Abstract:
From Newton da Costa’s works, many people in France know only the revival of paraconsistency. We give some reasons in defence of investigations in this part of logic. But above all we recall one of the major contributions of Newton da Costa: his proof, in 1991, in collaboration with Doria, of the g delian undecidability of motion in mathematical physics, a result which was somewhat foreseen on other grounds by Duhem in 1906.

Actually, Arithmetic is
considered as syntactically incomplete. However, there are different types of
arithmetical theories. One of the most important is the second-order
Categorical Arithmetic (AR), which interprets the principle of induction
with the so-called full semantics. Now, whoever concluded that AR is sintactically (or semantically, since categoricity implies equivalence of
the two types of completeness) incomplete? Since this theory is not effectively
axiomatizable, the incompleteness Theorems cannot be applied to it. Nor is it
legitimate to assert that the undecidability of the statements is generally
kept in passing from a certain theory (such as PA) to another that
includes it (such as AR). Of course, although the language of AR is semantically incomplete, this fact does not imply that the same AR is
semantically/sintactically incomplete. Pending a response to the previous
question, this paper aims to present a proof of the syntactic/semantical
incompleteness of AR, by examples based on the different modes of
representation (i.e. codes) of the
natural numbers in computation.

Abstract:
Par l’analyse du roman Villa Bunker (2009) de Sébastien Brebel, l’auteure trace les jalons d’une poétique de l’espace incertain qui s’érigerait sur un principe d’indécidabilité et d’illisibilité. L’étude de la représentation spatiale et l’analyse de l’action permettent, dans un premier temps, de voir comment l’espace s’y présente comme un lieu marqué par les brouillages de la perception et de l’oubli. Puis, sont examinées les modalités stylistiques (formes de l’excès et du ressassement) et narratives (instabilité de l’origine énonciative, autorité narrative ambigu ) de cette poétique de l’espace qui traduit à la fois les vertiges de l’interprétation et la problématicité de tout procès perceptif.Through an analysis of Sebastien Brebel’s novel Villa Bunker (2009), the author outlines a poetics of uncertain spaces erected upon a principle of undecidability and illegibility. Firstly, the study of spatial representation and analysis of action allow us to see how space in the novel is presented as being affected by the blurring effects of perception and forgetfulness. Subsequently, this paper examines the stylistic terms (forms of excess and iteration) and narrative aspects (instability of the enunciative source; ambiguous narrative authority) of this poetics of space, a poetics that translates both the vertigo of interpretation and the problematical nature of any perceptual process.

Abstract:
The author explores and criticises two arguments from ambiguity: S. Pinker’s argument from ambiguity in support of the ‘Language of Thought’ hypothesis, and the argument from ambiguity proposed by K. P. Parsons against Davidsonian ‘semantics of truth-conditions’. Leaning primarily on G. Harman and D. Davidson he aims to demonstrate that the Pinker/Parsons arguments share a common strategy, on the one hand, and imply and/or suggest, as he claims, an implausible view of ambiguity, on the other. Discussing Pinker’s argument he further attempts to elucidate the ways in which the modifications of public and inter-subjectively accessible aspects of the use of language reflect the differences in interpretations of an ambiguity. His exploration of the argument against ‘semantics of truth-conditions’ then aims to explain, contra Parsons, the sense in which talk about the truth conditions for ambiguity does not implicate a threat to Davidson’s perspective on the theory of meaning. Finally, the author argues for the view of ambiguity as a kind of ignorance/undecidability that, as he contends, represents both more realistic and more plausible theoretical option than the one on which both Pinker and Parsons found their arguments and which also comes out in Aristotle (under an interpretation), K. Bach and W. Lycan.

Abstract:
In this paper some undecidable problems on approximability of NP op-timization problems are investigated. In particular, the following problems are all undecidable: (1) Given an NP optimization problem, is it approal-mable in polynomial time? (2) For any polynomialtime computable function r(n), given a polynomial time approkimable NP optimization problem, has it a polynomialtime approximation algorithm with approkimation performance ratio r(n) (r(n)-approkimable)? (3) For any polynomial-time computable func-tions r(n), r'(n), where r'(n) < r(n) a.e., given an r(n)-approkimable NP opti-mization problem, is it r'(n)-approalmable?