Pragmatic Hypotheses in the Evolution of Science

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.

The e-value: a fully Bayesian significance measure for precise statistical hypotheses and its research program

“…The study of such logical desiderata was in part motivated as a way to contrast the statistical properties of the FBST with other statistical tests of hypotheses. Surprisingly, it is possible to travel this path in the opposite direction, that is, it is possible to start from consistent desiderata for logical properties of statistical tests and, from those, derive a complete characterization of a class of statistical significance measures and hypothesis tests that coherently generalizes the FBST, see [46,47,131] for further details. Moreover, this Generalized FBST finds interesting applications in metrology and related fields, were reliable bounds for the precision of experimental measurements can be obtained from sources external to the statistical experiment designed to test the hypothesis under scrutiny.…”

A sharper image: the quest of science and recursive production of objective realities

“…For further comments on evolution of scientific disciplines from the perspective of Objective Cognitive Constructivism, see Figure 11: Fixed-point method converging to x = cos(x) = 0.739085 . . .…”

“…In the Objective Cognitive Constructivism epistemological framework this situation is known as the Zero Probability Paradox -regarding the possibility of attesting strong statistical support for a statement describing an extremely improbable (zero measure) event. For an extended discussion of the Zero Probability Paradox and its epistemological consequences, see Stern (2011b); for the technical difficulties it poses to traditional methods for test of hypotheses in statistical science and how these difficulties are overcome by the e-value significance measure, see Stern and Pereira (2014) and Esteves et al (2019).…”

“…The Full Bayesian Significance Test (FBST) is a statistical test of hypothesis published by Pereira and Stern (1999) and further extended in Madruga et al (2003), Pereira et al (2008) and Esteves et al (2016Esteves et al ( , 2019. This solution is anchored by a novel measure of statistical significance known as the e-value, ev (H | X ), a.k.a.…”

“…Therefore, the e-value and the FBST can be used as a statistical touchstone that is taylor-made to the task of accessing the objectivity of scientific eigen-solutions, as this notion is defined in the context of objective cognitive constructivism. Further mathematical, statistical, and logical or compositional properties of the e-value are discussed in Borges and Stern (2007), Esteves et al (2016Esteves et al ( , 2019, Izbicki and Esteves (2015), and Stern et al (2017). The Classical or Frequentist school of mathematical statistics offers the p-value as its signature significance measure for statistical hypotheses.…”