Yang Zhouwanyue Nata

March 01, until August 27, 2024

Affiliation: MCMP, LMU

Research for a study about:

On the limitation of Carnap’s linguistic approach to the debate on the foundations of mathematics.

Carnap's conception of philosophy is epistemological, and is rooted in his realization that language use in philosophical discussions is often ambiguous and many philosophical debates are meaningless as they simply arise from confusions caused by the ambiguous use of languages. This phenomenon urges the choice of appropriate tools for philosophical work. For him, the appropriate tool is a linguistic device — artificially defined logically consistent languages, or possibly unambiguous fragments of natural languages. Using such languages to reconstruct philosophical theories makes it possible to eliminate meaningless sentences in philosophical discussions and to resolve most philosophical problems caused by the confusions. In his book, The Logical Syntax of Language, Carnap presented his method by taking the 20th century debate of the foundations of mathematics as a case study. Despite its undoubted fruitfulness, Carnap's method has its limitations, which affect the way in which he reconstructed the foundational theories in this debate. This project focuses on his reconstruction of the intuitionistic mathematics in order to show (some of) the limitations of his method, and to explain why Carnap cannot provide a better reconstruction.  In this way, this project shows the limitations that should be overcome in a new epistemological investigation of the debate.

Lecture

On the Neutrality of Carnap’s Tolerance — A Reconstruction of Beth’s Critique in Terms of Understanding

Philosophy of Science Colloquium

Date:  2024/05/02

Time: 16h45 pm (CET)

Venue: New Institute Building (NIG), Universitätsstraße 7, 1010 Wien, HS 3F

Abstract:

Carnap's conception of philosophy underscores that the tools used by philosophers shape the problems that intrigue or bother them. Particularly, the ambiguity in the linguistic tools often manifests in philosophical debates about concepts, where philosophers are talking at cross purposes because they cannot clearly formulate the concepts in question. Carnap sought to address this phenomenon of talking at cross purposes by clearly defined linguistic frameworks that clarify explicanda. The present investigation reflects the success condition for Carnap's approach by questioning what is the proportional attitude toward the outcomes of such linguistic frameworks. By considering the propositional attitude as understanding, it argues that these frameworks fail to eliminate the phenomenon of talking at cross purposes if the users of the frameworks cannot initially understand the explicanda. Two parts of the argument will be presented: First, it re-emphasizes that according to Carnap's conception of explicanda in Logical Foundations of Probability (1950), the main source of explicanda is one's intuition, which implies that an understanding of explicanda precedes an explication of explicanda through one's choice of an apt framework. And second, it introduces Beth's 1963 critique of Carnap to demonstrates the impossibility of understanding explicanda solely through the choice of a linguistic framework.

Report

My fellowship at IVC has had a very positive impact on my research.
At the beginning, I was so enthusiastic about the historical perspective that my colleagues at IVC specialize in. This was a factor that I had neglected during my doctoral research. I realized that Carnap's linguistic approach to philosophy stems from the Enlightenment idea. The goal of his Logical Syntax (LSS) can be better grasped if it is situated in relation to his broader philosophical interests. I also noticed that Carnap used the term “understanding” differently than how it is commonly used in contemporary epistemology. Since my work on the project serves specifically for my dissertation, in which I argue for the pluralism of mathematical understanding, it is important for me to make the difference clear.
After giving a talk on Carnap's tolerance principle, my listeners' feedbacks reminded me further problems, such as how to read Beth's critique of Carnap. Considering that Carnap's distinction between syntax and semantics was not made in the LSS, Beth's argument of the non-standard model may be seen as unfair and too demanding on Carnap. It may indicate a deeper difference in their approach to language. I have therefore focused on the role of language in Carnap's study of the philosophy of mathematics. With this consideration, I try to relate this role to the instrumental role of knowledge that the idea of enlightenment advocates. This may explain why Carnap's approach to the philosophy of mathematics did not pay much attention to mathematical practices.