Formalize!(?) - 5 

Schedule

15:15 - 15:30 Introduction
15:30 - 16:15 Talk 1:Colin Rittberg (Vrije Universiteit Brussels)
16:15 - 17:00 Talk 2: Jordi Fairhurst (UIB) and Seunghyun Song (Tilburg University)

17:00 - 17:30 Break and zoom photo

17:30 - 18:15 Talk 3: Robert Naylor (Manchester)
18:15 - 19:00 Talk 4:Aleksandra Vučković (Belgrade)
19:00 - 19:15 closing

19:15 -   The room will stay open for unofficial discussion

Abstracts and title (in the order of the talks): 

Jordi Fairhurst (Palma de Mallorca) and Seunghyun Song (Tilburg University)

Title: Epistemic value of deep disagreements: the case of mathematics

Abstract: This paper articulates the value of sustaining deep disagreements in fields of science. We illustrate our position based on a particular example of mathematics. Mathematics is considered to differ from other scientific disciplines due to its outstanding level of consensus. Mathematicians share clear agreements on, e.g., the right and wrong answers to fundamental questions in the field, valid and invalid proofs, or true and false theorems (see Wagner 2022 for a programmatic analysis). This high degree of consensus in mathematics, however, does not entail that it is completely free from disagreements. Recently there has been a growing body of literature noting the presence of deep disagreements within mathematics and noting their possible implications for mathematical practice (see Aberdein 2023; Kant 2023; Wagner 2023). We offer a working definition of deep disagreements in mathematics as instances in which mathematicians, despite sharing epistemic goals (e.g., bringing true beliefs in mathematics), are faced with persistent disagreements with no clear resolution because they rely on different fundamental beliefs and/or epistemic principles to attain these goals. These deep disagreements may pose a threat to mathematical progress, stagnating the production of knowledge about contentious mathematical topics.

This paper argues one need not fear mathematical deep disagreements since these disputes may be of great interest to mathematicians’ epistemic goals. The paper proceeds as follows. First, we provide a brief explanation regarding what deep disagreements are. On this basis, we offer two concrete case studies of deep disagreements found in the field of mathematics. Second, we discuss the valuable contributions these deep disagreements may offer to mathematics. Building on the work of De Cruz and De Smedt (2013), we argue that deep disagreements can provide three valuable contributions to mathematics: (i) new evidence and/or proofs, (ii) a re-evaluation of existing evidence, assumptions and/or proofs and (iii) an antidote to confirmation bias. By arguing thus, we critically refute that deep disagreements may pose a threat to mathematical progress. Third, we provide our normative take on the epistemic goals of mathematicians. We argue that mathematicians should uphold an epistemic principle of openness. This principle, if abided by in the context of deep disagreements by mathematicians, will transform deep disagreements into fertile grounds of epistemic pursuits. We illustrate our epistemic principle of openness in the context of scientific exchange, thereby establishing a good practice of knowledge impartment and uptake, where a scientist remains open to their peers’ arguments, claims and criticisms in the context of deep disagreements.

Robert Naylor (Manchester)

Title: Entangled Mathematics as a Tool of Reasoning in the Mid-Twentieth-Century UK Electricity Industry

Abstract: In the mid-twentieth century, the identity of those who oversaw the UK electricity grid tentatively and slowly began to shift from those who joined the electricity industry directly from secondary school to a university-educated elite with a higher level of technical education. At the same time, electricity infrastructure became increasingly centralised, leading to the creation of a national grid in 1938, meaning that control of electricity became concentrated in the hands of an ever-smaller group and increasing the stakes in debates over strategy. By using the case studies of power engineer Paul Schiller and mathematician Maurice Davies, this paper traces how the boundaries of what mathematics could or could not be used for were renegotiated between factions within the UK electricity industry. Schiller unsuccessfully attempted to use mathematics, including the authority of academic mathematicians, to reinforce controversial arguments about the strategic direction of the industry in the 1940s. Such arguments failed to resonate with a class of, as Schiller put it, “practical men” that still held considerable influence. Davies on the other hand was employed by the industry in the 1950s to improve efficiency, and was able to implement lasting measures in this effort by using the weather to forecast electricity demand, and successfully defended the usefulness of his work in the 1970s against colleagues who felt that forecasting could be done better with mathematical models without weather inputs. The contrast between these two stories shows how the influence of mathematical thinking was contingent upon existing power dynamics, and reinforce how the history of mathematics should be socially embedded.

Colin Rittberg (Vrije Universiteit Brussels)

Title: Epistemic injustice in mathematics

Abstract: We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept to highlight a potential danger of intellectual enculturation.

Aleksandra Vučković (Belgrade)

Title: The Impact of Large Language Models on Education and Academic Publishing

Abstract: The emergence and rapid development of large language models (LLMs), with the most notable example of GPT-4 and its predecessors, has transformed our perception and approach to various life spheres, including our understanding of creativity, authorship, and even our position on the work market. These topics converge in the discussions on LLMs' influence on education and academia, which makes these fields a promising area for further exploration of the ethical and epistemic challenges and potential of generative AI. From the perspective of AI development, the issue with LLMs is their lack of formal reasoning which makes them prone to mistakes. From a social perspective, the challenges arise due to the unequal distribution of technological advancements globally. This research aims to establish a minimal normative requirement for the successful inclusion of LLMs in education and academic publishing under the assumption that the purpose of such an inclusion is to provide a better learning and research environment while simultaneously maintaining the proven values of critical thinking and intellectual integrity.