Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that satisfy logical requirements. (...) However, Izbicki and Esteves shows that the only tests that are in accordance with three logical requirements (monotonicity, invertibility and consonance) are trivial tests based on point estimation, which generally lack statistical optimality. As a possible solution to this dilemma, this paper adapts the above logical requirements to agnostic tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis. Each of the logical requirements is characterized in terms of a Bayesian decision theoretic perspective. Contrary to the results obtained for regular hypothesis tests, there exist agnostic tests that satisfy all logical requirements and also perform well statistically. In particular, agnostic tests that fulfill all logical requirements are characterized as region estimator-based tests. Examples of such tests are provided. (shrink)

In this paper epistemological, ontological and sociological questions concerning the statistical significance of sharp hypotheses in scientific research are investigated within the framework provided by Cognitive Constructivism and the FBST (Full Bayesian Significance Test). The constructivist framework is contrasted with the traditional epistemological settings for orthodox Bayesian and frequentist statistics provided by Decision Theory and Falsificationism.

The main goal of this article is to use the epistemological framework of a specific version of Cognitive Constructivism to address Piaget’s central problem of knowledge construction, namely, the re-equilibration of cognitive structures. The distinctive objective character of this constructivist framework is supported by formal inference methods of Bayesian statistics, and is based on Heinz von Foerster’s fundamental metaphor of objects as tokens for eigen-solutions. This epistemological perspective is illustrated using some episodes in the history of chemistry concerning the definition (...) or identification of chemical elements. Some of von Foerster’s epistemological imperatives provide general guidelines of development and argumentation. (shrink)

Heinz Von Forester characterizes the objects “known” by an autopoietic system as eigen-solutions, that is, as discrete, separable, stable and composable states of the interaction of the system with its environment. Previous articles have presented the FBST, Full Bayesian Significance Test, as a mathematical formalism specifically designed to access the support for sharp statistical hypotheses, and have shown that these hypotheses correspond, from a constructivist perspective, to systemic eigen-solutions in the practice of science. In this article several issues related to (...) the role played by language in the emergence of eigen-solutions are analyzed. The last sections also explore possible connections with the semiotic theory of Charles Sanders Peirce. (shrink)

In this paper, the relationship between the e-value of a complex hypothesis, H, and those of its constituent elementary hypotheses, Hj, j = 1… k, is analyzed, in the independent setup. The e-value of a hypothesis H, ev, is a Bayesian epistemic, credibility or truth value defined under the Full Bayesian Significance Testing mathematical apparatus. The questions addressed concern the important issue of how the truth value of H, and the truth function of the corresponding FBST structure M, relate to (...) the truth values of its elementary constituents, Hj, and to the truth functions of their corresponding FBST structures Mj, respectively. (shrink)

Masters degree dissertation on -- Geometrical Aspects of General Relativity.

Foundherentism is a new and promising theory of epistemic justification that has not received its due in the secondary literature. Accordingly, in this paper, I will examine foundherentism with three principal concerns in mind. First, I explain the epistemic components of foundherentism. Second, I defend foundherentism against the charge of reliabilism. While third and finally, I argue that foundherentism needs to be supplemented with a virtuous component.

Introduction -- Foundationalism versus coherentism : a dichotomy disclaimed -- Foundationalism undermined -- Coherentism discomposed -- Foundherentism articulated -- The evidence of the senses : refutations and conjectures -- Naturalism disambiguated -- The evidence against reliabilism -- Revolutionary scientism subverted -- Vulgar pragmatism : an unedifying prospect -- Foundherentism ratified -- Selected essays -- "Know" is just a four-letter word -- Knowledge and propaganda : reflections of an old feminist -- "The ethics of belief" reconsidered -- Epistemology legalized : or, (...) truth, justice, and the American way. (shrink)

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for testing (...) scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

We need to find a middle way between the exaggerated deference towards science characteristic of scientism, and the exaggerated suspicion characteristic of anti-scientific attitudes — to acknowledge that science is neither sacred nor a confidence trick. The Critical Commonsensist account of scientific evidence and scientific method offered here corrects the narrowly logical approach of the Old Deferentialists without succumbing to the New Cynics' sociologism or their factitious despair of the epistemic credentials of science.

The evidence with respect to scientific claims is like ernpirical eviderwe generally — only more so: more complex, more dependent on instruments, etc., and usually a shared resource. Warranted scientific claims are always warranted by somebody's, or somebodies’, experience, and somebody's or, somebodies', reasoning; so a theory of warrant must begin with the personal and then move to the social before it can get to grips with the impersonal sense in which we speak of a well-warranted claim or ill-founded conjecture.

Foundherentism is a new and promising theory of epistemic justification that has not received its due in the secondary literature. Accordingly, in this paper, I will examine foundherentism with three principal concerns in mind. First, I explain the epistemic components of foundherentism. Second, I defend foundherentism against the charge of reliabilism. While third and finally, I argue that foundherentism needs to be supplemented with a virtuous component.