Pragmatic Hypotheses in the Evolution of Science

Luis Gustavo Esteves,Rafael Izbicki,Rafael Bassi Stern,Julio Michael Stern

doi:10.3390/e21090883

Luis Gustavo Esteves, Rafael Izbicki + Show 2 more

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https://doi.org/10.3390/e21090883

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Abstract

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais.

Highlights

Standard hypothesis tests can lead to immediate logical incoherence, which makes their conclusions hard to interpret
The analysis is based on the metaphor of evolutive hexagonal spirals [10,11], in which the logical modalities associated to scientific theories change over time, as in. We overcome this paradox by proposing the concept of a “pragmatic hypothesis” associated to a precise hypothesis
We propose to choose a pragmatic hypothesis in such a way that the imprecision in the end-user’s predictions is mostly due to his experimental conditions and not due to the level of imprecision in the theory that he uses

Summary

Introduction

Standard hypothesis tests can lead to immediate logical incoherence, which makes their conclusions hard to interpret. In order to overcome such an impossibility result, Esteves et al [2] propose agnostic hypothesis tests, which have three possible outputs: (A) accept the hypothesis, say H, (E) reject H, or (Y) remain agnostic about H These tests can be made logically coherent while preserving desirable statistical properties. These observations lead to the apparent paradox that, if the GFBST were used to test scientific theories, the acceptance step in the spiral of scientific theories would be forfeited We overcome this paradox by proposing the concept of a “pragmatic hypothesis” associated to a precise hypothesis. They build pragmatic hypotheses for simple hypotheses and prove that there exists a single way of extending this construction to composite hypotheses while preserving logical coherence in simultaneous hypothesis testing.

Gallais’ Hexagonal Spirals and the Evolution of Science

Pragmatic Hypotheses

Singleton Hypotheses

Composite Hypotheses

Applications

Final Remarks