MCMP – History of Philosophy

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.

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.

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.

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.

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.

Elena Tatievskaya (Augsburg) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "Gätschenberger on the "Given" and Carnap's Aufbau". Abstract: In his Aufbau Carnap rejects Gätschenberger’s (1920) statement that the pure language of the “given” is impossible. Gätschenberger who represents cognition as ordering reality by means of symbolizing holds an experience (“Erlebnis”) to be a natural symbol which posits some object identifiable on the basis of the effects of the experience and in particular actions induced by it. Carnap treats the given as an object and ordering reality as constructing things. I argue that Carnap’s concept of the given can be considered as a solution of some problems of Gätschenberger’s theory which explains the forming function of expe- rience through reference to the form and constituents of the object cognized which in their turn are de- fined by other means of symbolizing.

Thomas Mormann (San Sebastian) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "(Re)constructing Influences in the Aufbau". Abstract: Once upon a time, the Aufbau was succinctly described as an attempt “to account for the external world as a logical construct of sense-data... .” Consequently, the most important influence on the Aufbau could be precisely named as “Russell”. These idyllic times have long passed. A comprehensive interpretation of the Aufbau has turned out to be a difficult task that has to take into account many, and sometimes rather turbid, sources. My thesis is that at the origin of the Aufbau project stood a problem that haunted German philosophy since the end of the 19th century at the latest. Bluntly, it may be expressed as the conflict between “Leben” and “Geist”. I want to show that there exists striking similarities between the attempts of how Rickerts System der Philosophie (1921) and Carnap’s (unpublished ms.) Vom Chaos zur Wirklichkeit (1922) (“the germ of the constitution theory”) aimed to cope with this problem.

Thomas Meier (MCMP/LMU) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "Influences on Carnap's Structuralism in the Aufbau". Abstract: I present an analysis of the different influences on Carnap’s structuralism in the Aufbau. First, I show how Hilbert’s notion of implicit definition from his axiomatization of Euclidean geometry (Hilbert, 1899) had an influence on Carnap’s development of his notion of purely structural description. As one further point, I will also discuss Neo-Kantian influences on Carnap’s structuralism. This mainly concerns Carnap’s posi- tion of what has been identified as a form of epistemic structural realism in the modern literature (see Frigg & Votsis, 2011). I will argue that Carnap’s proposal for individuating certain relations as founded relations in §154 is of contemporary relevance for actual debates on the so-called Newman-Objection. The Neo-Kantian influence on Carnap’s epistemology becomes clearer if we consider his purely relational system of knowledge, in which objects are subordinate to relations, to the Grundrelationen. For Carnap, a Kantian thing-in-itself as such would not be knowable but through its relations.

Matthias Neuber (Tuebingen) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "The Aufbau and the Early Schlick". Abstract: Schlick’s influence on Carnap’s Aufbau will be considered under the aspect of Schlick’s early ‘critical realism.’ It will be shown that both Carnap’s structuralism and his distinction between the ‘met- aphysical’ and the ‘empirical’ conception of reality can be traced back to Schlick’s discussion of the real- ism issue in his early Allgemeine Erkenntnislehre (1918, 1925). By way of conclusion, I shall briefly discuss Herbert Feigl’s contention that the later (Viennese) Schlick converted—influenced by Carnap’s Aufbau— from his early critical realism to ‘phenomenalistic positivism.’

Paul Ziche (Utrecht) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "Theories of Order in Carnap's Aufbau". Abstract: "Order" is a key term in debates in, and between, fields such as logic, philosophy of mathemat- ics, theoretical biology and philosophy of science around 1900. In § 3 of the "Aufbau", Carnap refers af- firmatively to a number of relevant authors: Whitehead and Russell, Driesch, Ostwald, Husserl, and many more. This list already indicates how broad and, from today's point of view, internally heterogeneous the discourse on order has been in this period. This paper will motivate why the notion of "order" played such a crucial role around 1900, and what its strategic position in those debates has been: "order" was conceived of as an ultimately abstract and general concept that could, nevertheless, be given content via, among others, mathematical and logical methods, or within fields such as biology. On the other hand, these diverse lines of influence also shaped the status of the field of logic itself. In a second step, it will be asked how Carnap views this discourse on order, and how he reacts to it, and to the broader ideas that form the strategic background of the notion of "order".

Thomas Uebel (Manchester) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "Neurath's Influence on Carnap's Aufbau". Abstract: In his very prompt review of Carnap’s Aufbau, Neurath was both highly appreciative of Car- nap’s achievements there and but also critical of some of its features. Neurath, of course, is reported to have been one of the readers of the typescript of an earlier version of that book that circulated amongst members of Schlick’s discussion group. This talk will consider the question whether Neurath had any in- fluence on the final version and what form this influence may have taken.

Sébastien Gandon (Blaise Pascal, Clermont-Ferrand) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "Carnap and Wiener: a missed opportunity?". Abstract: In 1913, Norbert Wiener, then a young (19 years old) prodigy, went in Cambridge to work with Russell. Wiener was very impressed by Russell’s constructionalist program, and, from 1914 to 1922, he published four papers (one is more than 100 pages long) extending Russell’s project. My talk’s first aim is to present these little known researches. My second goal is to draw a comparison between Carnap’s and Wiener’s reception of Russell.

Christian Damböck (Vienna) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "The Notion of Objectivity in 19th Century German Philosophy and its Role for the Aufbau". Abstract: This paper compares Carnap’s empiricist and objectivist conception from the Aufbau with a certain family of accounts of the empirical and objectivity that had been emerged in 19th Century Ger- many. Although these accounts were marginalized at the beginning of the 20th Century there were traces of this German empiricist (and objectivist) tradition to be found both in the philosophy of the Dilthey- school and in neo-Kantianism. Therefore, we try to argue first that Dilthey and the neo-Kantians (or at least some of them) have been sympathetic to a certain kind of empiricist and objectivist reasoning, and second that Carnap’s own empiricist and objectivist conception most probably has been influenced by these German empiricists (and objectivists).

Thomas Ryckman (Stanford) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "What Carnap might have learned from Weyl". Abstract: There are easily discernible traces of the influence of Hermann Weyl in the writings of Carnap in the early to mid- 1920s. It is somewhat more difficult to find any palpable influence of Weyl in the Aufbau. On the other hand, Weyl’s 1926 Philosophie der Mathematik und Naturwissenschaften is the sole work singled out in Aufbau's Bibliography as “especially suitable for study of problems connected with construction theory” in both the “logical” and the “epistemological” categories. I shall argue that, in the crucial Aufbau passage (§176) “demonstrating” the non-constructability of the reality (as mind- transcendent) concept, Carnap may have had §17 of Weyl’s 1926 book very much in mind.

Alan Richardson (UBC Vancouver) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "The Mathematical Core of the External World Problem: Carnap's Construction of the External World and Karl Gerhards's 'Der mathematische Kern der Aussenweltshypothese'". Abstract: Carnap, in his "Intellectual Autobiography," tells the story of reading in 1921 Bertrand Russell's book, Our Knowledge of the External World. In this anecdote he calls Russell "the strongest influence" on his "philosophical thinking in general" during the period of writing the Aufbau. But, while the meth- odological lessons of Russell loomed large in Carnap's mind, the actual techniques developed in the Auf- bau for constructing the external world differ considerably from Russell's own. Thus, noting Russell's influence does not take us very far in figuring out what the external world problem was for Carnap or what resources might be brought in to solve it. In this essay, I compare some of the constructive proce- dures of the Aufbau to procedures developed in Karl Gerhards's paper "Der mathematische Kern der Aussenweltshypothese" of 1922. Not only does Carnap refer to this paper in the crucial sections of the Aufbau where the construction of the external world is sketched, but this paper was precirculated and discussed at the 1923 Erlangen Conference at which Carnap and Reichenbach met and which Carnap subsequently called "the small but significant initial step in the movement of a scientific philosophy in Germany." Not only are some of Gerhards's constructive procedures and resources more closely related to Carnap's than are Russell's, but also Gerhards places his own work in a context created by the work of Helmholtz and Mach. The point of this endeavor is to enrich the resources we bring to bear in thinking about Carnap's philosophical project in the Aufbau.

Michael Friedman (Stanford) gives a talk at the MCMP workshop "Influences on the Aufbau" (1-3 July, 2013) titled "From Intuition to Tolerance in Carnap's Philosophy of Mathematics". Abstract: I plan to discuss the evolution of Carnap's views on arithmetic and geometry from Der Raum, through the Aufbau period, to Logical Syntax and the semantic period. I will concentrate on the way in which he consistently distinguished the two cases -- where geometry, in Der Raum, is explicitly tied to spatial intuition, and then, even though it remains distinguished from arithmetic, its ties to spatial intui- tion become empirical rather than a priori. The character of Carnap's generally tolerant attitude towards philosophical disputes in the foundations of mathematics thereby changes as well. Carnap's attitude towards intuition in the arithmetical case, finally, becomes clarified in his exchange with E. W. Beth in the Schilpp volume -- and this clarifies his application of the principle of tolerance in this case as well.