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# Mathematical Analogies: Mini-Workshop and Brainstorming Session (24 June 2019)

24.05.2019

## Idea & Motivation

Arguments by analogy play significant roles in science. Scientists and engineers use physical analogies, such as scale models of bridges, along with other kinds of models, such as mathematical models, computer models, and model organisms. Such models are used for a variety of purposes but crucial to their utility is that they resemble or are in some sense analogous to the intended target system, such that it is possible to generate new hypotheses about the target system under investigation.Of particular interest here are mathematical analogies between two apparently different systems. For example, the logistic equation in ecology models the behaviour of a population growing to carrying capacity. This same equation crops up in many other places as well. In economics it is the diffusion of innovations equation and in chemistry it describes autocatalytic reactions. These three different physical systems apparently share a common mathematical core and this common core can serve as the basis for useful analogies (e.g. predicting behaviour of certain chemical reactions based on known features of population growth).

Mathematical analogies also play a central role in philosophy, where mathematics is frequently used as a model for other meta-empirical or a priori domains. Metaethicists in particular have started to use local structural parallels between mathematics and morality in order to corroborate realist views of morality, but mathematics has also been argued to share relevant features with the domains of logic, modality, and religion. The analogies featuring in those arguments share a common form: a local analogy between mathematics and another a priori domain is identified, from which a global conclusion is drawn about one or both of the domains. For example, Clarke-Doane (2012, 2014) argues that there is just as much fundamental disagreement in mathematics as there is in ethics, and that this fact undermines epistemically motivated arguments against moral realism. What is missing in the debates featuring mathematical analogies, however, is a discussion of (a) the plausibility of the relevant mathematical background assumptions (specifically in light of recent pluralist developments in set theory); (b) how to develop an adequate methodology for analogical reasoning about a priori domains; (c) the prospects of developing a unified framework for all a priori domains; (d) the role of mathematics in developing analogies across different scientific domains; and (e) the prospects of developing a unified approach to analogical reasoning across both priori and a posteriori domains.

The purpose of this 2-hour mini-workshop and brainstorming session is to discuss these questions in an informal setting in order to collect ideas on how they might best be tackled.

## Participants

• Erik Curiel
• Mark Colyvan
• Neil Dewar
• Joe Dewhurst
• John Dougherty
• Alistair Isaac
• Silvia Jonas
• Mary Leng
• Miklos Redei

• Silvia Jonas
• Mark Colyvan