Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional independence for discrete datasets. The full Bayesian (...) significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist’s significance tests (characterized by the calculation of the p-value). (shrink)

Inauguration speech at chair number 18 of the Brasilian Academy of Philosophy.

Departing from Anderson’s (2016) suggestion that there are three communities in Peirce’s thought corresponding to his three normative sciences of logic, ethics, and esthetics, I argue that these communities partake in a relationship of dependence similar to that found among the normative sciences. In this way, just as logic relies on ethics which relies on esthetics, so too would a logical community of inquirers rely on an ethical community of love, which would rely on an esthetic community of artists. A (...) community could conduct inquiry together only if it pursued the same goal; and it could pursue the same goal only if it first imaginatively construed it. Any logical or ethical community requires a shared imaginative repertoire of ideal ends. (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)

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 article discusses some continuous limit cases of Susan Haack’s crossword puzzle metaphor for the coherent development and foundation of science. The main objective of this discussion is to build a bridge between Haack’s foundherentism and the epistemological framework of objective cognitive constructivism, including its key metaphor of objects as tokens for eigen-solutions. The historical development of chemical affinity tables is used to illustrate our arguments.

In this paper, I argue that Plotinus’s critique of divine deliberation in Ennead 6.7 does not seek to banish teleology altogether from his philosophy of nature. Rather, his critique aims to situate teleology within his own metaphysical system so as to reconcile it with the basic principles governing the intelligible universe. In this sense, Plotinus does not propose that we expunge all reference to notions of utility and benefit from our natural explanations; he merely wishes to render those notions coherent (...) with an ontology in which the intelligible always takes precedence over sensible reality. To this end, Plotinus introduces, first, what I call a vertical teleology, where the different animal species create the necessary conditions for the maintenance of higher forms of intelligible life, such as genera. Second, Plotinus advances what I call a horizontal teleology, where the various animal organs serve to provide a minimal coefficient of noetic content to each species in its respective ontic level. Plotinus thus sketches the outlines of a properly ‘noetic’ teleology in Ennead 6.7. (shrink)

In this paper I argue that, to conceive transcendence, Levinas retrieves the Platonic concept of “separation” and deploys it in three ways: metaphysically, semantically, and affectively. Levinas finds in the interaction between being and the Good beyond being of Republic VI 509b a certain “formal structure of transcendence”—one in which a term is conditioned by another while remaining absolutely separated from it. This formal structure is subsequently deployed metaphysically, in the relation between creator and creature; semantically, in the relation between (...) meaning and sense; and affectively, in the relation between the desiring self and its desired aim. (shrink)

In this paper, I argue that Plotinus does not limit the sphere of free human agency simply to intellectual contemplation, but rather extends it all the way to human praxis. Plotinus’s goal in the first six chapters of Ennead 6.8 is, accordingly, to demarcate the space of freedom within human practical actions. He ultimately concludes that our external actions are free whenever they actualize, in unhindered fashion, the moral principles derived from intellectual contemplation. This raises the question of how the (...) freedom of practical actions might relate to the freedom of intellectual contemplation. After considering two previously offered models—a model of double activity, and an Aristotelian model of practical syllogism—I offer a third alternative, namely a model of moral attunement, according to which our rational desires assume a kind of ‘care of the soul’ through active supervision. Practical life is thus imbued with freedom to the extent that the soul supervises its actions to conform to its will and choice of the good. (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.

In this essay I will defend three points, the first being that Descartes- unlike the aristotelian traditon- maintained that abstraction is not a operation in which the intellect builds the mathematical object resorting to sensible ob- jects. Secondly I will demonstrate that, according to cartesian philosophy, the faculty of understanding has the ability to instatiate- within the process of abstraction- mathematical symbols that represent the relation between quantities, whether magnitude or multitude.And finally I will advocate that the lack of onthological (...) commitment with sensible experience found in cartesian philosophy of mathematics allows for the creation of a mathematical language that regards the objects of geometry and arithmetics through a system of rules and notations, in other words, algebra. (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)

The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for the unit root (...) hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test. (shrink)

This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective interpretations that (...) are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion. (shrink)

Comments presented at the 35th International Seminar on the -- New Institutional Economics -- Empirical Methods for the Law; Syracuse, 2018.

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)

This article describes the Full Bayesian Significance Test for the problem of separate hypotheses. Numerical experiments are performed for the Gompertz vs. Weibull life span test.

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)

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.

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)

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)

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. (shrink)

The full Bayesian signi/cance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.

Decoupling is a general principle that allows us to separate simple components in a complex system. In statistics, decoupling is often expressed as independence, no association, or zero covariance relations. These relations are sharp statistical hypotheses, that can be tested using the FBST - Full Bayesian Significance Test. Decoupling relations can also be introduced by some techniques of Design of Statistical Experiments, DSEs, like randomization. This article discusses the concepts of decoupling, randomization and sparsely connected statistical models in the epistemological (...) framework of cognitive constructivism. (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 notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages of using (...) the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed. (shrink)

El presente artículo busca hacer una revisión del concepto de verdad como fundamento del conocimiento científico: desde el pragmatismo de William James y Jürgen Habermas hasta las nociones pragmáticas de Charles -/- Sanders Peirce, con la intención de mostrar los rasgos pertinentes -/- e insuficiencias de cada postura. De manera complementaria, se -/- buscará dar cuenta de los niveles: pragmático (semiótico-filosófico) -/- y pragmatista (psicológico), en los que funciona dicho concepto -/- dentro de la filosofía peirciana. Finalmente, tal esbozo teórico (...) nos permitirá establecer una -/- definición operativa de verdad como condición trascendental, y -/- que resulte menos problemática para representar el conocimiento -/- científico. (shrink)

A new Evidence Test is applied to the problem of testing whether two Poisson random variables are dependent. The dependence structure is that of Holgate’s bivariate distribution. These bivariate distribution depends on three parameters, 0 < theta_1, theta_2 < infty, and 0 < theta_3 < min(theta_1, theta_2). The Evidence Test was originally developed as a Bayesian test, but in the present paper it is compared to the best known test of the hypothesis of independence in a frequentist framework. It is (...) shown that the Evidence Test is considerably more powerful when the correlation is not too close to zero, even for small samples. (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.

Abstract: In the present work we have made a critical review of the philosophical propo­ sal of Norwood R. Hanson with the aim of exposing the limits of its theoretical approach on the problem of interpretation in science. The first part of this work exposes the hansonian project, looking for evidence of his contributions to the philosophy of science and scientific thinking. In the following two sections we present a critique to his philosophical proposal. We present two exercises of philosophical (...) reflection that constitute two complementary moments of analysis. On one hand, at the level of methodological analysis, we present a discussion about how the “reversible perspective figures” that have been used for the author as arguments to explain his philosophical proposal, are insufficient to the descrip­ tion of the process of observation and interpretation. On the other hand, at the theoretical level, we question his notion of language and categories to show that his theoretical pro­ posed “vision-interpretation” has based on epistemological and analytic notions. From this perspective, it will be shown that the “hermeneutical-interpretative” approach of Hanson is incomplete, since it does not develop towards an ontology of language and observation. (shrink)

Sortition, i.e. random appointment for public duty, has been employed by societies throughout the years as a firewall designated to prevent illegitimate interference between parties in a legal case and agents of the legal system. In judicial systems of modern western countries, random procedures are mainly employed to select the jury, the court and/or the judge in charge of judging a legal case. Therefore, these random procedures play an important role in the course of a case, and should comply with (...) some principles, such as transparency and complete auditability. Nevertheless, these principles are neglected by random procedures in some judicial systems, which are performed in secrecy and are not auditable by the involved parties. The assignment of cases in the Brazilian Supreme Court is an example of such a procedure, for it is performed using procedures unknown to the parties involved in the judicial cases. This article presents a review of how sortition has been historically employed by societies and discusses how Mathematical Statistics may be applied to random procedures of the judicial system, as it has been applied for almost a century on clinical trials, for example. A statistical model for assessing randomness in case assignment is proposed and applied to the Brazilian Supreme Court. As final remarks, guidelines for the development of good randomization procedures are outlined. (shrink)

We review the definition of the Full Bayesian Significance Test (FBST), and summarize its main statistical and epistemological characteristics. We review also the Abstract Belief Calculus (ABC) of Darwiche and Ginsberg, and use it to analyze the FBST’s value of evidence. This analysis helps us understand the FBST properties and interpretation. The definition of value of evidence against a sharp hypothesis, in the FBST setup, was motivated by applications of Bayesian statistical reasoning to legal matters where the sharp hypotheses were (...) defendants statements, to be judged according to the Onus Probandi juridical principle. (shrink)

Abstract This essay seeks to realize the following question: what is the correspondence between the sign and the thing that names? In reality, what is significant is closely linked with the being, however in this case the sense will be a particular manifestation of an own subjectivity; therefore the determinant relation is limited to the capacity of representation, where the meaning is connected with the socio-cultural sense. In this regard, this work seek realize this problem from the analytical approach of (...) Ludwig Wittgenstein, who is based on the method of philosophical investigation through formal logic. In this first period of development, his speculative work, which in principle leads to the search for logical foundations for mathematics, practised it in direction to the study of the nature of the representation. Subsequently, and as necessary this test delimitation, will expose the confrontation —more not necessarily contradiction— of their approaches in the light of the own Wittgenstein who, in a second reflective period poured into his later work, is obliged to discuss the foundational in his speculative work logical-philosophical topics from a pragmatic point of view. (shrink)

Abstract This paper seeks to give an account of the semiotic and interpretive processes involved in the ambiguity of media representations and, in particular, of new and of different forms of construccion-difusion of information. For this reason, it is deemed the massive dissemination of information and journalistic exercis as a semiotic process in the construction of a fictitious reality. In this regard, it i sought to account for the media representation, as the contrast of the uniform character of the mass (...) expression (context of production) and the diversity of interpretations (context of reception). This review examines both component which are the concrete support that allows the individual to mean social conten non-, mid-, and intentional, thereby fostering a strong sense of social belonging. (shrink)

El propósito de este ensayo es mostrar un ámbito especulativo, necesario para el investigador social de la comunicación, para el entendimiento e investigación del fenómeno comunicativo en tanto hecho histórico-cultural. En razón de esto, se intenta describir una parte de Filosofía Alemana de la Historia, para exponer la utilidad de su lenguaje, categorías y relaciones, como instrumento teórico en la actividad analítica e interpretativa del comunicólogo, en aras de poder determinar, de manera general e integradora, el proceso histórico de la (...) comunicación, entendida esta última como manifestación semiótica de una cultura, pueblo, nación... (shrink)

This paper seeks to establish the reflexive fundamentals about the importance of language in initiave-functional college education, with the general objective of finding and developing categories that allow synthesizing schemes of different approaches to language, in order to contribute to the teaching practice with discourse analysis -/- techniques, which favor processes that promote the pupils’operative intellectual habits. To present this, we will show some propositions that underlie didactic strategies we have used, to motivate, stimulate, and provoke participation from the students (...) in the teaching-learning process of the topics raised in the different subjects that integrate the Sciences of Communication course at the National Autonomous University of Mexico (UNAM). -/- Therefore, the aim of this exposition of causes is to define: 1) our experiential context so to make explicit the limitations and challenges we experiment with and face in this academic exercise to provoke the pupils’ amazement or at least keep their interest; and 2) the theoretical assumptions that underlie our investigation about the relationship between observed language (system) and lived language (act). (shrink)

Este artículo tiene el objetivo de explorar algunas funciones semióticas que constituyen el espacio urbano. Se revisarán algunas categorías y operaciones semióticas relevantes en la comprensión del espacio para que, desde ahí, se pueda explorar el sentido de la noción Centro Histórico como un concepto fundamental en la construcción del imaginario social en las ciudades de occidente.

The notion “language” seems to be stablished in a problematic and confused way: although certainly it shows an essential reality of man, on the other hand it designates various areas within the same cultural reality. This essay parts from a supposition: only through verbal -/- signs (words) we can reach Knowledge. To demonstrate the previous -/- statement, we will show the approaches of philosophers and specialist, in their own scenario, consider the word as the language, like a -/- distinctive characteristic (...) of the human, that expresses its own rational -/- condition. And by virtue of this, it is aimed at creating a space for -/- reflection about the essential quality in human language, understood -/- not -/- as a repository of knowledge, but as the knowledge itself, the expression of the spirit of a people, loyal to its own image. (shrink)

-/- Este artículo analiza la posible superación teórica de la escisión moderna entre sujeto y objeto, por un lado, y delimita teóricamente la relación entre estas nociones, por el otro. Para tales propósitos, los autores se -/- fundamentan teóricamente en las propuestas de la hermenéutica de Wilhelm Dilthey y del estructuralismo de -/- Michel Foucault, tanto en su semejanzas (en el ámbito -/- de lo vivencial y el análisis de lo vivido, así como en su -/- preocupación por establecer un (...) ámbito de estudio en las -/- ciencias del espíritu) como en sus diferencias (pues el -/- primero propone la síntesis en la vivencia, mientras el -/- otro el análisis de lo vivido). (shrink)

This paper presents a central thesis: that humanistic language is the idiomatic context in which the Wes­ tern cultural universe orworld has existence, and, by extension, where the academic world has existence and sense. In this frame, the authors analyze two main topics: a) the way in which meaning units, that name the referent University, articulate and orga­ nize humanistic contents that adjust along to the academic world which men have been postulating throughout history; and b) the evidence of inherited (...) vocabulary of Western thought in the traditional discourse of the National Autonomous University of Mexico. (shrink)

In Posterior Analytics II 16-17, Aristotle seems to claim that there cannot be more than one explanans of the same scientific explanandum. However, this seems to be true only for “primary-universal” demonstrations, in which the major term belongs to the minor “in itself” and the middle term is coextensive with the extremes. If so, several explananda we would like to admit as truly scientific would be out of the scope of an Aristotelian science. The secondary literature has identified a second (...) problem in II 16-17: the middle term of a demonstration is sometimes taken as the definition of the minor term (the subject), other times as the definition (or the causal part of the definition) of the major (the demonstrable attribute). I shall argue that Aristotle’s solution to the first problem involves showing that certain problematic attributes, which appear to admit more than one explanation, actually fall into the privileged scenario of primary-universal demonstrations. In addition, his solution suggests a conciliatory way-out to our second problem (or so I shall argue): the existence of an attribute as a definable unity depends on its subject having the essence it has, which suggests that both the essence of subjects and the essence of demonstrable attributes can play explanatory roles in demonstrations. (shrink)

We show how the Full Bayesian Significance Test (FBST) can be used as a model selection criterion. The FBST was presented by Pereira and Stern as a coherent Bayesian significance test. Key Words: Bayesian test; Evidence; Global optimization; Information; Model selection; Numerical integration; Posterior density; Precise hypothesis; Regularization. AMS: 62A15; 62F15; 62H15.

Optimization and Stochastic Processes Applied to Economy and Finance. Textbook for the BM&F-USP (Brazilian Mercantile and Futures Exchange - University of Sao Paulo) Master's degree program in Finance.

This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.

We present SASC, Self-Adaptive Semantic Crossover, a new class of crossover operators for genetic programming. SASC operators are designed to induce the emergence and then preserve good building-blocks, using metacontrol techniques based on semantic compatibility measures. SASC performance is tested in a case study concerning the replication of investment funds.