Life, cognition and metabiology

Applied Mathematics and Computation

At the biological level what is innate is the result of an evolutive process “programmed” by natural selection. Natural selection is the coder (once linked to the emergence of meaning): at the same time at this level the emergence process is indissolubly correlated to the continuous construction of new cognitive formats in accordance with the unfolding of ever-new mathematics, a mathematics that necessarily moulds coder’s activity. Hence the necessity of articulating and inventing a mathematics capable of engraving itself in an evolutive and self-organizing landscape. In this sense, for instance, the realms of non-standard models and non-standard analysis represent, today, a fruitful perspective from which to point out, in mathematical terms, some of the basic concepts concerning the articulation of an adequate intentional information theory. This individuation, on the other hand, presents itself not only as an important theoretical achievement but also as one of the essential bases of our very evolution as intelligent organisms.

2009

Abstract We forward hypothesis that all what we refer to as mathematics are cognitive aspects of life, moreover, we have right to refer to mathematics as reference system of life. Mathematics and cognition are not distinguishable between themselves because what we call mathematics refer to the functionality by means of what (or via what) we are created by nature, or by God, be it question of our religious persuasion.

Paradigmi. Rivista di critica filosofica, 2015

In the last decades two different and apparently unrelated lines of research have increasingly connected mathematics and evolutionism. Indeed, on the one hand different attempts to formalize darwinism have been made, while, on the other hand, different attempts to naturalize logic and mathematics have been put forward. Those researches may appear either to be completely distinct or at least in some way convergent. They may in fact both be seen as supporting a naturalistic stance. Evolutionism is indeed crucial for a naturalistic perspective, and formalizing it seems to be a way to strengthen its scientificity. On the contrary, it will be underlined how those lines of research may be seen as conflicting, since the conception of knowledge on which they rest may be undermined by the consequences of accepting an evolutionary perspective.

To understand the phenomena present in the "Intimate Nature of the Universe", in its various evolutionary processes, it is necessary to look beyond the boundaries of our current knowledge, where the evolutionary processes are guided not by statistical science, but by an elementary form of Intelligence inherent in Universe system capable of guiding the “Spark of life”, regardless of where we collapse the Schrödinger Wave Function. The study of "Universal Reality" has been led onto false tracks, as the two foundations on which current science is based (Relativity and Quantum), in addition to not being reconcilable with each other, are incomplete and/or false compared to the " Intimate Nature of the Universe". This parameter needs to be represented by a new "Algebra of Nature", connected to the role of Geometry in the Universe, which lately is losing its historical identity. Instead of being in tune with the Multiplicity Universal, more and more elements are added to the Geometry in the Universe that cages it into "static syntheses", which constitute the pretext for eliminating the role of Intuition in geometry. From which it can be deduced that, as for the Causal Law, to represent our experience in "condensed matter", geometric axioms are little necessary, so we can think of spaces, and therefore geometries, in which completely different axioms are valid than our ones, as non-Euclidean geometry showed after Kant. We can therefore deduce that the foundation of mathematics lies in a "super-intuition" inherent in the illusion of the passage of Time, while recognizing that mathematics has its own content which comes directly from Intuition, and as such is independent as much as from sensorial experience, as well as from logical structuring. In this sense, logic is nothing but a guise that for communication purposes is imposed on contents that are completely independent of it, since mathematics is like a magician's hat, from which anything put inside first can come out. We can deduce here that the Algebra of the "Intimate Nature of the Universe", through the phenomenon of Resonance, represents the existing relationship between Form and Frequency, where Nature, visible and invisible to us, behaves like an enormous transceiver antenna, as it is DNA with its characteristics of electronic conduction and self-symmetry. The DNA evolves through a modality that transcends the second principle of thermodynamics, as for example Life is born and evolves by gathering around itself everything that it serves him, transforming it into "order" and not into "disorder" as entropy would like. This "intelligent evolutionary path" inherent in the "intimate nature of the Universe", in order to function, requires the function of Intuition and Error, which between the Past, Present and Future perform the function of driving the "Universal Evolutionary Arrow". The meaning of "Error" is seen as the need to interrupt a state of "Perfection" in order to exist, creating the pulsation present in every corner of this Universe. This vision of Universal Reality leads us to understand that Nature is pure Art, powered by a form of intrinsic Universal Intelligence, which has nothing to do with Artificial Intelligence, which cannot be "Intelligent" as it lacks Intuition . Finally, we note that due to the current stalemate of contemporary Science, many questions still remain open in our coexistence with the Harmony of Universal Nature, which should be addressed with courage and imagination, through the support of a new, more scientific vision close to the Intimate Nature of the Universe, investigated in this article.

2024

This is an essay in what might be called "mathematical metaphysics." There is a fundamental duality that runs through mathematics and the natural sciences. The duality starts at the logical level; it is represented by the Boolean logic of subsets and the logic of partitions since subsets and partitions are category-theoretic dual concepts. In more basic terms, it starts with the duality between the elements (Its) of subsets and the distinctions (Dits, i.e., ordered pairs of elements in different blocks) of a partition. Mathematically, the Its & Dits duality is fully developed in category theory as the reversethe-arrows duality. The quantitative versions of subsets and partitions are developed as probability theory and information theory (based on logical entropy). Classical physics was based on a common-sense view of reality as definite all the way down. In contrast, quantum physics embodies (objective) indefiniteness. And finally, there are the two fundamental dual mechanisms at work in biology, the selectionist mechanism and the generative mechanism, two mechanisms that embody the fundamental duality.

Foundations of science, 2006

In the past decades, recent paradigm shifts in ethology, psychology, and the social sciences have given rise to various new disciplines like cognitive ethology and evolutionary psychology. These disciplines use concepts and theories of evolutionary biology to understand and explain the design, function and origin of the brain. I shall argue that there are several good reasons why this approach could also apply to human mathematical abilities. I will review evidence from various disciplines (cognitive ethology, cognitive psychology, cognitive archaeology and neuropsychology) that suggests that the human capacity for mathematics is a category specific domain of knowledge, which can be explained as the result of natural selection.

According to Wittgenstein, mathematics is embedded in, and partly constituting, a form of life. Hence, to imagine different, alternative forms of elementary mathematics, we should have to imagine different practices, different forms of life in which they could play a role. If we tried to imagine a radically different arithmetic we should think either of a strange world (in which objects unaccountably vanish or appear) or of people acting and responding in very peculiar ways. If such was their practice, a calculus expressing the norms of representation they applied could not be called false. Rather, our criticism could only be to dismiss such a practice as foolish and to dismiss their norms as too different from ours to be called ‘mathematics’.

in Danish I moderne matematikfilosofi findes en raekke forskellige naturalistiske forklaringer af matematik. I denne afhandling praesenterer jeg tre forskellige typer af sådanne sådanne forklaringer, og diskuterer deres styrker og svagheder. Disse tre naturalistiske forklaringstyper tager udgangspunkt i hhv. 1) evolutionaer biologi, 2) kognitionsvidenskab og 3) videnssociologi. Hver af disse retninger inden for naturalismen haevder, at matematisk viden kan forklares med en bestemt type af kendsgerninger om menneskets natur, men den praecise type af kendsgerning varierer fra retning til retning; den evolutionaere tilgang til naturalismen peger på kendsgerninger om evolutionaere historie, den kognitionsvidenskabelige tilgang peger på kendsgerninger om menneskets kognitive apparat og den videnssociologiske tilgang peger på sociale kendsgerninger.

In historical claims for nativism, mathematics is a paradigmatic example of innate knowledge. Claims by contemporary developmental psychologists of elementary mathematical skills in human infants are a legacy of this. However, the connection between these skills and more formal mathematical concepts and methods remains unclear. This paper assesses the current debates surrounding nativism and mathematical knowledge by teasing them apart into two distinct claims. First, in what way does the experimental evidence from infants, nonhuman animals and neuropsychology support the nativist hypothesis? Second, granting that infants have some elementary mathematical skills, does this mean that such skills play an important role in the development of mathematical knowledge?

2013