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, 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, 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. (shrink)

A global pandemic on the scale of Covid-19 upsets all standard decision protocols. Pressure from politicians to "open up" the economy presumes that individuals grant credible trust to politicians and merchants eager to recover customers. The asymmetric concern for safety compounds normal heuristics. The Peircean pragmatic maxim reminds us that it is the perceived effects of a post-pandemic society and economy that will drive human volition in the aftermath of Covid-19. Opening up does not equal showing up.

According to the instrumentalism of Friedman and Machlup it is irrelevant whether the explanatory principles or “assumptions” of a theory satisfy any criterion of “plausibility,” “realism,” “credibility,” or “soundness.” In this view the main or only criterion for selecting theories is whether a theory yields empirically testable implications that turn out to be consistent with observations. All we should require or expect from a theory is that it is a useful instrument for the purpose of prediction. Considerations of the “efficiency” (...) of a theory for the purpose of ordering our experiences are permitted, but considerations of “plausibility” are not. “Explanatory assumptions” are not really explanatory in the sense that they claim to represent underlying causal processes in reality; they only serve to generate, by deduction, implications that are in accordance with as many observations as possible. (shrink)

The author makes an introduction to non-standard analysis, then extends the dialectics to “neutrosophy” – which became a new branch of philosophy. This new concept helps in generalizing the intuitionistic, paraconsistent, dialetheism, fuzzy logic to “neutrosophic logic” – which is the first logic that comprises paradoxes and distinguishes between relative and absolute truth. Similarly, the fuzzy set is generalized to “neutrosophic set”. Also, the classical and imprecise probabilities are generalized to “neutrosophic probability”.