Mathieu Marion

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.

By North-American standards, philosophy is not new in Quebec: the first men tion of philosophy lectures given by a Jesuit in the College de Quebec dates from 1665, and the oldest logic manuscript dates from 1679. In English-speaking universities such as McGill, philosophy began to be taught later, during the second half of the 19th century. The major influence on English-speaking philosophers was, at least initially, that of Scottish Empiricism. On the other hand, the strong influence of the Catholic Church on French-Canadian society meant that the staff of the facultes of the French-speaking universities consisted, until recently, almost entirely of Thomist philosophers. There was accordingly little or no work in modem Formal Logic and Philosophy of Science and precious few contacts between the philosophical communities. In the late forties, Hugues Leblanc was a young student wanting to learn Formal Logic. He could not find anyone in Quebec to teach him and he went to study at Harvard University under the supervision of W. V. Quine. His best friend Maurice L' Abbe had left, a year earlier, for Princeton to study with Alonzo Church. After receiving his Ph. D from Harvard in 1948, Leblanc started his profes sional career at Bryn Mawr College, where he stayed until 1967. He then went to Temple University, where he taught until his retirement in 1992, serving as Chair of the Department of Philosophy from 1973 until 1979.

In this paper, we provide a detailed critical review of current approaches to ecthesis in Aristotle’s Prior Analytics, with a view to motivate a new approach, which builds upon previous work by Marion & Rückert (2016) on the dictum de omni. This approach sets Aristotle’s work within the context of dialectic and uses Lorenzen’s dialogical logic, hereby reframed with use of Martin-Löf's constructive type theory as ‘immanent reasoning’. We then provide rules of syllogistic for the latter, and provide proofs of e-conversion, Darapti and Bocardo and e-subalternation, while showing how close to Aristotle’s text these proofs remain.

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.