Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Lewis’ Theory of Counterfactuals and Essentialism

La logique contemporaine a connu de nombreux développements au cours de la seconde moitié du siècle dernier. Le plus sensationnel est celui de la logique modale et de sa sémantique des mondes possibles (SMP) dû à Saul Kripke dans les années soixante. Ces dans ce cadre que David Lewis exposera sa sémantique des contrefactuels (SCF). Celle-ci constitue une véritable excroissance de l’architecture kripkéenne. Mais sur quoi finalement repose l’architecture kripkéenne elle-même ? Il semble bien que la réponse soit celle d’une ontologie raffinée ultimement basée sur la notion de mondes possible. Ce mémoire comporte quatre objectifs. Dans un premier temps, nous allons étudier ce qui distingue les contrefactuels des autres conditionnels et faire un survol historique de la littérature concernant les contrefactuels et leur application dans différent champs du savoir comme la philosophie des sciences et l’informatique. Dans un deuxième temps, nous ferons un exposé systématique de la théorie de Lewis telle qu’elle est exposée dans son ouvrage Counterfactuals. Finalement, nous allons explorer la fondation métaphysique des mondes possible de David Lewis dans son conception de Réalisme Modal.

La sémantique des noms descriptifs

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Tyhjyyden reunalla, helvetin kannella : Yhtenäisen subjektin hajoaminen Saul Bellowin Herzogissa

The study shows that the reading paradigm derived from codes Roland Barthes presented in his S/Z exposes the postmodernic nature of Saul Bellow s Herzog (1964), and embodies in which way the novel is organized as a radical rewriting of modernism and its ideology. I explore how solid, compact and modernistic subject breaks down at every level of Herzog s narration. I actually argue that the heteroglossic novel is representative of an early American postmodern movement in literaure, and it should by no means be dissected narrowly as a realistic or naturalistic novel at all. The intertextual code verifies that the interpretation of Herzog remains inadequate if one doesn t take account of the novel s significant intertextual references to other texts. In fact, even the mind of Moses Herzog, the protagonist of the novel, is a mosaic of citations. It emerges from the dissertation that the figure of Don Quixote follows Moses Herzog as an ambiguous shadow while the professor of history struggles with his anxiety and anguish, and travels in a mentally confused state around the U.S. for five days in the early 1960s, encountering the impending atmosphere of transition as the country is on the threshold of a significant cultural and social change. There is a strong necessity for updated interpretation of Herzog partly because its centrality to Bellow s own career as a writer but mainly because it has been previously read trough modernistic lenses. I shall try to proof in my study that American Jewish Saul Bellow s (1915 2005) Herzog escapes any kind of simple, elemental or essentialistic construction or reading and in real terms it doesn t offer any comprehensive, total or coherent solution or system for those philosophical doctrines it criticizes and makes fun of. The philosophical, conceptual and cultural substance of Herzog does not constitute an independent or autonomous theoretical tract which would have a life of its own. Altough the novel reflects the continuity of Bellow s writing it is clearly some kind of conscious or unconscious experiment during his long career as a writer. He hasn t been so radical before or since the publication of Herzog. It is unarguably his most postmodern novel.The reading paradigm based on specific codes demonstrates how deep into the basic questions of his personal life and existence itself he must dive in oder to find his many ways towards authentic or primordial self in fragmented and shattered world which is constanly rewritten and which makes human being a tourist of his own life. In that ongoing process the protagonist has to accept the ultimate plurality of his mind and self. He must confront that the modernistic definition of identity as a solid, monolithic and stable entity has broken down into different, inconsistent and even contradictory possibilities of identification. Moses Herzog embodies obviously Stuart Hall s description of the postmodern self his identity has turn into a movable feast.

Letter - John Ralston Saul to Donald Ziraldo, 2002

A letter from His Excellency John Ralston Saul 2 May, 2002. He comments on the efforts made by Mr. Ziraldo to protect the agricultural land of Niagara. He also discusses the role of Canadian wine in the international market and tourism in the area.

Efectos de diferentes riegos, substratos y fertilizantes en la producción de: Celtis laevigata Willd. en viveros [por] Edwars Saul Sanzetenea Terceros

Tesis (Maestría en Ciencias Forestales) U.A.N.L.

Hi ha veritats necessàries a posteriori?

En aquest treball es discuteix l’afirmació de Kripke de que certes identitats teòriques són exemples de veritats necessàries a posteriori