Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.
All content for MCMP – History of Philosophy is the property of MCMP Team and is served directly from their servers
with no modification, redirects, or rehosting. The podcast is not affiliated with or endorsed by Podjoint in any way.
Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.
Paolo Busotti (San Marino in Storia della Scienza) gives a talk at the MCMP Colloquium (7 May, 2015) titled "Giuseppe Veronese: The Fascination of Infinity". Abstract: Giuseppe Veronese (1854-1917) is one of the most interesting mathematicians lived between the end of the 19th century and the beginning of the 20th. He gave important contributions to geometry, in particular he developed the non-Archimedean geometries and David Hilbert (1862-1943) mentioned some of Veronese’s results in his Grundlagen der Geometrie. In connection to his geometrical researches, Veronese developed a theory of infinite numbers. In his huge (more than 600 pages) essay Fondamenti di geometria, 1891 (Foundations of geometry), Veronese premised an introduction which is a very treatise (about 200 pages) in which he developed a theory of the continuum and of the infinite numbers which was completely different from Cantor’s (1845-1918) and which, in the mind of his author, had to represent an alternative to Cantorian set theory. The great difference, in comparison to Cantor, was that Veronese admitted the existence of infinitesimal actual numbers, while Cantor always denied this possibility. Basing on his actual infinite and infinitesimal numbers Veronese constructed the continuum in a manner which is different from Cantor’s and Dedekind’s (1831-1916). Other mathematicians, as Paul Dubois-Reymond (1831-1889) and Otto Stolz (1842-1905) faced the problem of the infinite actual magnitudes in an original way, but they did not develop an entire theory, while Veronese did. From a mathematical point of view Veronese’s theory is problematic, because there are some serious inaccuracies and it is not developed in every detail. Nevertheless, the situation is very interesting from an epistemological and logical standpoint because many of the ideas carried out by Veronese were resumed by Abraham Robinson (1918-1995) in his famous book Non standard Analysis (1966), where a coherent theory of non-archimedean numbers is explained. Many of Robinson’s idea had already been expounded by Veronese, though in nuce. In my talk, I am going to explain Veronese’s theory of infinite numbers in comparison to Cantor’s as well as Veronese’s conception of the continuum.
MCMP – History of Philosophy
Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.
