Women in the History of Analytic Philosophy - Springer
The book Women in the History of Analytic Philosophy (2022), edited by Jeanne Peijnenburg and Sander Verhaegh, is part of the Springer series Women in the History of Philosophy and Sciences and presents a collection of papers from the workshop held in October 2019 in Tilburg, Netherlands, dedicated to highlighting the contributions of female philosophers to the development of early analytic philosophy. In the following, we present the two contributions “Rózsa Péter on the Philosophy and Foundations of Mathematics: A Reappraisal” by Andrea Reichenberger and “Ruth Barcan Marcus’s Role in the Mid-Twentieth Century Debates on Analyticity and Ontology” by Gregory Lavers.
Rózsa Péter on the Philosophy and Foundations of Mathematics: A Reappraisal – Andrea Reichenberger
Stephen Kleene (1909–1994) once praised the Hungarian mathematician and logician Rózsa Péter (1905–1977) as “the leading contributor to the special theory of recursive functions” (Kleene, 1952). Her works broke new ground and helped to establish recursion theory as a mathematical discipline. Today, Kleene is much better known in the philosophy of mathematics than Péter. In this chapter, I provide an overview of Rózsa Péter’s work and describe her active role in communicating these results to a broader audience in her book Playing with Infinity (1944/1961). First, I will briefly summarize the content and key statements of Péter’s book, including an overview of its reception. Second, I will focus on a case study: Péter’s popular sketch of Gödel’s proof. Third, I will contextualize this case study against the historical background of Hilbert’s program and the decision problem. This includes Péter’s research on recursion theory. Last, but not least, I will discuss Church’s thesis and Péter’s interpretation of it. I conclude with some reflections on the relevance of Péter’s work from a philosophical, conceptual and practical perspective.
‘When I began my college education, I still had many doubts about whether I was good enough for mathematics. Then a colleague said the decisive words to me: it is not that I am worthy to occupy myself with mathematics, but rather that mathematics is worthy for one to occupy oneself with.’ ~ Rózsa Péter
This is a quote from Péter’s essay “Mathematics is Beautiful” (Péter, 1990, 58). The essay dates back to a lecture delivered to high school teachers and students which Péter held in Rostock, German Democratic Republic, in 1963. The lecture was first published in 1964 in the German journal Mathematik in der Schule. The English translation by Leon Harkleroad appeared in the journal The Mathematical Intelligencer in 1990.
Ruth Barcan Marcus’s Role in the Mid-Twentieth Century Debates on Analyticity and Ontology – Gregory Lavers
Quine’s ‘Two Dogmas of Empiricism’ is generally seen as overturning Carnap’s epistemological picture of mathematics and the sciences. However, I wish to stress how this paper grew out of arguments not having anything to do with large-scale epistemological concerns, but ones originally presented against quantified modal logic. Quine thought he could demonstrate the impossibility of adding anything like ordinary quantification to modal logic, but Barcan Marcus did exactly this. In fact, as I will argue, ‘Two Dogmas …’ can be seen as growing out of a 1947 paper of Quine’s where Barcan Marcus is the explicit target. Later, in certain exchanges with Quine, Barcan Marcus puts forward and defends a consistent and interesting position on matters of ontology and the philosophy of language. This chapter will examine Barcan Marcus’s role in both the debate over analyticity and the debate on (meta-)ontology.
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