Wittgenstein and the formal sciences

An analogous investigation? Later Wittgenstein on psychological and mathematical discourse by S. Bangu
In a remark in what has come to be known as the second part of his Philosophical Investigations, Wittgenstein says that “An investigation is possible in connection with mathematics, which is entirely analogous to our investigation of psychology." The aim of this talk is to explain what he may have had in mind.

***

Rethinking the epistemology of deep disagreements through the lens of Wittgenstein’s later philosophy by J. Fairhurst
Deep disagreements are generally understood as systematic and persistent disagreements rooted in contrary worldviews where there is no mutually recognized method of resolution because the parties involved often reason and analyze evidence using different epistemic frameworks. Despite the centrality of deep disagreements in our life and interaction with others, there is little consensus regarding how we ought to understand the nature and epistemology of deep disagreements. My research aims to fill this lacuna. Drawing on Ludwig Wittgenstein’s later philosophical method and insights, I propose to motivate, develop, and explore a novel conception of the nature and epistemology deep disagreements. Against existing theories of deep disagreements, I defend that it is a mistake to assume that deep disagreements are epistemologically uniform and can only be adequately explained by one true global theory. Instead, deep disagreements are complex phenomena which form a complex unity in terms of a family unified by a network of crisscrossing similarities and kindships. Accordingly, I propose to rectify existing theories by restricting them to local descriptions that clarify the epistemology of particular kinds of deep disagreements on a case-by-case basis by responding to their specific epistemological features. By adopting a methodology that is more in line with Wittgenstein’s later philosophy and understanding deep disagreements in this way, my research will provide a novel and attractive account of the nature and epistemology of deep disagreements that furthers our understanding of a central part of our lives.

***

Does Artificial Intelligence Use Private Language? by R. Miller
The Private Language Argument [PLA] (Philosophical Investigations §243-271) is perhaps Wittgenstein’s most lasting contribution. In Harris (2007)’s reconstruction, the PLA has the following structure: language requires rule-following, rule-following requires the possibility of error, the error is precluded in pure introspection, and inner mental life is known only by pure introspection, thus language cannot exist entirely within inner mental life. Jerry Fodor’s influential Language of Thought (1975, 2010) thus seems vulnerable to the PLA. Fodor defends his computational theory of mind by offering the following dilemma from computer science. If privacy is understood narrowly, then inner mental life can be known outside of pure introspection, by tracking the changes in the physical supervenience base of the system, that is, the state of the computer hardware. On the other hand, if privacy is understood broadly, then the very existence of computers running machine languages should count as a reductio ad absurdum of the premise that language requires the possibility of error. Fodor takes it that computers genuinely understand predicates whenever their use comports with the conditions specified in the representation in an appropriate meta-language, even though the machine cannot fail to use predicates in accord with the specified rules.

I suggest that the developing field of artificial intelligence (deep learning neural networks) tends to vitiate Fodor’s defense and hence vindicate the PLA. The first horn of Fodor’s dilemma requires language to encompass genuinely internal mental life, that is, non-projected intentional states, which are not exhibited in classical machine learning but only by deep learning neural networks (Ressler, 2003). Such networks act as black boxes whose state, however, cannot be understood by tracking the changes in their supervenience bases without shared con- text (López-Rubio, 2021), and that shared context introduces the possibility of error (von Eschenbach, 2021). The language of artificial intelligence is not private.

***

Arithmetic as Symbolic Knowledge in the Tractatus by Gisele Secco

In a recent paper [1] I compared the main features of the Leibnizian notion of symbolic knowledge with some passages from the Tractatus on arithmetic. I take such a comparison, first advanced by Sören Stenlund ([2], [3]), to accomplish three things: (i) it sheds a new light on the specificities of the Tractarian definition of number, compared to those of Frege and Russell; (ii) it highlights the young Wittgenstein understanding of the nature of mathematical knowledge as symbolic or formal knowledge; (iii) it provides evidence for the claim that Wittgenstein was a philosopher of mathematical practice avant la lettre. In my talk, I intend to focus on the reasons for claim (ii).

References

[1] SECCO, G.D. (2020) Aritmética e conhecimento simbólico: notas sobre o Tractatus logico-philosophicus e o ensino de filosofia da matemática.

[2] STENLUND, S. (2013) “Wittgenstein and Symbolic Mathematics”. O que nos faz pensar, v.22, n.33, 2013, pp. 7-34.

[3] STENLUND, S. (2014) “On the Origin of Symbolic Mathematics and Its Significance for Wittgenstein’s Thought” Nordic Wittgenstein Review, 4, n.1, 2015, pp. 7-92.

***

What is mathematical use? By R. Wagner
Abstract: I believe that the most fundamental move in Wittgenstein's philosophy of mathematics is the rejection of the question "what constitutes a mathematical statement?" in favor of "what constitutes a mathematical use of a statement?" (to which the answer is: setting a standard for descriptions). I will briefly review this move, and then try to follow Wittgenstein by replacing the question "what does a mathematical term refer to?" by "what constitutes a mathematical use of a term?". The answer will be: its embedding in a network of unstable translations between concrete presentations.