Piotr Dehnel

The paper discusses a relatively underexamined element of Wittgenstein’s philosophy of mathematics associated with his critique of set theory. I outline Wittgenstein’s objections to the theories of Dedekind and Cantor, including the confounding of extension and intension, the faulty definition of the infinite set as infinite extension and the critique of Cantor’s diagonal proof. One of Wittgenstein’s major objections to set theory was that the concept of the size of infinite sets, which Cantor expressed by means of symbols אₒ and c, had no application, i.e. that there was no grammatical technique that could show how such expressions were to be used. Notions of set theory are, so to speak, exterior – they find themselves outdoors, outside of what we usually do. They form a discourse that takes us beyond the horizon of everydayness and commonality. They are like an engine idling of the language of mathematics.

Maria Kokoszyńska-Lutmanowa (1906-1981) was a Polish philosopher and student of Kazimierz Twardowski, the founder of the Lvov-Warsaw School. In 1938 she went to the University of Cambridge (Newnham College) on a Sarah Smitton Fellowship. There she attended George Edward Moore’s lectures as well as one of Ludwig Wittgenstein’s Lectures on the Foundations of Mathematics in 1939. In this interview which was conducted with Alois Eder she talks about her encounter with Wittgenstein. It was published in 1978 in the Polish art and culture magazine Odra and is her only published memoir about Wittgenstein. The interview is republished here both in English translation and as facsimile of the original publication with the kind permission of the Odra magazine.

Samuel J. Wheeler defends Wittgenstein's criticism of Cantor's set theory against the objections raised by Hilary Putnam. Putnam claims that Wittgenstein's dismissal of the basic tenets of this set theory concerning the noncountability of the set of real numbers was unfounded and ill‐conceived. In Wheeler's view, Putnam's charges result from his failure to grasp Wittgenstein's intention and, in particular, to consider the difference between empirical and logical impossibility. In my paper, I argue that Wheeler's defence is unsuccessful and, at the same time, that Putnam's objections go too far.

Spanning the period between Wittgenstein's return to Cambridge in 1929 and the first version of Philosophical Investigations in 1936, Piotr Dehnel explores the middle stage in Ludwig Wittgenstein's philosophical development and identifies the major issues which engrossed him, including phenomenology, philosophy of mathematics and philosophy of language. Contrary to the dominant perspective, Dehnel argues that this period was intrinsically different from the early and late stages and should not be viewed as a mere transitional phase. The distinctiveness of Wittgenstein's middle work can be seen in his philosophical thinking as it unfolds in a non-linear trajectory: thoughts do not follow upon each other, ideas do not appear sequentially one by one, and insights do not form a straight chain. Dehnel portrays the diffused and multifarious quality of Wittgenstein's middle thinking, enabling readers to form a more comprehensive view of his entire philosophy and acquire a better grasp of his conceptual trajectory, complete with the intricacies and challenges that it poses.

The aim of the article is to present Marek Siemek’s interpretation of modernity, focusing on problems related to understanding of the modern subject that arose from the reading of Max Horkheimer and Theodor W. Adorno’s Dialectic of Enlightenment. Siemek seems to endorse a general drive of Habermas’ theory of intersubjective communication intended to overcome the dialectics of Enlightenment and to complete the project of modernity. However, his position is that its foundation can be traced back to the philosophies of Fichte and Hegel and their mutually complementary intersubjectivity models. Siemek seeks to reconcile the idea of the philosophy of intersubjectivity underlying Fichte’s and Hegel’s philosophies with the tenets of the philosophy of consciousness.

This article aims to analyse Wittgenstein’s 1929–1932 notes concerning Frege’s critique of what is referred to as old formalism in the philosophy of mathematics. Wittgenstein disagreed with Frege’s critique and, in his notes, outlined his own assessment of formalism. First of all, he approvingly foregrounded its mathematics-game comparison and insistence that rules precede the meanings of expressions. In this article, I recount Frege’s critique of formalism and address Wittgenstein’s assessment of it to show that his remarks are not so much a critique of Frege as rather a defence of the formalist anti-metaphysical investment.