In this paper, we trace the conceptual history of the term ?metamathematics? in the nineteenth century. It is well known that Hilbert introduced the term for his proof-theoretic enterprise in about 1922. But he was verifiably inspired by an earlier usage of the phrase in the 1870s. After outlining Hilbert's understanding of the term, we will explore the lines of inducement and elucidate the different meanings of ?metamathematics? in the final decades of the nineteenth century. Finally, we will investigate the (...) earlier occurrences and come to the conclusion that the conceptual prehistory of the Hilbertian notion of metamathematics dates back to 1870, whereas the history of the word starts in 1799 at the latest. What is this: metamathematics? It is something amazing everybody, [?] since it makes the mind dizzy and withdraws thinking its sole fulcrum.1 1 Brunner 1898, p. 832: ?Was ist das: Metamathematik? Es ist etwas, was einen Jeden in das äusserste Staunen versetzt, [?] was das Gehirn schwindlig macht und dem Denken seinen einzigen Stütz- und Angelpunkt zu entziehen droht? (shrink)

The integration of ethics into the day-to-day work of research and innovation is an important but difficult challenge. However, with the Aachen method for identification, classification and risk analysis of innovation-based problems an approach from an engineering perspective is presented that enables the integration of ethical, legal and social implications into the day-to-day work of R&I practitioners. AMICAI appears in particular capable of providing a procedural guidance for R&I practitioners based on a method established in engineering science, breaking down the (...) object of consideration into partial aspects and prioritizing the innovation-based problems in dependence of potential risk. This enables the user to apply AMICAI continuously during all stages of the research and development process and to analyze and choose between certain sociotechnical alternatives. In this way, problems that affect ethical, legal, and social aspects can be understood, reflected and considered in the mostly technically focused R&D process. The paper gives a general guidance about AMICAI by describing principles and assumptions, providing the steps of analysis and application aids, giving an example application, explaining the necessary adjustments of AMICAI compared to the methodical basis of failure mode, effects, and criticality analysis and discussing the advantages and limits. AMICAI’s simple applications can stimulate interdisciplinary cooperation in the R&D process and be a starting point for the development of an “open RRI risk analysis platform” allowing society to evaluate innovation-based problems. (shrink)

Lembecks Philosophiebegriff ist keine Zumutung Content Type Journal Article Pages 1-9 DOI 10.1007/s10743-011-9098-6 Authors Matthias Wille, Institut für Philosophie, Fakultät für Geisteswissenschaft, Universität Duisburg-Essen, Universitätsstraße 12, 45117 Essen, Germany Journal Husserl Studies Online ISSN 1572-8501 Print ISSN 0167-9848.

Gottlob Frege’s Grundgesetze der Arithmetik (Basic Laws of Arithmetic, Vol. I/II; 1893/1903) is a modern classic. Since the 1930s it has belonged to an exclusive class of only eleven works in the history of symbolic logic, which contain the ‘first appearance of a new idea of fundamental importance’ [Church, 1936, p. 122], and its author is the only one whose other major works — Begriffsschrift (1879) and Die Grundlagen der Arithmetik (1884) — also belong to this distinguished group. Together with (...) the seminal paper ‘Über Sinn und Bedeutung’ these three monographs represent the essential contributions to one of the most fascinating foundational projects in mathematics, then and now. For decades Frege struggled with the question, ‘how are we to apprehend logical objects, in particular, the numbers? What justifies us in acknowledging numbers as objects?’ [Frege, 2013, ‘Afterword’, p. 265]. His favourite answer, for a long time, was that arithmetic is a complex branch of logic. But since there is no logicism without logic, Frege started in Begriffsschrift with the invention of a nearly perfect formalization of higher-order classical predicate logic. To discover how far we can get in arithmetic by analytic means alone, it was even necessary to clarify the semantic character of the concept of number. This was done in a marvellous way by Frege five years later, in Grundlagen. The next step was nothing less than the complete execution of his logicist project, a monumental undertaking; and it is well known that here Frege failed, due to Russell’s derivation of the antinomy in 1902. But, despite the contradiction, Grundgesetze contains Frege’s legacy to logicism, which became more and more attractive. (shrink)

There is nothing straightforward about translating Frege. Up to now there has been no coherent and commonly accepted standard for his logico-philosophical terminology, and several researchers in th...

The book under review is a carefully chosen and excellently organized collection of 16 essays written over a period of 25 years, complete with a comprehensive introduction. The essays all deal in o...