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.

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.

Emerging media are a product of the digital world that Alan Turing fathered. In 1936 Turing transformed the ancient notion of _algorithm_—by the 1920s central to mathematical logic—into the idea of a stored program computer. He based this transformation on the notion of a human “computor” calculating with pencil and paper, thereby envisioning the far-reaching implications of this work for everyday life. Like the philosopher Wittgenstein, with whom he discussed the foundations of mathematics, Turing recast the notions of truth and ontology by taking what we say and do as part of the world. The key philosophical ideas here are those of an _interface_ and of the _emergence_ of meaning. First, complexity and meaning are, in general, unforeseeable, while emerging in use. Second, what people say and what they mean can and often do diverge. Third, by _using_ emerging media we can study such phenomena.

This chapter explores the epistemic role that surprise and other psychological reactions play in mathematics. The chapter pursues the issue for its own sake, but also for its usefulness in illuminating certain themes in Wittgenstein's philosophy of mathematics. In order to understand Wittgenstein's views in this area, we must acknowledge the significance of his “obsession” with the “patter” [_Geschwätz_] surrounding mathematical activity, e.g., expressions concerning heuristics, evaluations, diagrams, and other intuitive aids for understanding mathematical results. Due largely to the influence of Frege and Russell, it is widely held that the intuitive and the psychological are obstacles to proper understanding in mathematics and logic. Wittgenstein's middle and later work rejects this brand of anti-psychologism, or at least develops a complicated relationship to it. And, as the chapter's suggestive and mostly sympathetic treatment shows, there is a wealth of somewhat neglected material in Wittgenstein's writing on these issues, of importance especially for the question of what is involved in understanding a mathematical proof.

The distinction between the notions of “practice” [Praxis] and “technique” [Technik] plays a distinctive role in the maturation of Wittgenstein’s philosophy 1937–1945, the time he composed Philosophical Investigations and his later remarks on the foundations of logic and mathematics. It allows him to sophisticate his idea that meaning arises “in the practice of language”, emphasizing that it is the fact that there are a variety of “techniques” for embedding symbols in forms of life and within practices that shapes our concept of rule-following. His “anthropological” turn, radicalized in his remarks on the “beginnings” of mathematics and logic, offers a deepening response to Spengler’s and Frazer’s philosophies of culture, and allows for his mature responses to Frege, Russell, Ramsey, Hilbert, and Turing— responses that involve self-criticism.Kripke linked Wittgenstein’s idea of a “practice” to social consensus and the extrusion of “privacy”; others have contrasted Praxis with theory or joined it to forms of conventionalism, incommensurability, and “primitive” normativity. But a “practice” always already involves practitioners in disputes, understandings, and alternative routes of proceeding, the mastery of differing techniques. This is of central importance for the mature Wittgenstein.

This interview offers a view from an outside perspective: Juliet Floyd, who is not a philosopher of religion but a renowned Wittgenstein scholar thinks about the future of philosophy of religion after Wittgenstein (motivated by questions from Esther Heinrich-Ramharter). She comments on a passage from the book by her teacher and friend Hilary Putnam, published about 30 years ago, which bears the programmatic title Renewing Philosophy. Looking to the future, she argues that inter-religious, intercultural understanding is a field where there is much to learn from Wittgenstein.

A survey of Parikh’s philosophical appropriations of Wittgensteinian themes, placed into historical context against the backdrop of Turing’s famous paper, “On computable numbers, with an application to the Entscheidungsproblem” (Turing in Proc Lond Math Soc 2(42): 230–265, 1936/1937) and its connections with Wittgenstein and the foundations of mathematics. Characterizing Parikh’s contributions to the interaction between logic and philosophy at its foundations, we argue that his work gives the lie to recent presentations of Wittgenstein’s so-called metaphilosophy (e.g., Horwich in Wittgenstein’s metaphilosophy. Oxford University Press, Oxford, 2012) as a kind of “dead end” quietism. From early work on the idea of a feasibility in arithmetic (Parikh in J Symb Log 36(3):494–508, 1971) and vagueness (Parikh in Logic, language and method. Reidel, Boston, pp 241–261, 1983) to his more recent program in social software (Parikh in Advances in modal logic, vol 2. CSLI Publications, Stanford, pp 381–400, 2001a), Parikh’s work encompasses and touches upon many foundational issues in epistemology, philosophy of logic, philosophy of language, and value theory. But it expresses a unified philosophical point of view. In his most recent work, questions about public and private languages, opportunity spaces, strategic voting, non-monotonic inference and knowledge in literature provide a remarkable series of suggestions about how to present issues of fundamental importance in theoretical computer science as serious philosophical issues.

Turing was a philosopher of logic and mathematics, as well as a mathematician. His work throughout his life owed much to the Cambridge milieu in which he was educated and to which he returned throughout his life. A rich and distinctive tradition discussing how the notion of “common sense” relates to the foundations of logic was being developed during Turing’s undergraduate days, most intensively by Wittgenstein, whose exchanges with Russell, Ramsey, Sraffa, Hardy, Littlewood and others formed part of the backdrop which shaped Turing’s work. Beginning with a Moral Sciences Club talk in 1933, Turing developed an “anthropological” approach to the foundations of logic, influenced by Wittgenstein, in which “common sense” plays a foundational role. This may be seen not only in “On Computable Numbers” and Turing’s dissertation ), but in his exchanges with Wittgenstein in 1939 and in two later papers, “The Reform of Mathematical Phraseology and Notation” and “Solvable and Unsolvable Problems”.

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.

A Just-So story, intended as plausible philosophical reconstruction, of the mutual impact of Wittgenstein and Turing upon one another. Recognizably Wittgensteinian features of Turing’s diagonal argumentation and machine-model of human computation in “On Computable Numbers, with an Application to the Entscheidungsproblem” (OCN) and his argumentation in “Computing Machinery and Intelligence” (Turing 1950) are drawn out, emphasizing the anti-psychologistic, ordinary language and social aspects of Turing’s conception. These were indebted, according to this story, to exposure to Wittgenstein’s lectures and dictations. Next Wittgenstein’s manuscripts on the foundations of mathematics 1934-1942 are interpreted in light of the impact of Turing’s analysis of logic upon them. Themes will include the emergence of rule-following issues, the notion of Lebensform, a suggestion about a strand in the private language remarks, and anti-psychologism. The payoff is a novel and more adequate characterization, both of Turing’s philosophy of logic and of Wittgenstein’s.