Juliet Floyd

This book addresses the growing use of computerized systems to influence people’s decisions without their awareness, a significant but underappreciated sea-change in the way the world works. To assess these systems, this volume’s contributors explore the philosophical and ethical dimensions of algorithms that guide people’s behavior by nudging them toward choices preferred by systems architects. Particularly in an era of heightened awareness of bias and discrimination, these systems raise profound concerns about the morality of such activities. This volume brings together a diverse array of thinkers to critically examine these nudging systems. Not only are high-level perspectives presented, but so too are of those who use them on a day-to-day basis. While algorithmic nudging can produce benefits for users there are also many less-obvious costs to using such systems, costs that require examination and deliberation. This book is a major step towards delineating these concerns and suggesting ways to provide a sounder basis for future policies for algorithms. It should be of interest to system designers, public policymakers, scholars, and those who wonder more deeply about the nudges they receive from various websites and on their phones.

A revisiting and distillation of themes, questions, and results of the book’s chapters, with a description of possible alternative pathways through the volume. Open problems and suggestions for further research are also offered, laying out a vision of the field as a whole, and calling for future research, especially into topics relating to qualitative vs. quantitative uses of big data, the concept of “media”, issues in the history of philosophy and digital humanities, normative questions concerning social justice, race, gender, and disability, religion, human transformation, virtual and non-virtual reality, collective and individual experience, self-consciousness, personal identity, human enhancement through digital means, privacy, speech-act theory, documentality, history, and the intersection of research into psychological and social cognition.

L'idée de « progrès » en philosophie, ancrée dans la devise des Recherches Philosophiques, est à la fois grammaticale et autobiographique. Où se trouvait le progrès de Wittgenstein dans les années qui avaient suivi le Tractatus? Quelles leçons tirer de son parcours? Pour répondre à la question, il faut repenser la manière dont la grammaire du « progrès » doit être pesée et mesurée en philosophie. Nous nous appuyons sur l'essai de Jacques Bouveresse « Les ténèbres de notre temps (1991)» et l'idée de Stanley Cavell selon laquelle la pratique philosophique de Wittgenstein dans le Tractatus et les Recherches Philosophiques s'appuient partout sur le fait de voir à travers les réalités les possibilités, traiter la « forme » comme une possibilité de la structure. Cela permet de retracer le destin de tournants de pensée apparaissant déjà dans le Tractatus : variations sur des lignes de pensée que Wittgenstein reprendra plus tard et qu’il réorchestrera d'une nouvelle manière.

Throughout his philosophy of mathematics, Steiner’s views bear affinities and contrasts with those of Wittgenstein. From his early insistence on an intelligible notion of mathematical “explanation”, to his remarks on the necessity of certain extensions of mathematical concepts, to his analysis of the ideas of logicism, “surveyability” and “applicability” in mathematics and his reading of Kripke on rule-following, Steiner probed fundamental issues in contemporary philosophy of mathematics. This essay responds to Steiner’s interpretations of Wittgenstein, focusing especially on his Humean reading of rules as “hardened” regularities.

This Tractatus’s engagement with the issue of the nature of truth and falsity emerged from engagement with Russell. This engagement reverberated through the Vienna Circle and in particular affected Gödel. The Tractatus’s “elementary sentences” must be seen against the backdrop of Russell’s “multiple relation theory of judgment”, his theory of truth in Principia Mathematica, which Wittgenstein discussed at length with Russell in 1912–1913 and Gödel studied in 1929–1932. Russell’s approach was directed against both Idealism and William James’s pragmatist view of truth. It aimed at a direct treatment of the distinction between truth and falsity in terms of particular, logically simple beliefs (judgments lacking in truth-functional and quantification complexity). Schlick rejected Russell’s view in favor of his more holistic correspondence theory, one which, however, tipped easily into pragmatism, conventionalism and verificationism. The Tractatus begins, rather, with Russell’s bottom-up approach truth, and then draws in two further ideas: (1) The need for a medium of representation and (2) The importance of modality (possibility and necessity) to logic. This approach was developed further in his later work, i.e., Philosophical Investigations.Aware of the Tractatus and Russell’s engagement with Wittgenstein on truth, Gödel continued to engage with Russell’s multiple relation theory of truth and Principia philosophically up through 1944. The parallel yet distinct engagements of Gödel and Wittgenstein with Russell on truth (and Vienna positivism) show that each regarded Russell’s view as requiring amendment. However, their philosophical differences with one another are not merely to be understood in terms of the dichotomy between conventionalism (the usual view of Wittgenstein) and Platonism (the usual view of Gödel). They must rather be seen to emerge from the original approach to truth we find in Russell.

An investigation of the concept of “surveyability” as traced through the thought of Hilbert, Wittgenstein, and Turing. The communicability and reproducibility of proof, with certainty, are seen as earmarked by the “surveyability” of symbols, sequences, and structures of proof in all these thinkers. Hilbert initiated the idea within his metamathematics, Wittgenstein took up a kind of game formalism in the 1920s and early 1930s in response. Turing carried Hilbert’s conception of the “surveyability” of proof in metamathematics through into his analysis of what a formal system (what a step in a computation) is in “On computable numbers, with an application to the Entscheidungsproblem” (1936). Wittgenstein’s 1939 investigations of the significance of surveyability to the concept of “proof “in Principia Mathematica were influenced, both by Turing’s remarkable everyday analysis of the Hilbertian idea, and by conversations with Turing. Although Turing does not use the word “surveyability” explicitly, it is clear that the Hilbertian idea plays a recurrent role in his work, refracted through his engagement with Wittgenstein’s idea of a “language-game”. This is evinced in some of his later writings, where the “reform” of mathematical notation for the sake of human surveyability (1944/45) may be seen to draw out the Hilbertian idea. For Turing, as for Wittgenstein, the need for “surveyability” earmarks the evolving culture of humans located in an evolving social and scientific world, just as it had for Hilbert.

This volume presents an historical and philosophical revisiting of the foundational character of Turing's conceptual contributions and assesses the impact of the work of Alan Turing on the history and philosophy of science. Written by experts from a variety of disciplines, the book draws out the continuing significance of Turing's work. The centennial of Turing's birth in 2012 led to the highly celebrated "Alan Turing Year", which stimulated a world-wide cooperative, interdisciplinary revisiting of his life and work. Turing is widely regarded as one of the most important scientists of the twentieth century: He is the father of artificial intelligence, resolver of Hilbert's famous Entscheidungsproblem, and a code breaker who helped solve the Enigma code. His work revolutionized the very architecture of science by way of the results he obtained in logic, probability and recursion theory, morphogenesis, the foundations of cognitive psychology, mathematics, and cryptography. Many of Turing's breakthroughs were stimulated by his deep reflections on fundamental philosophical issues. Hence it is fitting that there be a volume dedicated to the philosophical impact of his work. One important strand of Turing's work is his analysis of the concept of computability, which has unquestionably come to play a central conceptual role in nearly every branch of knowledge and engineering.

Wittgenstein's treatment of number words and arithmetic in the Tractatus reflects central features of his early conception of philosophy. In rejecting Frege's and Russell's analyses of number, Wittgenstein rejects their respective conceptions of function, object, logical form, generality, sentence, and thought. He, thereby, surrenders their shared ideal of the clarity a Begriffsschrift could bring to philosophy. The development of early analytic philosophy thus evinces far less continuity than some readers of Wittgenstein, from Russell and the Vienna positivists to many contemporary readers of the Tractatus, have supposed.

In 1969 Stanley Cavell's Must We Mean What We Say? revolutionized philosophy of ordinary language, aesthetics, ethics, tragedy, literature, music, art criticism, and modernism. This volume of new essays offers a multi-faceted exploration of Cavell's first and most important book, fifty years after its publication. The key subjects which animate Cavell's book are explored in detail: ordinary language, aesthetics, modernism, skepticism, forms of life, philosophy and literature, tragedy and the self, the questions of voice and audience, jazz and sound, Wittgenstein, Austin, Beckett, Kierkegaard, Shakespeare. The essays make Cavell's complex style and sometimes difficult thought accessible to a new generation of students and scholars. They offer a way into Cavell's unique philosophical voice, conveying its seminal importance as an intellectual intervention in American thought and culture, and showing how its philosophical radicality remains of lasting significance for contemporary philosophy, American philosophy, literary studies, and cultural studies.

For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics grew from his Early and Middle philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.

I defend Putnam’s modal structuralist view of mathematics but reject his claims that Wittgenstein’s remarks on Dedekind, Cantor, and set theory are verificationist. Putnam’s “realistic realism” showcases the plasticity of our “fitting” words to the world. The applications of this—in philosophy of language, mind, logic, and philosophy of computation—are robust. I defend Wittgenstein’s nonextensionalist understanding of the real numbers, showing how it fits Putnam’s view. Nonextensionalism and extensionalism about the real numbers are mathematically, philosophically, and logically robust, but the two perspectives are often confused with one another. I separate them, using Turing’s work as an example.

In his Tractatus Logico-Philosophicus, Wittgenstein conveyed the idea that ethics cannot be located in an object or self-standing subject matter of propositional discourse, true or false. At the same time, he took his work to have an eminently ethical purpose, and his attitude was not that of the emotivist. The trajectory of this conception of the normativity of philosophy as it developed in his subsequent thought is traced. It is explained that and how the notion of a ‘form of life’ (Lebensform) emerged only in his later thought, in 1937, earmarking a significant step forward in his philosophical method. We argue that the concept of Lebensform represents a way of domesticating logic itself, the very idea of a claim or reason, supplementing the idea of a ‘language game’, which it deepens. Lebensform is contrasted with the phenomenologists’ Lebenswelt through a reading of the notions of ‘I’, ‘world’ and ‘self’ as they were treated in the Tractatus, The Blue and Brown Books and Philosophical Investigations. Finally, the notion of Lebensform is shown to have replaced the notion of culture (Kultur) in Philosophical Investigations. Wittgenstein’s spring 1937 ‘domestication’ of the nature of logic is shown to have been fully consonant with the idea that he was influenced by his reading Alan Turing’s 1936/1937 paper, ‘On computable numbers, with an application to the Entscheidungsproblem’.

If we consider Wittgenstein's career as a whole, it appears that he wrote more on the philosophy of logic and mathematics than any other subject. Yet his writings on these subjects have exerted little influence. Indeed, the tide of response to Remarks on the Foundations of Mathematics, which contains the bulk of his latest views of mathematics, has been for the most part overwhelmingly negative. Given his later emphasis on the context-bound character of language, mathematics and logic--where language apparently operates in an maximally precise, clear and general way--represent two of the most difficult cases for Wittgenstein to confront. My thesis aims to defend Wittgenstein from the charges of benighted arrogance traditionally levelled against him. I argue that Wittgenstein's later discussions of mathematics form a central part of a larger philosophical project, internally related to Philosophical Investigations and shaping in specific ways Wittgenstein's reaction to both scepticism and accounts of the nature of logical and mathematical truth. I see Wittgenstein criticizing the unreflective use of mathematical tools in philosophy, not offering a competing philosophy of mathematics. ;Too few of Wittgenstein's readers have been willing to offer detailed exegesis of his writing . This has made it difficult to understand how the aphoristic style of his late writing bears on the philosophical problems being discussed. On my view, the quality of Wittgenstein's writing is intrinsic to his later conception of the nature of logic, mathematics and philosophy. Line by line engagement with his texts is thus imperative in order to achieve an understanding of his philosophical objectives and criticisms. My dissertation offers as a paradigm of such reading a detailed exegesis and criticism of the opening five sections of Remarks on the Foundations of Mathematics. ;I briefly explore in some detail the origin and genesis of Wittgenstein's interest in rule-following, from its roots in the Tractatus's conception of logical syntax. This background illuminates Wittgenstein's later conception of logical truth and his criticisms of Frege's and Russell's arguments for logicism. To explore these criticisms, I focus on Wittgenstein' s discussions of the Frege-Russell definition of "Number" in "logical" terms. Placed in their appropriate philosophical and historical context, Wittgenstein's seemingly outrageous remarks about the nature of proof, mathematical logic and the foundations of mathematics do not simply betray his ignorance. Nor do they commit him to a revisionist attitude toward mathematical practice. Rather, they raise fundamental questions about the philosophical presuppositions lying behind attempts to bring particular mathematical results to bear in philosophy

A German translation with 2017 postscript of Floyd, Juliet. 2012. "Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing." In Epistemology versus Ontology, Logic, Epistemology: Essays in Honor of Per Martin-Löf, edited by P. Dybjer, S. Lindström, E. Palmgren and G. Sundholm, 25-44. Dordrecht: Springer Science+Business Media. An analysis of philosophical aspects of Turing's diagonal argument in his (136) "On computable numbers, with an application to the Entscheidungsproblem" in relation to Wittgenstein's writings on Turing and Cantor.

BOOK REVIEWS 475 mean the traditional notion of arche, i.e., a present homogeneous origin/kingdom" . The significance of this Ursprung is that of the event of world pretheoretically yielding itself itself and things . Van Buren's basic contention is that Heidegger's demythologized question about being in the early Freiburg period is overtaken by remythologizing tendencies, from the existential-transcendental configuration of the question in Being and Time to various mythopoetic reconfigurations. The latter developments are at odds with Heidegger's earlier Freiburg elaboration of the concrete historicity and the personal, lived, anarchic character of the question of being. One intriguing and far-reaching implication of van Buren's interpretation is that Being and Time amounts to an Abweg, a mistaken by-way, from which Heidegger, despite the Kehre, never fully recovers. The choice of the meta- phor of an Abwegis revealing and, in this connection, perhaps not entirely felicitous. For, if Being and Time is truly "off track," then there is presumably a right way and it must be possible to demonstrate both that right way and the nature of Being and Time's deviation from it. The terms of this crucial argument have been expertly set by van Buren in his monumental..