Apocalyptic relevance

In their book, Relevance, Sperber and Wilson make an important contribution towards constructing a credible theory of this unforthcoming notion. All is not clear sailing, however. If it is accepted as a condition on the adequacy of any account of relevance that it not be derivable either that nothing is relevant to anything or that everything is relevant to everything, it can be shown that Sperber and Wilson come close to violating the condition.     

Les “règles de la discussion légitime” dans la logique de Port-Royal

In the XVIIth century the conflict which opposed the jansenists to the jesuits involved the problem of the due process in theological matter. The jesuits heralded the thesis that the infallibility of the Church has to be extended from dogmatics (quaestio iuris) to the historical facts (quaestio facti). On the opposite side Arnauld maintained that such an opinion was monstruous: also in religious matters the fact has to be proved according to the principles of a due process, and not by authority. In this article the thesis pleaded by the jansenists is considered in connection with the model of argumentative procedure offered by the Port-Royal logic.The Logique ou Art de penser (1622) by Antoine Arnauld and Pierre Nicole seems to have rediscovered the classical principles of the theory of argumentation: from the burden of proof to the idea of probable truth. But really a new model of adversary-system has been introduced into the modern mind, which is very different in concept from the topical tradition. The basic metaphor of combat, implying that the truth will prevail in the fight, is compatible with the epistemological premises of the modern logic (as the separation between fact and value). Therefore the problem of the fact-finding seems to be attracted into the area of the logic of information, and not of the theory of argumentation.

     

Beyond postmodernism: Logic as rhetoric

The essay reviews the relationship between logic and rhetoric under the conditions of historicity and shows how (and why) the rules of logic may be construed as projected from the rhetorical practices of actual societies; why and how they are subject to revision; and why there is reason to think it could not be otherwise.     

Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic

We describe a sequent calculus, based on work of Herbelin, of which the cut-free derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.     

Interpolation and Amalgamation; Pushing the Limits. Part I

Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open.Related issues of universal algebra and of algebraic logic are discussed, too. In particular we investigate the possibility of extending the characterization of interpolability to arbitrary algebraizable logics.