Wittgenstein and the formal sciences 4

Diego Morales (Eindhoven University of Technology)
Title: Wittgenstein on the Infelicity of the Question “Can Machines Think?” 

This presentation will be about the language that we employ when we talk about artificial intelligence (AI) and how Wittgenstein’s philosophy may provide valuable insights to understand its challenges. In particular, I am interested in addressing a concern related to the use of cognitive and psychological terms when describing the attributes and abilities of AI systems and AI-enabled agents. This worry may be stated as follows: Cognitive and psychological terms, that is, terms that denote cognitive processes and psychological states, have become part of the basic lexicon of the field of AI. As such, it is customary to say that some AI entities infer, understand, and learn; some are thought of as being capable of holding beliefs, acquiring knowledge and having hallucinations, and some as possessing attentive capacities, memory, and instantiating neural networks. However, more often than not, cognitive and psychological terms fail to accurately depict how AI entities actually are and what they can actually do. In fact, the worry goes, these terms contribute to the formation of a mirage: they support misrepresentations of properties and capabilities of AI, and they elicit misguided expectations about their performance. Despite this concern being recognized within the AI field, its underlying causes have received limited contemporary attention. In this talk, I aim to fill this gap by drawing on the philosophy of Ludwig Wittgenstein. His reflections on the semantics of psychological predicates and their use to describe machines provide interesting insights to frame the worry mentioned above, understand why it arises, and explain its persistence. The first part of the talk will introduce the main concern regarding the use of cognitive and psychological terms in contemporary AI. The second part will delve into Wittgenstein’s insights, offering an explanation of the issue based on his philosophy.

Alexander Porto (Duquesne University) 

Title: Naturalizing Negation: Responding to the Threefold Puzzle of Negation 

In The Threefold Puzzle of Negation and the Limits of Sense, Jean-Phillipe Narboux offers a picture of negation that is conceptually bound up with the limits of sense and intentionality. Narboux argues that in order to begin thinking about limit and thought’s answerability to reality, one must attend to a threefold structure of negation: a fold about intentionality; a fold about intelligibility; and a third fold about the apparent uni- and equivocality of negation. Throughout the essay, Narboux provides blueprints for addressing each aspect of the trilemma by emphasizing the two-way unity and distinction, borrowed from Wittgenstein, between the determination and employment of sense. Narboux explicitly sets out to show that the puzzle of negation is only a pseudo-puzzle and to show that one can begin to unfold the puzzle by transposing it into a sceptical tone. I suggest that this is mistaken. I will argue that Narboux’s sceptical treatment of the puzzle of negation stands in the way from a thoroughly ameliorative account of the trilemma. At best, to place the puzzle into the sceptical register allows us to see its complex form; at worst, it prevents us from saying anything about it. I will show that in order to work toward putting the puzzle to rest, we must put it into a naturalized register. The basic idea will be that we ought to see negation as natural to and necessary for thought, something that is bound up with every possible judgment one makes. It is at this point that we can begin to see how negation is bound up with limits of intelligibility and intentionality. 

Paul Hasselkuß (Heinrich Heine University Düsseldorf)      

Title: Wittgenstein, Open Texture and Mathematics

The notion of ‘open texture’ has gained renewed attention in recent years. Originally introduced by Waismann (1945) as a feature of empirical concepts, open texture describes the possibility that, for a concept, there may exist some object o such that neither the established use of the concept nor external nonlinguistic facts determine whether o falls under the concept. According to Waismann, this inherent indeterminacy makes empirical concepts porous and resistant to complete definition.

While Waismann carefully limited open texture to empirical concepts, recent work by Shapiro (2016), Tanswell (2018), Shapiro & Roberts (2021), Zayton (2022) and Vecht (2023) explores whether it might also apply to mathematical concepts. These authors suggest that some—but not all—mathematical concepts may exhibit open texture, though mathematical practice often has ways to address and potentially resolve such indeterminacies.

In this talk, I will investigate whether a notion akin to open texture can be identified in Wittgenstein’s later philosophy, particularly in his treatment of mathematics. I will also distinguish open texture from Wittgenstein’s concept of family resemblance, highlighting their theoretical and practical implications.

Colin Rittberg (Vrije Universiteit Brussel)

Title: Petrification in Contemporary Set Theory: The Multiverse and the Later Wittgenstein

First, we argue that Wittgenstein’s notion of petrification can be used to explain phenomena in advanced mathematics, sometimes better than more popular views on mathematics, such as formalism, even though petrification usually suffers from a diet of examples of a very basic nature (in particular a focus on addition of small numbers). Second, we analyse current disagreements on the absolute undecidability of CH under the notion of petrification and hinge epistemology. We argue that in contemporary set theory the usage of construction techniques for set-theoretic models in which the Continuum Hypothesis holds and those in which it fails have petrified into the normative demand that CH remain undecidable. That is, the continuous and successful practices involving the construction of various set-theoretic models now act as a normative hinge shared among practitioners, i.e., have normative force in the discipline. However, not all hinges are universal, which is why we find disagreements in set theory. We will show that this is a refinement of, and partially conflicts with, the arguments presented by set theorist Joel David Hamkins.