Scielo RSS <![CDATA[Manuscrito]]> vol. 38 num. 2 lang. pt <![CDATA[SciELO Logo]]> <![CDATA[HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS]]> Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution. <![CDATA[DISAGREEING OVER EVALUATIVES: PREFERENCE, NORMATIVE AND MORAL DISCOURSE]]> Abstract Why would we argue about taste, norms or morality when we know that these topics are relative to taste preferences, systems of norms or values to which we are committed? Yet, disagreements over these topics are common in our evaluative discourses. I will claim that the motives to discuss rely on our attitudes towards the standard held by the speakers in each domain of discourse, relating different attitudes to different motives -mainly, conviction and correction. These notions of attitudes and motives will allow me to claim that different domains of evaluative discourse have a different distribution of disagreements driven by them. <![CDATA[A SECOND OPINION ON RELATIVE TRUTH]]> In 'An undermining diagnosis of relativism about truth', Horwich claims that the notion of relative truth is either explanatorily sterile or explanatorily superfluous. In the present paper, I argue that Horwich's explanatory demands set the bar unwarrantedly high: given the philosophical import of the theorems of a truth-theoretic semantic theory, Horwich's proposed explananda, what he calls acceptance facts, are too indirect for us to expect a complete explanation of them in terms of the deliverances of a theory of meaning based on the notion of relative truth. And, to the extent that there might be such an explanation in certain cases, there is no reason to expect relative truth to play an essential, ineliminable role, nor to endorse the claim that it should play such a role in order to be a theoretically useful notion. <![CDATA[PROLEGÓMENOS PARA UNA TEORÍA FORMAL DE ESTRUCTURAS (DESPUÉS DE N.DA COSTA)]]> Resumen El articulo tiene por objetivo la reconstrucción alternativa del concepto de estructura, motivado por los articulos(1)y(3), como una generalización abstracta de lo que es un objeto matemático. Primero, mostramos su construcción, que tiene que ver con la teoría de tipos y orden en lógica, dando a lugar a propiedades y varios ejemplos interesantes. Luego avanzamos hacia una semántica concreta, para su análisis, y para permitirnos operar sobre ellas, sabiendo de este modo, lo que es "lo verdadero en ella". Obtenido ello, mostraremos los resultados de reducción de orden y de individuos, pero vistos en este contexto, así formalizando completamente en nuestra teoría de tipos la discusión de(1)(Ver también(2)y(3)) sobre estos temas.<hr/>Abstract The present article has for objective to present an alternative reconstruction of Concept of Structure, motivated by the articles(1)and(3), as an abstract generalization of what is a mathematical object. First, its construction is presented, that is related to the Type Theory and Order in Logic. Which give us a context for properties and several interesting examples. Secondly, we will proceed towards a concrete semantic for analysing structures and letting us operate in them. Thus we are able to know "what itXB is true in it". Results of order and individuals reduction are presented through our construction. In the end, we formalized the discussions referred completely in our Type Theory. <![CDATA[TOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY]]> Abstract In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC, a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence.