### Abstract

The purpose of this paper is to discuss the role of financial practice in the development of mathematics as applied in human judgement. The basis of the paper is in historical research from the 1990s that argues that the monetisation of western commerce, which abstracted value into quantified price, was synthesised with scholastic analysis resulting in a “mathematical mechanistic world picture” that led to the widespread use of mathematics in science from the seventeenth century. An aspect of this process was the quantification of chance that led to the development of mathematical probability, the branch of mathematics most relevant to judgement and the focus of this paper. Ideas from this historical research are related to the fundamental theorem of asset pricing (FTAP), the foundational theory of contemporary financial mathematics. The paper observes that vestiges of medieval scholastic attitudes to financial ethics can be discerned in the FTAP, offering a novel interpretation of the mathematical theorem. The paper then considers the Dutch book argument (DBA), the most popular justification for subjective probability. The paper’s main contribution is in describing the significance of financial practice in validating the DBA and the paper explains how the FTAP addresses some criticisms of how the DBA represents beliefs. The conclusions emphasise the distinction between pure and practical reasoning and that this should be mirrored in a distinction between the mathematics of physica and practica. This point is important as mathematics is becoming more widespread in modelling, and directing, social systems.

Original language | English |
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Journal | Synthese |

Early online date | 20 Apr 2020 |

DOIs | |

Publication status | E-pub ahead of print - 20 Apr 2020 |

### Keywords

- Dutch book argument
- Ethics
- Financial markets
- Mathematics
- Probability

### ASJC Scopus subject areas

- Philosophy
- Social Sciences(all)

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## Profiles

## Timothy Johnson

- Research Centres and Themes, Centre for Finance & Investment - Associate Professor
- School of Mathematical & Computer Sciences - Associate Professor
- School of Mathematical & Computer Sciences, Actuarial Mathematics & Statistics - Associate Professor
- Research Centres and Themes, Energy Academy - Associate Professor

Person: Academic (Research & Teaching)