27/06, 16h at CLE

Abstract. After a brief survey of the different meanings of consistency, the study is restricted to consistency understood as non-contradiction of sets of sentences. The philo- sophical reasons for this requirement are discussed, both in relation to the problem of sense and the problem of truth (also with historical references). The issue of mathematical truth is then addressed, and the different conceptions of it are put in relation with consistency. The formal treatment of consistency and truth in mathematical logic is then considered, with particular attention paid to the relation between syntactic and semantic properties of sets and calculi. After the crisis of mathematical intuition and the dominance of the formalistic view, it seemed that consistency could totally replace the requirement of truth in mathematics, also in the sense that the existence of “objects” of axiomatic systems could be granted by their consistency. A rejection of this claim is presented, whose central point is a detailed analysis of the theorem that any consistent set S of sentences of first order logic has a model. A critical scrutiny shows that this model is very peculiar, being offered by the elements of the same language that is being interpreted, and the satisfia- bility conditions for any sentence being constituted by the mere fact of belonging to S. Though not being insignificant from a metatheoretical point of view, this theorem fails to endow consistency (even in this privileged case) with an “ontological creativity”, that is, with the capability of providing a model ontologically distinct from the language itself (which is the precondition for the classical notion of truth that is also preserved in the Tarskian semantics and model theory). A final discussion regarding the different “ontolog- ical regions” and the referential nature of truth clarifies the different aspects of the whole issue discussed.


EVANDRO AGAZZI completed his studies in Philosophy at the Catholic University of Milan and in Physics at the State University of the same city. He then did postgraduate study and resesarch stays at the Universities of Oxford, Marburg and Münster. He obtained the venia legendi in Philosophy of Science (1963) and in Mathematical Logic (1966), and occupied several teaching positions: at the Department of Mathematics of the University of Genoa (Advanced Geometry, Complementary Mathematics, Mathematical Logic), at the Higher Normal School of Pisa (Symbolic Logic), at the Catholic University of Milan (Philosophy of Science, Mathematical Logic), before and after becoming full professor of Philosophy of Science at the University of Genoa (1970). He also had the chair of Philosophical Anthropology, Philosophy of Nature and Philosophy of Science at the University of Fribourg in Switzerland (1979-1998), and taught as a visiting professor at the Universities of Düsseldorf, Berne, Pittsburgh, Stanford, Geneva, UAM (Mexico) as well as at other universities for shorter times. At present he is Professor Emeritus of Philosophy at the University of Genoa and Professor at the Universidad Panamericana of Mexico City. He was an invited speaker at many international congresses, conferences and symposia, and has given numerous lectures in all continents. He is Doctor honoris causa of the Artentinian Universities of Cordoba, Santiago del Estero and Cuyo/Mendoza, Ricardo Palma of Lima (Peru) of Urbino and Insubria (Italy), of Valladolid (Spain). He is member of the Russian Academy of Sciences. And the Mexican Academy of Sciences

He is President of the International Academy of Philosophy of Science (Brussels), Honorary President of the International Federation of the Philosophical Societies (FISP), Honorary President of the International Institute of Philosophy (Paris), and of several other Academies and learned institutions of different countries. In the past he was (twice) President of the Italian Society of Logic and Philosophy of Science, of the Italian Philosophical Society, of the Swiss Society of Logic and Philosophy of Science, of the International Federation of the Philosophical Societies, of the International Institute of Philosophy, and of many other learned institutions. He was also Treasurer of the International Council for Philosophy and Humanities of UNESCO. He was member of the Italian National Committee for Bioethics and is presently member of the Committee for the Ethics of Research and Bioethics of the Italina National Research Council.

His publications include more than 80 books, of which he is the author and/or the editor, and more than 1000 papers and articles, including contributions to books, anthologies, encyclopaedias, and journals, apart from many book reviews and newspaper articles. He is the editor of Epistemologia, an Italian journal for the Philosophy of Science, and of Nuova Secondaria, an Italian journal for high school teachers, and is a consulting editor of the international journals Erkenntnis, Revue Internationale de Philosophie, Zeitschrift für Allgemeine Wissenschaftstheorie, Medicina e Morale, Modern Logic, Physis, Kos, Sandhan, Anthopos & Iatria, A&P. Anthropology and Philosophy. He has been and is a member of the editorial board of learned dictionaries and encyclopaedias.