Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...) along with a new concept to abstractly model the functions of a brain. (shrink)

Cognitive science depends on abstractions made from the complex reality of human behaviour. Cognitive scientists typically wish the abstractions in their theories to be universals, but seldom attend to the ontology of universals. Two sorts of universal, resulting from Galilean abstraction and materialist abstraction respectively, are available in the philosophical literature: the abstract universal—the one-over-many universal—is the universal conventionally employed by cognitive scientists; in contrast, a concrete universal is a material entity that can appear within the set of entities it (...) describes, of which it represents the essential, paradigmatic case. The potential role of concrete universals in cognitive science is discussed. (shrink)

The use of mathematics in economics has been widely discussed. The philosophical discussion on what mathematics is remains unsettled on why it can be applied to the study of the real world. We propose to get back to some philosophical conceptions that lead to a language-like role for the mathematical analysis of economic phenomena and present some problems of interest that can be better examined in this light. Category theory provides the appropriate tools for these analytical approach.

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological com¬position. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this category-theoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis and his followers (...) regarded as unsurmountable. As a concrete example of structural universals groups are considered in some detail. (shrink)

A cluster of similar trends emerging in separate fields of science and philosophy points to new opportunities to apply biosemiotic ideas as tools for conceptual integration in theoretical biology. I characterize these developments as the outcome of a “relational turn” in these disciplines. They signal a shift of attention away from objects and things and towards relational structures and processes. Increasingly sophisticated research technologies of molecular biology have generated an enormous quantity of experimental data, sparking a need for relational approaches (...) that could help to find recurrent patterns in the mass of data. Earlier conceptions of relational biology and cybernetics, once deemed too abstract and speculative, are now resurrected and applied by means of new computational and simulation tools. I think this receptivity should be extended to incorporate nets of semiotic relations as heuristic guides for discerning global patterns of interactions in living systems. In this article I review aspects of systems biology and new directions in evolutionary theory, focusing on the role of circular and downward causation in relational structures and dynamical networks. I also indicate promising avenues of integration of some ideas of biosemiotics with those emerging from these new currents in biology. Relational developments in biology bear a telling similarity to a parallel relational turn presently manifest in the philosophy of science, rooted in the philosophy of physics and mathematics and in different varieties of structural and informational realism. The recognition of the relational nature of reality within these disciplines entails a tacit repudiation of nominalistic biases in science that have hindered the reception of semitiotic conceptions in biology. In previous investigations I explored connections between two kinds of relational structures: the networks of self-referential circular loops that appear pervasively in living systems, and the triadic relational structures that Peircean semiotics places at the basis of all semiotic transactions. Current relational views in the sciences seem oblivious to the difference between dyadic and triadic relations. Incorporating this essential distinction from biosemiotics into other fields could be a first step in seizing the opportunities opened by the relational turn for a renewal of biology and of natural philosophy in general, across disciplinary boundaries. (shrink)

Emergent phenomena are quite interesting and amazing, but they present two main scientific obstacles: to be rationally understood and to be mathematically modelled. In this paper we propose a powerful mathematical tool for modelling emergent phenomena by applying category theory. Furthermore, since great part of biological phenomena are emergent, we present an essay of how to access an emergence from observational data. In the mathematical perspective, we utilize constructs (categories whose objects are structured sets), their operations and their corresponding generalized (...) underlying functor (which are not necessarily faithful) to define emergence. From this definition, we elaborate several results concerning homomorphism between emergences, representability, pull-back, push-out, equalizer, product and co-product of emergences among other results. After we have presented such mathematical model, we utilize a hierarchical structure as example—from molecules to a flatworm—, in order to understand the relation between biological systems and its underlying emergence in a hierarchical model. (shrink)