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)

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)

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)

Emphasis in historiography of science is naturally placed on the discoveries and inventions which scientists make and generally less on new methods of doing science, but sometimes the latter can he an important clue to help us understand the former. For example, while we all acknowledge how great the contributions of Maxwell, Boltzmann, Planck, and Einstein were to physics from roughly 1870 to 1920, we often overlook the significance of a methodological phrase which was popular during that same period, namely, (...) what in German was called “Bildtheorie” or in English “picture theory”. But even before we can properly study its significance we have to know what the theory was, but even this presents problems, since the meaning changed. In fact, this paper is an attempt not only to describe the history of that change from Maxwell to Wittgenstein but to study in particular how Boltzmann’s conception of Bildtheorie seems to have been at least partly incorporated into the approach of Ludwig Wittgenstein. (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)

Ludwig Boltzmann’s work in theoretical physics exhibits an approach to the construction of theory that he transmitted to the succeeding generation by example. It involved the construction of clear models, allowed more than one, and was not based solely on the existing facts, with the intent of examining and criticizing the assumptions that made each model work. This tacit program influenced physicists like Ehrenfest and Einstein and the philosopher Wittgenstein, suggesting ways that they used to make further advances.

Despite several scholars referring to the relationships between the philosophy of Boltzmann and Wittgenstein, this topic is still to be explored. The aim of this paper is to analyse the similarities between their views on mathematical continuum and on the meaning of physical theories and phenomenological states of affairs. In several arguments, they both aim to achieve a similar task: by clarifying the meaning of theories in their concrete use, both authors persuade the reader to abandon an apparently intuitive way (...) of thinking in order to overcome theoretical problems by dissolving them. (shrink)

U tekstu izlažemo rješenje razlike između Wittgensteinove uporabe modela u TLP i modeliranja u PI, RFM i OC temeljem analize razlike u izboru samih riječi i opisa pojmova fenomena u njegovim napomenama. Metoda je pojmovna analiza Wittgensteinova tretiranja znanstvenih modela i modeliranja. Dodatno, tekstualna raščlamba i poredba korištena je pri istraživanju njegovih glavnih napomena na tu temu. Ako je otkrivena razlika između modela i modeliranja i kontinuitet ovisnosti oba pojma o pojmu slike, pri čemu je razlika slike i oslikavanja uzeta (...) kao zadana, zaključujemo kako je Wittgenstein svoj stari pojam modela nastojao inkorporirati u novi pojam modeliranja. Eksplicirana razlika i inkorporiranje pridonosi pojašnjenju teme Wittgensteinovog posrednog i neposrednog utjecaja na filozofiju znanosti. (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 physiologist and neo-Kantian philosopher Johannes von Kries (1853-1928) wrote one of the most philosophically important works on the foundation of probability after P.S. Laplace and before the First World War, his Principien der Wohrscheinlich-keitsrechnung (1886, repr. 1927). In this book, von Kries developed a highly original interpretation of probability, which maintains it to be both logical and objectively physical. After presenting his approach I shall pursue the influence it had on Ludwig Wittgenstein and Friedrich Waismann. It seems that von (...) Kries's approach had more potential than recognized in his time and that putting Waismann's and Wittgenstein's early work in a von Kries perspective is able to shed light on the notion of an elementary proposition. (shrink)

Ludwig Boltzmann’s Bildtheorie has been portrayed as a pre-cursor of the semantic view of theories and as such, the word “Bild” is translated as model. But this anachronistic understanding of Boltzmann’s use of Bilder fails to account for the wide range of roles they play in his understanding of scientific methodology. When the concept of Bild is understood historically in Viennese thought, a much broader sense emerges that leads to the investigation of its use in multiple ways in various contexts (...) in the process of proposing, pursuing, and justifying scientific beliefs. (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)