Wittgenstein and the formal sciences 5

Title:"Applying Wittgenstein: To what extent can AI-generated pieces be regarded as music?".

 By: Chun Cai (University of Southampton),

Abstract:

My paper examines the research question of to what extent can people regard AI-generated pieces as music. I will apply Ludwig Wittgenstein's tool of language-games for grammatical investigations. Specifically, I will introduce some of his music-language analogical remarks and compare them with his remarks on the surroundings of language. I aim to clarify that in the cases of regarding AI-generated pieces as music, aesthetic reasons as a more essential surrounding are lacking. One of the conclusions of this paper will be: Considering the surroundings of the language-games in which people use 

My paper examines the research question of to what extent can people regard AI-generated pieces as music. I will apply Ludwig Wittgenstein's tool of language-games for grammatical investigations. Specifically, I will introduce some of his music-language analogical remarks and compare them with his remarks on the surroundings of language. I aim to clarify that in the cases of regarding AI-generated pieces as music, aesthetic reasons as a more essential surrounding are lacking. One of the conclusions of this paper will be: Considering the surroundings of the language-games in which people use 

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Title: Defining mathematical problems with Wittgenstein and Feferman

By: Matteo De Ceglie (IUSS Pavia)

Abstract: 

Defining the right mathematical problem is the fundamental first step in mathematical practice. Wittgenstein remarks in his Nachlass that “[...] the correct formulation of the question is already the answer.” (Wittgenstein Nachlass Ms-305,1[4]). Wittgenstein starting position was that mathematical open problems were not genuine propositions, and have no proper sense (see 208, 50r of Wittgenstein (2012)). This position seems akin to Feferman (2014)), in which the interest of finding a solution to CH is challenged on the grounds that it is not a correctly formulated mathematical problemm, and it is instead "sensless". However, Wittgenstein position later evolved towards a more balanced approach, in which the propositions forming a mathematical open problem are not completely devoid of meaning, and can in some sense still be understood. The reason why Wittgenstein can claim that there is some sort of understanding stems from the fact that mathematicians usually have (justified?) beliefs about open problems that tend to guide their practice (see, for example, Wittgenstein (2009) and Säätelä (2011)). In this talk I explore the similarities and differences between Wittgenstein’s and Feferman’s accounts of mathematical open problems. My overall goal in this talk is to show that (surprisingly) Feferman’s account doesn’t account for current set-theoretic practice as much as Wittgenstein’s (later) one.

References

• Feferman, S. (2014). “The Continuum Hypothesis is neither a definite mathematical problem or a definite logical problem”. Unpublished.

• Säätelä, Simo (2011). “From Logical Method to ‘Messing About’: Wittgenstein on ‘Open Problems’ in Mathematics”. In: The Oxford Handbook of Wittgenstein. Oxford University Press. isbn: 9780199287505.

• Wittgenstein, Ludwig (2009). Philosophical investigations. John Wiley & Sons.

• — (2012). The big typescript: TS 213. John Wiley & Sons.

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Title: Wittgenstein and Turing on Contradictions Revisited

By: Zhao Fan (Vrije Universiteit Brussel) 

Abstract: Wittgenstein’s exchanges with Turing over the issues of contradictions in Wittgenstein’s 1939 Lectures on the Foundations of Mathematics (LFM) have been widely discussed in the literature. Recent interpretations of these exchanges focus on Turing’s notorious example of a collapsing bridge – a bridge that might fall because of a contradictory calculus. Scrutinizing their exchanges on the bridge example, scholars have argued that Wittgenstein was exercising his therapeutic method to reveal and dispel Turing’s philosophical confusions on contradictions. The text of LFM, nevertheless, seems to indicate a rather more complex narrative. In this talk, I will present a close reading of the Wittgenstein-Turing exchanges on contradictions. I will argue, (1) The collapsing bridge example is not clear enough to reveal Wittgenstein’s and Turing’s position on contradictions, and (2) more effort should be made in interpreting the prison example in LFM.

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Title: Wittgenstein’s Deconstruction of Platonic Object Realism in Mathematics
By Nicola Gianola (University of Rome Tor Vergata) 

 The aim of this talk is to present an original argument against mathematical Platonism, based on a set of remarks by Ludwig Wittgenstein that — in my view — have not yet received adequate attention in the literature. The central idea is that Wittgenstein does not merely criticise what the SEP describes as truth-value realism, which he himself characterises as the “telescopic” conception of proof: the thesis that mathematical proofs are epistemic instruments allowing us to assign truth-values to propositions that possess meaning independently of the proof and that refer to a domain of abstract entities. I will argue instead that Wittgenstein also seeks to deconstruct the entire Platonist picture of mathematics by uncovering the genealogy of the — illusory — idea of the existence of such abstract entities, thereby criticising the ontological component of Platonism as well, namely object realism. Beginning from the problem of the generality of proofs, I will show how Wittgenstein identifies in ordinary language (“prose”) the source of the grammatical misunderstanding that leads us to transform our linguistic and demonstrative paradigms into supposed “pure forms.”

References:

• Hardy, G. H. Mathematical Proof. Mind, New Series, 1929.

•  Linnebo, Ø. Platonism in the Philosophy of Mathematics. Stanford Encyclopedia of Philosophy, 2024.

• Schroeder, S. Wittgenstein on Mathematics. Routledge, 2021.

• Steiner, M. “Empirical Regularities in Wittgenstein’s Philosophy of Mathematics.” Philosophia Mathematica, 2009.

• Stillwell, S. “Empirical Inquiry and Proof.” In Proof and Knowledge in Mathematics. Routledge, 1992.

• Wittgenstein, L. Lectures on the Foundations of Mathematics, Cambridge 1939. Edited by Cora Diamond. Chicago University Press, 1989.

• Wittgenstein, L. Remarks on the Foundations of Mathematics. Edited by G. E. M. Anscombe, Rush Rhees, and G. H. von Wright. John Wiley & Sons, 1981.