Knowledge, Chess, Wittgenstein and Dedekind: A (History of) Analytic Philosophy Workshop

Talks (abstracts below)

10.15 Welcome & coffee

10.30 - 11.45
Sander Verhaegh (TiLPS, Tilburg University)
Justified True Belief: The Remarkable History of ‘Mainstream’ Epistemology

12 - 13 Lunch

13.00 - 14.15
Martin Gustafsson (Åbo Akademi)
Philosophical reflections on the development of chess

14.20 - 15.35
Anna Boncompagni (UC Irvine)
Sraffa, Piccoli, and Wittgenstein’s 1931 remarks on gestures: a reassessment

15.45 - 17.00
Dan Isaacson (Oxford)
Richard Dedekind and the nature of mathematics

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Abstracts:

Sander Verhaegh (TiLPS, Tilburg University)
Justified True Belief: The Remarkable History of ‘Mainstream’ Epistemology
Abstract: In 1963, Edmund Gettier published a landmark paper arguing that the JTB definition of knowledge “does not state a sufficient condition for someone’s knowing a given proposition”. The article quickly attracted a large number of responses from philosophers, who began exploring alternative definitions and supplementary conditions. In fact, the analysis of knowledge became such a popular discipline that opponents (formal epistemologists, experimental philosophers, and feminist epistemologists) started labeling it ‘mainstream’ epistemology. From a historical perspective, it is quite puzzling how Gettier-style epistemology became so popular. Gettier published his paper in a philosophical environment that was generally opposed to the idea that we can or should state the necessary and sufficient conditions for everyday epistemic concepts. In the 1950s, Anglophone philosophy was dominated by logical empiricism, ordinary language philosophy, and the more traditional approaches of Russell and Moore. Yet none of these schools would have accepted the presuppositions of Gettier’s program. Russell believed that knowledge is “a term incapable of precision” (1948, 516). Carnap was not interested in ordinary language and attempted to explicate technical notions such as ‘confirmation’ and ‘probability’ (1950, ch. 1). And Wittgenstein rejected the assumption that everyday concepts can be strictly defined (1958, 19). This paper reconstructs the origins of mainstream epistemology, highlighting the philosophical and methodological debates that led to its rapid development. I argue that debates about knowledge in the 1940s and 1950s led to exchanges between different schools of analytic philosophy and show how they gave rise to new ideas about the nature of analysis. Finally, I turn to Gettier's intellectual development and argue that his paper was influenced by some of these debates, suggesting that even his interpretation of Plato’s epistemology can be traced back to discussions from this period.
 
Martin Gustafsson (Åbo Akademi)
Philosophical reflections on the development of chess
Abstract: I will discuss certain philosophically significant moments in the history of chess and tie it to themes in Wittgenstein and Saussure.
 
Anna Boncompagni (UC Irvine)
Sraffa, Piccoli, and Wittgenstein’s 1931 remarks on gestures: a reassessment
Abstract: This paper sheds light on a crucial period in Wittgenstein’s work, the early 1930s, by paying close attention to biographical, exegetical, and theoretical details. My starting point is the episode of the Neapolitan gesture that Sraffa showed Wittgenstein, asking him about its grammar, which is often recounted as fundamental in Wittgenstein’s shift towards ordinary language and forms of life. While the literature on this usually focuses on methodological aspects and the emergence an anthropological outlook, I turn the attention to the surprisingly neglected topic of gestures themselves. In particular, I examine Wittgenstein’s 1931 reflections on gestures of rejection and pointing gestures in the light of his intellectual exchanges with Piero Sraffa and Raffaello Piccoli. From the historiographical point of view, this will offer evidence that helps set a date for that famous but still undated episode, and highlight the importance of Piccoli, professor of Italian in Cambridge, a friend of both Wittgenstein and Sraffa but (unlike Sraffa)  actually Neapolitan. From the theoretical point of view, this work shows that it was precisely the reflection about gestures – in connection with negation on the one hand, and with pointing and ostension on the other – that led Wittgenstein to abandoning his previous views and setting the stage for his later approach.
 
Dan Isaacson (Oxford University)
Richard Dedekind and the nature of mathematics
Abstract: Richard Dedekind published two pamphlets, in 1872 and 1888, in which he axiomatized the real numbers and the natural numbers, respectively, the most fundamental structures of mathematics (the continuous and the discrete). Dedekind thereby established axiomatization as a methodology in the practice of mathematics, and in so doing changed how we can and should understand the nature of mathematics. I will discuss how Dedekind came to think in these terms, and how he succeeded in characterizing these fundamental structures and, for his axiomatization of the natural numbers, succeeded (by means of his proof of categoricity— any two models of those axioms are isomorphic) in establishing that he had succeeded. I will consider how this changed the practice of mathematics, as in the work of David Hilbert, arguably the most influential mathematician in the late 19th and early 20th century, in Zermelo’s axiomatization of set theory, and continuing in the work of the French Bourbaki, and to the present day. I will note that not everyone accepted Dedekind’s method of axiomatization, as when Russell declared that axiomatization, as opposed to what Russell called the method of construction, has “the advantages of theft over honest toil” (a particularly unfortunate claim for Russell given his reliance on the Axiom of Reducibility). Dedekind’s axiomatizations also established a new philosophy of mathematics, structuralism (though not labelled as such till the mid-twentieth century). I will focus on Dedekind’s axiomatization of the natural number. I will discuss Dedekind’s use of second-order logic in his axiomatization of arithmetic and how his second-order axiomatization, which is essential for categoricity, gives rise to first-order axiomatization, which despite lacking categoricity, has virtues that second-order axiomatization lacks. I will say something about the misattribution in the usage “Peano Arithmetic”, which has become standard for what should be called Dedekind Arithmetic.