This study examines the relativistic aspects of Arnold Schoenberg's harmonic and aesthetic theories in the light of a framework of ideas presented in the early writings of Ludwig Wittgenstein, the logician, philosopher of language, and Schoenberg's contemporary and Austrian compatriot. The author has identified correspondences between the writings of Schoenberg, the early Wittgenstein, and the Vienna Circle of philosophers, on a wide range of topics and themes. Issues discussed include the nature and limits of language, musical universals, theoretical conventionalism, word-to-world (...) correspondence in language, the need for a fact- and comparison-based approach to art criticism, and the nature of music-theoretical formalism and mathematical modeling. Schoenberg and Wittgenstein are shown to have shared a vision that is remarkable for its uniformity and balance, one that points toward the reconciliation of the positivist-relativist dualism that has dominated recent discourse in music theory. Contrary to earlier accounts of Schoenberg's harmonic and aesthetic relativism, this study identifies a solid epistemological core underlying his thought, a view that was very much in step with Wittgenstein and the Vienna Circle, and thereby with the most vigorous and forward-looking stream in early twentieth century intellectual history. (shrink)

Rom Harré has recently proposed that there is a difference between the driving force behind the early and the later Wittgenstein. According to Harré, in the early work, the major inspiration came from science, while, in the later, it came from religion. I show that only Harré’s first proposal is fully justified. In section one of my paper, I examine the picture theory, the theory of truth-functions, the meaning of propositions, and Tractatus §6.3. In section two, about the Philosophical Investigations, (...) I show that Harré is misleading. In a first step, I argue that science plays the same role in this later work as in the Tractatus, namely the role of source of inspiration. In a second step, I show that science plays also the role of a contrast against which the rich world of meaning can be discerned. I examine this contrastive role not only as regards religion, but also as regards psychology, and as regards the repercussions of Wittgenstein’s later work on science-studies. My final proposal is that the distinction between science as source of inspiration and science as a contrast goes beyond Wittgenstein: it characterises much twentieth century philosophical work in this area. (shrink)

Today I want to talk about an element in the milieu in which Ludwig Wittgenstein conceived the Tractatus Logico-Philosophicus that has not been recognized to date: the generalization of the methodology of experimental scale models that occurred just about the time he was writing it. I find it very helpful to keep in mind how this kind of model portrays when reading the Tractatus — in particular, when reading the statements about pictures and models, such as:That a picture is a (...) fact ,That a picture is a model of reality ,That the “pictorial relationship” that makes a picture a picture is part of that picture , andThat a picture must have its pictorial form in common with reality in order to able to depict it. (shrink)

The German physicist Heinrich Hertz played a decisive role for Wittgenstein's use of a unique philosophical method. Wittgenstein applied this method successfully to critical problems in logic and mathematics throughout his life. Logical paradoxes and foundational problems including those of mathematics were seen as pseudo-problems requiring clarity instead of solution. In effect, Wittgenstein's controversial response to David Hilbert and Kurt Gödel was deeply influenced by Hertz and can only be fully understood when seen in this context. To comprehend the arguments (...) against the metamathematical programme, and to appreciate how profoundly the philosophical method employed actually shaped the content of Wittgenstein's philosophy, it is necessary to make an intellectual biographical reconstruction of their philosophical framework, tracing the Hertzian elements in the early as well as in the later writings. In order to write Wittgenstein's biography, we have to take seriously the coherence of his thought throughout his life, and not let convenient philosophical ideologies be our guidance in drawing up a “Wittgensteinian philosophy”. To do so, we have to take a second look upon what he actually wrote, not only in the already published material, but in the entire Nachlass. Clearly, this is not easily done, but it is a necessary task in the historical reconstruction of Wittgenstein's life and work. (shrink)

The influence of Heinrich Hertz's The Principles of Mechanics on Ludwig Wittgenstein's Tractatus Logico‐Philosophicus has been studied for decades, but it has never become a mainstream topic in the Wittgensteinian literature. This paper focusses on Tractarian notions of objects, elementary facts and elementary sentences and discusses their similarities with Hertz's concepts of mass, its constituents and their mechanistic images. As the paper demonstrates, the Hertzian context provides some fruitful interpretational leads concerning several controversial ideas endorsed by early Wittgenstein, namely propositional (...) analysis, logical independence of elementary facts, logical independence of elementary sentences, and modalities. (shrink)

In 1929 Wittgenstein began to work on the first philosophical manuscripts he had kept since completing the Tractatus Logico-Philosophicus in 1918. The impetus for this was his conviction that the logic of the TLP was flawed: it was unable to account for the fact that a proposition that assigns a single value on a continuum to a simple object thereby excludes all assignments of different values to the object . Consequently Wittgenstein's "atomic propositions" could not be logically independent of one (...) another. ;Initially he thought he could replace the "logically perfect language" of the TLP with a "phenomenological language" in which experiential propositions about various "spaces" would form systems. The system described by a phenomenological language would be independent of the one described by ordinary "physicalistic" language; the physical "world" was known only by inference from the phenomenological. But he soon realized there was a fundamental error in this conception: phenomenology has to describe the same world as physics or it fails to provide a foundation for it. This suggests that there is only one world, and one language with two different modes of expression. Wittgenstein's now comes to his fundamental insight: ordinary language is biased towards the description of physical objects and their relations, but it is our only method of expressing phenomenological or abstract concepts. Failure to recognize this difficulty leads to the misapplication of physicalistic concepts, i.e., to grammatical errors. ;This insight had the following impact: the task of philosophy is not to invent logical or phenomenological languages, but to understand the grammar of ordinary language; the notion of a language of pure experience was itself connected with a false, physicalistic idea of the soul as an observer of a private world; the conception of analysis that had guided philosophy since Frege was based on a misused metaphor taken from the grammar of physics: the analysis of an object into its parts or chemical constituents. These ideas reach their ultimate expression in Wittgenstein's Philosophical Investigations. Thus his "later" work actually begins with these 1929--30 manuscripts. (shrink)

Dans cet article, j’essaie de montrer que le dépassement et le rejet du dogmatisme sont un aspect décisif du changement dans la pensée de Wittgenstein qui a eu lieu au début des années 30, quand il commence à mettre en valeur l’autonomie de la grammaire du langage et à parler d’images grammaticales et de jeux de langage en tant qu’objets de comparaison. En examinant certains traits fondamentaux de ce changement, je mettrai en évidence l’impulsion et les idées décisives que Wittgenstein (...) a reçues des nouveaux développements dans les mathématiques et la science naturelle du début du 20e siècle.It will be argued that the overcoming and avoiding of dogmatism is a decisive feature of the change in Wittgenstein’s thinking that takes place in the beginning of the 1930’s when he starts to emphasise the autonomy of the grammar of language and to talk about grammatical pictures and language games as objects of comparison. By examining certain crucial features in this change in Wittgenstein’s thinking, it will be shown that he received decisive impulses and ideas from new developments in mathematics and natural science in the early 20th century. (shrink)

In an influential article, Gerd Grasshoff has argued for the identification of the objects in Wittgenstein's Tractatus with the ultimate constituents of reality in Heinrich Hertz's Principles of Mechanics. Grasshoff's interpretation is based on two interrelated claims: The specific determination of the objects in the world and the relation among them is the primary theme in Wittgenstein's early philosophy, because it is the primary theme for Hertz. Wittgenstein did not assume the existence of simple objects on purely logical grounds without (...) having specific examples of simple objects in mind, because Hertz did not do this. (shrink)

Ludwig Wittgenstein's conception of the role of objects in our philosophical understanding of the logic of our language is critical for his early philosophy in the Tractatus Logico-Philosophicus. While the important connections between Heinrich Hertz's Principles of Mechanics and Wittgenstein's Tractatus have long been recognized, recent work by Jed Buchwald has deepened our knowledge of the importance of the object-orientation of Hertz's scientific work in a manner that should also deepen our understanding of the nature of objects in the Tractatus. (...) I will argue that there are important ontological links, involving "a certain physical scheme, one that had powerful implications for thinking as well as doing," between Hertz's work and Wittgenstein's early philosophy. (shrink)

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...) today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

This article is an investigation of parallel themes in Heinrich Hertz's philosophy science and Kant's theory of schemata, symbols and regulative ideas. It is argued that Hertz's "pictures" bears close similarities to Kantian "schemata", that is, they are rules linking concepts to intuitions and provide them with their meaning. Kant's distinction between symbols and schemata is discussed and related to Hertz's three pictures of mechanics. It is argued that Hertz considered his own picture of mechanics as symbolic in a different (...) way than the force and energy pictures. In the final part of the article it is described how Harald Høffding soon after the publication of Hertz's Principles of Mechanics developed a general theory of analogical reasoning, relying on the ideas of Hertz and Kant. (shrink)