Jürgen Mittelstraß gives a talk at the Symposium "Wolfgang Stegmüller und die Rückkehr der analytischen Philosophie" (1 June, 2013) titled "Philosophische Scholastik. Der Streit der Schulen in den 1960er und 1970er Jahren".

Godehard Link gives a talk at the Symposium "Wolfgang Stegmüller und die Rückkehr der analytischen Philosophie" (1 June, 2013) titled "Das Technische in der Philosophie. Logik und Mathematik in Stegmüllers Werk".

Felix Mühlhölzer gives a talk at the Symposium "Wolfgang Stegmüller und die Rückkehr der analytischen Philosophie" (1 June, 2013) titled "Wolfgang Stegmüller und die Einfachheit".

Stephan Hartmann and Julian Nida-Rümelin open the Symposium "Wolfgang Stegmüller und die Rückkehr der analytischen Philosophie" (1 June, 2013).

C. Ulises Moulines gives a talk at the Symposium "Wolfgang Stegmüller und die Rückkehr der analytischen Philosophie" (1 June, 2013) titled "Stegmüllers Wende zum "Non-Statement View"".

Wolfgang Spohn gives a talk at the Symposium "Wolfgang Stegmüller und die Rückkehr der analytischen Philosophie" (1 June, 2013) titled "Einige persönliche Gedanken über vergangene Zeiten".

Hans Rott gives a talk at the Symposium "Wolfgang Stegmüller und die Rückkehr der analytischen Philosophie" (1 June, 2013) titled "Erklärung - Begründung - die Logik des "weil"".

Ulrich Gähde gives a talk at the Symposium "Wolfgang Stegmüller und die Rückkehr der analytischen Philosophie" (1 June, 2013) titled "Wolfgang Stegmüllers Vorstellung von der Anwendung empirischer Theorien - und deren Probleme".

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.

Matthias Schirn (LMU) gives a talk at the MCMP Colloquium (20 November, 2013) titled "Hilbert's metamathematics, finitist consistency proofs and the concept of infinity". Abstract: The main focus of my talk is on a critical analysis of some aspects of Hilbert’s proof-theoretic programme in the 1920s. During this period, Hilbert developed his metamathematics or proof theory to defend classical mathematics by carrying out, in a purely finitist fashion, consistency proofs for formalized mathematical theories T. The key idea underlying metamathematical proofs was to establish the consistency of T by means of weaker, but at the same time more reliable methods than those that could be formalized in T. It was in the light of Gödel’s incompleteness theorems that finitist metamathematics as designed by Hilbert and his collaborators turned out to be too weak to lay the logical foundations for a significant part of classical mathematics. In the 1930s, Hilbert responded to Gödel’s challenge by extending his original finitist point of view. The extension was guided by two central, though possibly conflicting ideas: firstly, to make sure that it preserved the quintessence of finitist metamathematics; secondly, to carry out, within the extended proof-theoretic bounds, a finitist consistency proof for a large part of mathematics, in particular for second-order arithmetic. I begin by briefly characterizing Hilbert’s metamathematics in the 1920s, with particular emphasis on his conception of finitist consistency proofs for formalized mathematical theories T. In subsequent sections, I try to shed light on some difficulties to which his project gives rise. One difficulty that I discuss is the fact, widely ignored in the pertinent literature, that Hilbert’s language of finitist metamathematics fails to supply the conceptual resources for formulating a consistency statement qua unbounded quantification. Another difficulty emerges from Hilbert’s tacit assumptions of infinity in metamathematics. On the way, I shall comment on the relationship between finitism and intuitionism, on Gentzen’s “finitist” consistency proof for number theory (1936) and on W. W. Tait’s objection to an interpretation of Hilbert’s finitism by Niebergall and Schirn. I conclude with remarks on the extension of the finitist point of view in Hilbert and Bernays’s monumental work Grundlagen der Mathematik (vol 1, 1934; vol. 2, 1939) and philosophical remarks on consistency proofs and the notion of soundness.

Iulian Toader (Bucharest) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "Quasianalytic Individuation: Carnap's Aufbau as against Weylean Skepticism". Abstract: Carnap maintained that, unlike mathematics, the empirical sciences must individuate their ob- jects, and that they can (and should) do so via univocal systems of structural definite descriptions. In this paper, I evaluate Carnap's strategies for univocality, against the Southwest German neo-Kantian demand for a “logic of individuality”, but also against the challenge of Weylean skepticism – the view that objec- tivity and understanding are opposite ideals of science.