Developments in Logic : Carnap , Gödel , and Tarski

Oxford UP, 2019

In Wittgenstein on Logic as the Method of Philosophy, Oskari Kuusela discusses Wittgenstein’s early and later philosophies of logic, situating them in the context of early and middle analytic philosophy, with particular reference to Frege, Russell, Carnap and Strawson. He argues that throughout his career Wittgenstein sought to solve problems with Frege’s and Russell’s philosophies of logic, address the limitations thereof, and to further develop a broadly Fregean–Russellian logical-philosophical methodology, aiming to achieve the philosophical progress that originally motivated this approach. By re-examining the roots and development of analytic philosophy, Kuusela seeks to open up covered-up paths for the further development of analytic philosophy. Offering a new interpretation of the philosopher, he explains how Wittgenstein extends logical methods beyond calculus-based methods, and how his novel account of the status of logic enables one to do justice to the richness and complexity of thought and language use while retaining rigour and ideals of logic such as simplicity and exactness. In addition, this volume outlines the new kind of non-empiricist naturalism developed in Wittgenstein’s later work, and explains how his account of logic can be used to dissolve the long-standing dispute between the ideal and ordinary language schools of analytic philosophy. It is aimed at philosophers and students of philosophy interested in the philosophy of logic and language, philosophical methodology, and the history of analytic philosophy, and anyone interested in logical methods or the question of how to manage complexity through simplification and idealization without falsification.

Argumenta , 2021

Studying the literature on the history of analytic philosophy may leave the impression that the members of the Vienna Circle?or more appropriately, the Schlick Circle and the associated advocates of logical empiricism?were the main agents leading philosophy to take the so-called linguistic turn. One may also think that the Circle's inspiration was, in turn, born out of the philosophical and logical contentions of Ernst Mach,1 followed by Gottlob Frege, Bertrand Russell, and the young Ludwig Wittgenstein. It is true that the seemingly rapid penetration of logical empiricism into early twentieth-century thought widely influenced the choice of markedly ana lytic topics in the philosophy of language, among them accounts of refer ence, predication, truth, and intentionality. It is equally true that

- Trabalho da Disciplina História da Lógica -, 2024

Is it possible for a rational individual to defend Mill’s position regarding standard arithmetic validly? Can anyone claim that numbers are empirical facts and that mathematical truths can be based on physical induction? Mill believed in the affirmation of these questions and, not only, thought he could demonstrate the standard arithmetic from empirical observations; Frege already believed, in his own Platonism »and this is something his interpreters find questionable, i.e., that he was a Platonic philosopher«, that this was an absurd thesis and arguments. In the following work, we will conclude that it is possible to have a sympathetic, although not entirely welcoming, critique of the doctrine of logical theses in Mill’s System of Logic. We wil give a brief overview of Frege’s Theory of Sense and Reference – Sinn und Bedeutung –, his definition of numbers and his logicist conception of standard arithmetic – already demonstrated as impossible in the 20th century, even though certain individuals try to revive it -; Mill’s main theses about arithmetic, as he conceives it, will be exposed, so that we can see a new approach to structuralist and mereological standard arithmetic based on his doctrine. And we will see if it is possible to pave the way for a logical-empirical theory of the logic of mathematics.

History and Philosophy of Logic, 2024

In many accounts of the history of logic, especially from the second half of the twentieth century and partly still today, Frege's rst book, Begri sschrift (1879), is singled out as the beginning of modern logic. In the English-speaking literature, this assessment goes back to the 1950s-60s when Frege's logical writings were rediscovered, after an initial period of neglect (although thinkers like Russell, Wittgenstein, and Carnap had paid close attention to it earlier). This is also the period during which modern logic consolidated itself, with its now standard sub elds: set theory, proof theory, model theory, and recursion theory. Good illustrations of this assessment of Frege's contributions can be found in William and Martha Kneale's book, The Development of Logic (1962), and in Jean van Heijenoort's revealingly entitled collection, From Frege to Gödel: A Source Book in Mathematical Logic. 1879-1931 (1967). The assessment was grounded in writings by a number of in uential logicians, including Alonzo Church, W.V.O. Quine, and Michael Dummett. Some of these writings, especially those by Dummett, include strong claims about how utterly original Frege's logical ideas were, thus representing a radical new beginning (cf. Reck 2023). Within the last 30-40 years such claims about the originality of Frege's views have been challenged and partly refuted in a number of ways. Thus, interpreters such as Christian Thiel, Gottfried Gabriel, Hans Sluga, etc. have pointed out the roots of some of Frege's logical ideas, including aspects of his logicist project, in neo-Kantian or post-Kantian philosophers like Hermann Lotze, J. F Herbart, and Wilhelm Windelband (cf. Gabriel 2002, Gabriel and, also the literature mentioned in them). Other interpreters of Frege, including Mark Wilson, Jamie Tappenden, and I, have discussed sources for Fregean ideas in mathematics, especially in nineteenth-century geometry, Bernhard Riemann's writings, and other works to which Frege was exposed in his mathematical education (cf. Tappenden 2008. Similarly, logical and mathematical in uences on Frege in works by Hermann and Robert Grassmann, Hermann Hankel, etc. may be worth exploring further, partly to clarify what Frege was reacting against (cf. Kreiser 2001). Yet another way in which the claim that modern logic started abruptly in 1879, with Begri sschrift, has been called into question is by rediscovering and highlighting earlier contributions by other logicians, such as George Boole, members of the Boolean school, as well as Bernard Bolzano (cf. Peckhaus 1997, Rusnock and. As this shows, it CONTACT Erich H. Reck

Critical Essays

Philosophy in review, 2014

faculty.unlv.edu

2018