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. (shrink)

The notion of forms of life points to a crucial aspect of Wittgenstein’s philosophical approach that challenges an influential line in the philosophical tradition. He portrays intellectual activities in terms of a cohesion of things held together in linguistic scenes rooted in the lives of people and the facts of the world. The original inspiration with which Wittgenstein worked on this approach is still relevant today in the recent technological turn associated with AI. He attacked a conception that treated human (...) activities as material to be examined by external models of rationality. Along with other modernists such as Musil, he saw the danger of losing faith in human intellectual and moral capacities. In contrast, Wittgenstein elucidates and substantively defends an idea of forms of life in which the great normative enterprises, from science to the works of the imagination, are based on our individual capacity to take the next step from a normative authority that rests entirely with us, as agents who can claim it in the name of others, in the name of arithmetic, in the name of our native language, in the name of justice, and so on. Forms of life are the place to look to claim this authority over the mistrust we feel compelled to cultivate in our human endeavors. (shrink)

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. (shrink)

In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so-called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that we have adopted (...) a paraconsistent logic, Wittgenstein's answer to Turing is that if we run into trouble building our bridge, it is either because we have made a calculation mistake or our calculus does not actually describe the phenomenon it is intended to model. The possibility of either kind of error is not particular to contradictions nor inconsistency, and thus contradictions do not have any special status as a thing to be avoided. (shrink)

Contemporary neo-Aristotelianism attempts to ground normative constraints on action on the notion of human nature and this opens it to two main objections: Firstly, human nature seems to be too indeterminate to set constraints on action; secondly, it is unclear why knowledge of human nature should motivate agents. This essay considers the contribution that Wittgenstein’s notion of form of life can give in answering these challenges. It suggests that forms of life are not objects of analysis, but rather a new (...) philosophical method, which allows us also to investigate human volitional capacities and their normative significance for practical rationality. (shrink)