Mathieu Marion

After presenting the rules of Eleatic antilogic, i.e., dialectic, I argue that Zeno was a practitioner, and, on the basis of key passages from Plato’s Parmenides (127e-128e and 135d-136c), that his paradoxes of divisibility and movement were notreductio ad absurdum, but simple derivation of impossibilities (adunaton) meant to ridicule Parmenides’ adversaries. Thus, Zeno did not try to prove that there is no motion, but simply derived this consequence from premises held by his opponents. I argue further that these paradoxes were devised, in accordance with Eleatic antilogic, following a scheme that included hypotheses and their contradictories, within which the subject is to be treated both “in relation to itself,” and “in relation to other things”.

This volume is a collation of original contributions from the key actors of a new trend in the contemporary theory of knowledge and belief, that we call “dynamic epistemology”. It brings the works of these researchers under a single umbrella by highlighting the coherence of their current themes, and by establishing connections between topics that, up until now, have been investigated independently. It also illustrates how the new analytical toolbox unveils questions about the theory of knowledge, belief, preference, action, and rationality, in a number of central axes in dynamic epistemology: temporal, social, probabilistic and even deontic dynamics.

We will discuss a mathematical proof found in Wittgenstein’s Nachlass, a constructive version of Euler’s proof of the infinity of prime numbers. Although it does not amount to much, this proof allows us to see that Wittgenstein had at least some mathematical skills. At the very last, the proof shows that Wittgenstein was concerned with mathematical practice and it also gives further evidence in support of the claim that, after all, he held a constructivist stance, at least during the transitional period of his thought (1929-33).

L’idéalisme britannique est un mouvement qui a dominé les universités britanniques pendant une cinquantaine d’années à la fin du xixe siècle et au début du xxe siècle, mais qui est passé presque totalement inaperçu dans le monde francophone. Rejetés en bloc par les philosophes analytiques, ces auteurs ont aussi été ignorés pendant longtemps dans leur pays, mais certains d’entre eux, notamment Bradley et Collingwood, jouissent d’un regain d’intérêt à la faveur d’un renouveau des études sur les origines de la philosophie analytique. Ce texte est une introduction à l’idéalisme britannique, qui retrace, dans une première partie plus historique, les grandes lignes de sa genèse, son développement et son déclin. Dans une deuxième partie, nous donnons quelques arguments en faveur d’une étude plus approfondie de ce mouvement.British Idealism is a philosophical movement that dominated British universities , for fifty years around the turn from the XIXth to the XXth century, but it went largely unnoticed in the French-speaking world. Condemned by analytic philosophers, these authors were also ignored in their own country, but some of them, notably Bradley and Collingwood, are now enjoying a newly found popularity within the larger trend towards a study of the origins of analytic philosophy. This text is an introduction to British Idealism that plots, in an historical first part, the outlines of its rise, development and decline. In the second part, we provide reasons for further studies of this movement

John Cook Wilson (1849–1915) was Wykeham Professor of Logic at New College, Oxford and the founder of ‘Oxford Realism’, a philosophical movement that flourished at Oxford during the first decades of the 20th century. Although trained as a classicist and a mathematician, his most important contribution was to the theory of knowledge, where he argued that knowledge is factive and not definable in terms of belief, and he criticized ‘hybrid’ and ‘externalist’ accounts. He also argued for direct realism in perception, criticizing both empiricism and idealism, and argued for a moderate nominalist view of universals as being in rebus and only ‘apprehended’ by their particulars. His influence helped swaying Oxford away from idealism and, through figures such as H. A. Prichard, Gilbert Ryle, or J. L. Austin, his ideas were also to some extent at the origin of ‘moral intuitionism’ and ‘ordinary language philosophy’ which defined much of Oxford philosophy until the second half of the twentieth-century. Nevertheless, his name and legacy were all but forgotten for generations after World War II. Still, his views on knowledge are with us today, being in part at work in the writings of philosophers as diverse as John McDowell, Charles Travis, and Timothy Williamson

In this chapter, Kobayashi and Marion first provide reasons to reject the many readings of Collingwood that sought to draft him as a participant in the Hempel-Dray debate about the status of covering laws in history. After all, this debate was not part of Collingwood’s context and, although one can pry from his writings a contribution to it, one may simply, by doing so, misunderstand what he was up to. In the second part, they present the Gabbay-Woods Schema for abductive reasoning, as it occurs in the context of inquiry, as triggered by an ignorance problem, and as being ‘ignorance preserving’. They then argue that this allows us better to see the point of Collingwood’s ‘logic of questions and answers’, as derived from his own practice in archaeology, and his use of the ‘detective model of the historian’, as opposed to merely focussing on understanding what ‘re-enactment’ could mean as a contribution to the Hempel-Dray debate.

According to the realist, the meaning of a declarative, non-indexical sentence is the condition under which it is true and the truth-condition of an undecidable sentence can obtain or fail to obtain independently of our capacity, even in principle, to recognize that it obtains or that fails to do so.1 In a series of papers, beginning with “Truth” in 1959, Michael Dummett challenged the position that the classical notion of truth-condition occupied as the central notion of a theory of meaning, and proposed that it should be replaced by the anti-realist (and intuitionistic) notion of assertability-condition. Taken together with normalization results obtained by Dag Prawitz, Dummett’s work truly opened up the anti-realist challenge at the level of proof-theoretical semantics.2 There has been since numerous rejoinders from partisans of classical logic, which were at times met with by attempts at watering down the anti-realist challenge, e.g., by arguing that anti-realism does not necessarily entail the adoption of intuitionistic logic. Only a few anti-realists, such as Crispin Wright and Neil Tennant, tried to look instead in the other direction, towards a more radical version of anti-realism which would entail deeper revisions of classical logic than those recommended by intuitionists.3 In this paper, which is largely programmatic, we shall also argue in favour of a radical anti-realism which would be a genuine alternative to the traditional anti-realism of Dummett and Prawitz. The debate about anti-realism has by now more or less run out of breath and we wish to provide it with a new lease on life, by taking into account the profound changes that took place in proof theory during the intervening years. We have in mind in particular the considerable development within Gentzen-style proof theory of non-classical, substructural logics other than intuitionistic logic, which seriously opens up the possibility that anti-realism, when properly understood, might end up justifying another logic, and the development of closer links between proof theory and computational complexity theory that has renewed interest in a radical form of anti-realism, namely strict finitism.