Wittgenstein. Five papers examine different aspects of it: one on the philosophy of young Wittgenstein, one on his transitional period, and the final three on the philosophy of mature (...) class='Hi'>Wittgenstein, chiefly his Philosophical Investigations. The last of these papers, which serves as the concluding chapter, concerns the analytical school of philosophy that grew chiefly under its influence. Wittgenstein’s posthumous Philosophical Investigations ignores formal languages while retaining the view of metaphysics as meaningless -- declaring that all languages are metaphysics-free. It was very popular in the middle of the twentieth century. Now it is passé. Wittgenstein had hoped to dissolve all philosophical disputes, yet he generated a new kind of dispute. His claim to have improved the philosophy of life is awkward just because he prevented philosophical discussion from the ability to achieve that: he cut the branch on which he was sitting. This, according to the author, is the most serious critique of Wittgenstein. (shrink)

Wittgenstein's Remarks on the Foundations of Mathematics was poorly received by the critics when it was first published, and only a few sympathetic commentators have made much of it since then. The book has not had a great success, because the majority of people interested in the philosophy of mathematics these days have a quite different approach to the subject from Wittgenstein. But not only that, they have a quite different logic from Wittgenstein. I believe one (...) of the main sources of the antipathy felt towards the Remarks lies in the foreignness of the logic Wittgenstein develops there. I hope, in what follows, to make that logic more understandable, and with it the philosophy of mathematics it supports. (shrink)

So-called 'hinge propositions', Wittgenstein's version of our basic beliefs, are not propositions at all, but heuristic expressions of our bounds of sense which, as such, cannot meaningfully be said but only show themselves in what we say and do. Yet if our foundational certainty is necessarily an ineffable, enacted certainty, any challenge of it must also be enacted. Philosophical scepticism – being a mere mouthing of doubt – is impotent to unsettle a certainty whose salient conceptual feature is that (...) it is lived. I appeal to psychopathology to show that the lived refutation of a basic certainty is not a manifestation of uncertainty, but of madness. (shrink)

In On Certainty Wittgenstein presents an argument against both G. E. Moore and the Cartesian skeptic, exposing both positions as flawed. His main contention is that what "stands fast" for us-certainty-is not subject to doubt, truth, or falsehood. Whatever is subject to these ascriptions is propositional in form and belongs to our language-games. But certitude is not so subject; certitude is principally non-propositional and therefore stands outside the language-game. Action is the locus of certainty, the things about which we (...) are certain constitute the "foundation" upon which all our knowledge turn. What Moore had once called our "obvious truisms" are, under Wittgenstein's direction, recognized first as inherent in our human natural history, and second, as grounded or based in human societies, cultures, forms of life. It is this human-centered kind of foundationalism that distinguishes Wittgenstein from what Moyal-Sharrock characterizes as the super-human kind of traditional, Cartesian foundationalism. Due to the human emphasis, Wittgenstein's new kind of foundationalism is quite different than the traditional Cartesian variety; it makes no guarantees of absoluteness or universality. Instead, Wittgenstein identifies a common groundwork, a "footing" on which our language-games rest. This new kind of foundationalism shows the way our language-games are anchored to the world. Therefore, in On Certainty, I argue that Wittgenstein presents a new kind of foundationalism. (shrink)

Locke reports, in his discussion of substance and with some amusement, on the Indian philosopher who, when asked what the earth rests on, postulated an elephant and then, when asked in turn about the elephant, decided to go with a tortoise. Locke's amusement, of course, is justified. But it is also tempered if not downright equivocal. For he sees that at some point a very special elephant or—if we stick to the Indian's story—a very special tortoise will have to be (...) invoked. Locke's own tortoise, or elephant, substratum or substance, has some very peculiar properties or, alternatively, an equally alarming lack of them—so much so that, as he is painfully aware, it might well seem totally implausible. Enough of Locke though. Wittgenstein's problem, unlike Locke's, lies in epistemology. His elephant consists of an indefinitely large and varied set of bench-marks or paradigms—Moore's examples, in fact, along with some additions—that function as an epistemological ‘foundation’, ‘river bed’, ‘bedrock’, ‘rock bottom’, a ‘substratum’, no less. Where is the tortoise? Wittgenstein's answer to this is that there is no tortoise, none at all. A non-existent tortoise, however, is as unacceptable here as a regular common-or-garden one. Even the Indian realized that an elephant is no good without a tortoise. (shrink)