Stegmüller Symposium, 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".

MCMP – History of Philosophy

Philosophische Scholastik. Der Streit der Schulen in den 1960er und 1970er Jahren

Stegmüller Symposium, 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".

Das Technische in der Philosophie. Logik und Mathematik in Stegmüllers Werk

Stegmüller Symposium, 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".

Wolfgang Stegmüller und die Einfachheit

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

Einführung und Willkommen

Stegmüller Symposium, 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"".

Stegmüllers Wende zum "Non-Statement View"

Stegmüller Symposium, 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".

Einige persönliche Gedanken über vergangene Zeiten

Stegmüller Symposium, 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"".

Erklärung - Begründung - die Logik des "weil"

Stegmüller Symposium, 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".

Wolfgang Stegmüllers Vorstellung von der Anwendung empirischer Theorien - und deren Probleme

Colloquium Mathematical Philosophy, 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.

Giuseppe Veronese: The Fascination of Infinity

Colloquium Mathematical Philosophy, 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.

Hilbert's metamathematics, finitist consistency proofs and the concept of infinity

Workshop on Influences on the Aufbau, 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.

Quasianalytic Individuation: Carnap's Aufbau as against Weylean Skepticism

Workshop on Influences on the Aufbau, Guillermo E. Rosado Haddock (Puerto Rico) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "The Old Husserl and the Young Carnap". Abstract: In his ‘Intellectual Autobiography’ Carnap barely refers to Husserl and not once with reference to his own work. He mentions Kant and a pair of Neo-Kantians as the main philosophical influences in Der Raum, and Mach, Rusell and the Gestalt psychologists as main influences in Der logische Aufbau der Welt. Moreover, he stresses that he heard three lecture courses by Frege. On the other hand, there are some signs in Husserl’s late correspondence not only of having known Carnap, but also of a lack of sympathy for him. The present paper addresses this mysterious relation and the fact that Husserl was a decisive influence precisely in those two writings of Carnap.

The Old Husserl and the Young Carnap

Workshop on Influences on the Aufbau, Clinton Tolley (San Diego) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "The Context and Development of Carnap's Views on Logic up to the Aufbau". Abstract: I will identify key components of Carnap's early conception of logic, as it develops in the period leading up to the Aufbau, looking especially at Der Raum and also Abriss der Logistik. I will also situate the development of Carnap's views within the context of the main influences upon his thinking at the time. Finally, I will identify points of contrast between his views in this period and his views after the Aufbau.

The Context and Development of Carnap's Views on Logic up to the Aufbau

Workshop on Influences on the Aufbau, Hans-Joachim Dahms (Vienna) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "Rudolf Carnap and Wilhelm Ostwald". Abstract: When Rudolf Carnap started work on his dissertation Der Raum in Summer 1920 he also hosted a conference with some of his Jena friends in his Buchenbach home about „a system of the sciences“. Carnap proposed as starting point for that discussion a scheme and ideas developed by Wilhelm Ostwald (1853-1932), the nobel-price winning chemist (1909) and monistic philosopher. Ostwald is also men- tioned and discussed in the Aufbau. What Carnap might have attracted to Ostwald’s work, are the fol- lowing items of common interest: (i) the construction of international artificial languages for everyday use (like esperanto), but also for sci-entific purposes, (ii) monism and the unity of the sciences, (iii) theories of colour, and last but not least: (iv) ethics. After a brief discussion of these points I will conclude with a tentative answer to the question why Ost- walds influence on Carnap seems to have diminished in the decade since the Buchenbach conference.

Rudolf Carnap and Wilhelm Ostwald

Workshop on Influences on the Aufbau, Andre Carus (Hegeler Institute) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "Carnap and Phenomenology: What Happened in 1924?". Abstract: The sketch of the Aufbau system in "Vom Chaos zur Wirklichkeit" (1922) employs phenome- nology to describe the system basis, as do other writings before 1924. But in January 1925, we find a new principle of " ̈Überwindung der Subjektivität" and a new emphasis on "Einheit des Gegenstands- bereichs." Russell's "construction principle" becomes the motto of the published book. The earlier ap- proach is explicitly rejected. Why this radical change? This question is discussed here on the basis of evidence from Carnap's papers, and a somewhat unexpected conclusion is reached.

Carnap and Phenomenology: What Happened in 1924?

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.

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MCMP – History of Philosophy

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