Intentional sampling methods are non-probabilistic procedures that select a group of individuals for a sample with the purpose of meeting specific prescribed criteria. Intentional sampling methods are intended for exploratory research or pilot studies where tight budget constraints preclude the use of traditional randomized representative sampling. The possibility of subsequently generalize statistically from such deterministic samples to the general population has been the issue of long standing arguments and debates. Nevertheless, the intentional sampling techniques developed in this paper explore pragmatic (...) strategies for overcoming some of the real or perceived shortcomings and limitations of intentional sampling in practical applications. (shrink)

This article explores the metaphor of Science as provider of sharp images of our environment, using the epistemological framework of Objective Cognitive Constructivism. These sharp images are conveyed by precise scientific hypotheses that, in turn, are encoded by mathematical equations. Furthermore, this article describes how such knowledge is pro-duced by a cyclic and recursive development, perfection and reinforcement process, leading to the emergence of eigen-solutions characterized by the four essential properties of precision, stability, separability and composability. Finally, this article discusses (...) the role played by ontology and metaphysics in the scientific production process, and in which sense the resulting knowledge can be considered objective. (shrink)

In this article, we discuss some issues concerning magical thinking—forms of thought and association mechanisms characteristic of early stages of mental development. We also examine good reasons for having an ambivalent attitude concerning the later permanence in life of these archaic forms of association, and the coexistence of such intuitive but informal thinking with logical and rigorous reasoning. At the one hand, magical thinking seems to serve the creative mind, working as a natural vehicle for new ideas and innovative insights, (...) and giving form to heuristic arguments. At the other hand, it is inherently difficult to control, lacking effective mechanisms needed for rigorous manipulation. Our discussion is illustrated with many examples from the Hebrew Bible, and some final examples from modern science. (shrink)

In this article, we discuss some issues concerning magical thinking—forms of thought and association mechanisms characteristic of early stages of mental development. We also examine good reasons for having an ambivalent attitude concerning the later permanence in life of these archaic forms of association, and the coexistence of such intuitive but informal thinking with logical and rigorous reasoning. At the one hand, magical thinking seems to serve the creative mind, working as a natural vehicle for new ideas and innovative insights, (...) and giving form to heuristic arguments. At the other hand, it is inherently difficult to control, lacking effective mechanisms needed for rigorous manipulation. Our discussion is illustrated with many examples from the Hebrew Bible, and some final examples from modern science. (shrink)

This paper investigates some classical oppositional categories, like synthetic vs. analytic, posterior vs. prior, imagination vs. grammar, metaphor vs. hermeneutics, metaphysics vs. observation, innovation vs. routine, and image vs. sound, and the role they play in epistemology and philosophy of science. The epistemological framework of objective cognitive constructivism is of special interest in these investigations. Oppositional relations are formally represented using algebraic lattice structures like the cube and the hexagon of opposition, with applications in the contexts of modern color theory, (...) Kantian philosophy, Jungian psychology, and linguistics. (shrink)

This article considers distinct ways of understanding the world, referred to in psychology as functions of consciousness or as cognitive modes, having as the scope of interest epistemology and natural sciences. Inspired by C.G. Jung’s simile of the spectrum, we consider three basic cognitive modes associated to: (R) embodied instinct, experience, and action; (G) reality perception and learning; and (B) concept abstraction, rational thinking, and language. RGB stand for the primary colors: red, green, and blue. Accordingly, a conceptual map between (...) cognitive modes and primary and secondary colors is built based on the physics and physiology of color perception and epistemological characteristics of the aforementioned cognitive modes, leading to logical relations structured as an hexagon of opposition. Finally, this model of cognitive modes is applied to the analysis and interpretation of some important episodes in the historical development of physics and technology. (shrink)

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

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)

Karl Pearson is the leading figure of XX century statistics. He and his co-workers crafted the core of the theory, methods and language of frequentist or classical statistics – the prevalent inductive logic of contemporary science. However, before working in statistics, K. Pearson had other interests in life, namely, in this order, philosophy, physics, and biological heredity. Key concepts of his philosophical and epistemological system of anti-Spinozism (a form of transcendental idealism) are carried over to his subsequent works on the (...) logic of scientific discovery. This article’s main goal is to analyze K. Pearson early philosophical and theological ideas and to investigate how the same ideas came to influence contemporary science, either directly or indirectly – by the use of variant theories, methods and dialects of statistics, corresponding to variant statistical inference procedures and their specific belief calculi. (shrink)

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be logically (...) consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations. (shrink)

Randomization procedures are used in legal and statistical applications, aiming to shield important decisions from spurious influences. This article gives an intuitive introduction to randomization and examines some intended consequences of its use related to truthful statistical inference and fair legal judgment. This article also presents an open-code Java implementation for a cryptographically secure, statistically reliable, transparent, traceable, and fully auditable randomization tool.

If there are two dependent positive real variables x1 and x2, and only x1 is known, what is the probability that x2 is larger versus smaller than x1? There is no uniquely correct answer according to “frequentist” and “subjective Bayesian” definitions of probability. Here we derive the answer given the “objective Bayesian” definition developed by Jeffreys, Cox, and Jaynes. We declare the standard distance metric in one dimension, d(A,B)≡|A−B|, and the uniform prior distribution, as axioms. If neither variable is known, (...) P(x2x1)=P(x2>x1). This appears obvious, since the state spaces x2x1 and x2>x1 have equal size. However, if x1 is known and x2 unknown, there are infinitely more numbers in the space x2>x1 than x2x1. Despite this asymmetry, we prove P(x2x1∣x1)=P(x2>x1∣x1), so that x1 is the median of p(x2|x1), and x1 is statistically independent of ratio x2/x1. We present three proofs that apply to all members of a set of distributions. Each member is distinguished by the form of dependence between variables implicit within a statistical model (gamma, Gaussian, etc.), but all exhibit two symmetries in the joint distribution p(x1,x2) that are required in the absence of prior information: exchangeability of variables, and non-informative priors over the marginal distributions p(x1) and p(x2). We relate our conclusion to physical models of prediction and intelligence, where the known ’sample’ could be the present internal energy within a sensor, and the unknown the energy in its external sensory cause or future motor effect. (shrink)

This paper reconsider the fundamental de Finetti’s representation theorem. It is stressed its role at the front-line between Probability Theory and Inferential Statistics and its relation to the fundamental problem of relating past observations with future predictions i. e. the problem of induction.

This paper investigates some classical oppositional categories, like synthetic versus analytic, posterior versus prior, imagination versus grammar, metaphor versus hermeneutics, metaphysics versus observation, innovation versus routine, and image versus sound, and the role they play in epistemology and philosophy of science. The epistemological framework of _objective cognitive constructivism_ is of special interest in these investigations. Oppositional relations are formally represented using algebraic lattice structures like the cube and the hexagon of opposition, with applications in the contexts of modern color theory, (...) Kantian philosophy, Jungian psychology, and linguistics. (shrink)