Heyting Day 2022 - Wittgenstein's Tractatus

The Tractatus gives rise to many exciting issues of interpretation. The speakers of the Heyting Day will throw light on some of these issues, especially on Wittgenstein’s views on the nature of logic and on the role of the first person in the Tractatus. The day will provide ample room to reflect together about what the book has to tell us.

• 09.30 a.m. - 10.00 a.m. arrival with coffee or tea
• 09.30 a.m. - 10.00 a.m. Arrival with coffee or tea
• 10.00 a.m. - 10.15 a.m. Opening
• 10.15 a.m. - 11.15 a.m. Wim Vanrie: Tautology and showing in Wittgenstein’s Tractatus
• 11.15 a.m. - 11.30 a.m. Coffee and tea break
• 11.30 a.m. - 12.30 p.m. Maria van der Schaar: The Tractatus and the First Person
• 12.30 p.m. - 2.00 p.m. Lunch
• 2.00 p.m. - 3.00 p.m. Victor Gijsbers: No privileged numbers? Infinity in the Tractatus
• 3.00 p.m. - 3.15 p.m. Coffee and tea break
• 3.15 p.m. - 4.15 p.m. Oskari Kuusela: The Tractatus’ epistemology of logic 
• 4.15 p.m. - 4.30 p.m. Plenary discussion led by Martin Stokhof
• 4.30 p.m. - 5:30 p.m. Reception

The Tractatus gives rise to many exciting issues of interpretation. The speakers of the Heyting Day will throw light on some of these issues, especially on Wittgenstein’s views on the nature of logic and on the role of the first person in the Tractatus. The day will provide ample room to reflect together about what the book has to tell us.

Victor Gijsbers

Victor Gijsbers is assistant professor of philosophy at Leiden university, where he works on topics in the philosophy of causation, time, modality and understanding. In 2022 he published a new Dutch translation of Wittgenstein's Tractatus.

No privileged numbers? Infinity in the Tractatus

According to Tractatus 5.453 there are no numbers in logic; there are, as Wittgenstein phrases it, "keine ausgezeichneten Zahlen", no privileged numbers. This claim puts strong restrictions on Tractarian logic. If it turns out, for instance, that Wittgenstein's account of quantification only works if the total number of objects in the world has a cardinality less than Aleph-zero, then there would seem to be a privileged number after all, namely Aleph-zero. In the current talk, I want to canvas some of the potential spots of trouble for Wittgenstein, and then discuss two possible strategies for a solution, one which attempts to extend the Tractarian logic through indefinite levels of infinity, and one which attempts to safeguard it by rejecting transfinite numbers altogether.

Oskari Kuusela

Oskari Kuusela is an Associate Professor at the University of East Anglia, UK. His research interests include philosophical methodology, the philosophy of logic and language, moral philosophy, and the history of analytic philosophy, especially Wittgenstein. His single authored books include The Struggle against Dogmatism (Harvard UP 2008) Wittgenstein on Logic as the Method of Philosophy (Oxford UP 2019). He is also the co-editor of five collections on Wittgenstein’s philosophy

The Tractatus’ epistemology of logic 

The Tractatus’ view according to which there can be no propositions or theses about logic has confused its readers. Following the traditional interpretation, according to which this view is a consequence of a thesis about language put forward in the book (the so-called picture theory), it has become standard to describe the Tractarian account of logic as entangled in a paradox. (The paradox arises if Wittgenstein is putting forward a logical thesis from which it allegedly follows that there can be no logical theses.) Relatedly, interpreters have struggled to explain the purpose or logical role of the sentences of the Tractatus, given Wittgenstein’s characterization of them as nonsense. In my talk I outline an interpretation that dissolves the paradox. This explains how the sentences of the Tractatus can simultaneously be understood as not constituting propositions or theses about logic, and as indirectly articulating an account of logic. In short, the purpose of the sentences of the Tractatus is to introduce the formal concepts and principles constitutive of a logical notation which is the proper expression for Wittgenstein’s account of logic. Accordingly, after the sentences have done their introductory work, they can be thrown away, as Wittgenstein maintains. Combined with his assumption that any language user must already possess a tacit comprehension of logic, this interpretation can render comprehensible various further points that Wittgenstein makes about logic and knowledge thereof, as I will explain. What emerges is a view of logic as a clarificatory discipline that clarifies something language users already know that is more fundamental than propositions or theses could express, and which underlies their possibility. I conclude by observing certain similarities between the Tractatus’ view and the account of logic articulated by Saul Kripke some 100 years later, according to which logic is something that cannot be adopted in the manner of a scientific theory. 

Maria van der Schaar

Maria van der Schaar is senior lecturer at the Institute of Philosophy, Leiden University. Her work is in philosophy of logic and its history. She has been working in the philosophy of constructive type theory, on the Brentano School, and on the influence of phenomenology on early analytic philosophy. Occasionally she writes on women in early analytic philosophy. She is now working on a project: the First Person in Early Analytic Philosophy (Frege, Russell, Wittgenstein).

The Tractatus and the First Person

Where Wittgenstein’s ‘Notes on Logic’ are still under the influence of Russell’s approach to philosophical questions, in the years to come Wittgenstein develops a very different method. As I will explain in the talk, a first-person method is essential to the Tractatus: questions concerning language, logic and ethics have to be addressed as a first person, from the inside. During the talk I address the following questions: Does the use of this method not imply a form of psychologism? Does it mean that Wittgenstein is committed to transcendental idealism and metaphysical solipsism? And, how are we to understand the first person?

Wim Vanrie

Wim Vanrie is a postdoctoral researcher in Philosophy at Ghent University, Belgium. He wrote his PhD dissertation at Ghent University on Frege's conception of the logical categories and their elucidation. More generally, his research focuses on the history of analytical philosophy, mainly on topics related to the philosophy of logic. In his spare time, Wim enjoys eating cakes.

Tautology and showing in Wittgenstein’s Tractatus 

Wittgenstein's claim that all propositions of logic are tautologies is rightly seen as constituting a cornerstone of the Tractatus. Usually, readers take the upshot of this claim to be that the propositions of logic make no assertion about the world, that they say nothing. According to the Tractatus, however, tautologies do not merely say nothing, they show that they say nothing. My aim is to explore how properly taking into account this centrality of the notion of showing to Wittgenstein's conception of tautology stands to deepen our understanding of the conception of logic and the philosophical project of the Tractatus.