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Functorial Erkennen

Dentamaro, Dario and Loregian, Fosco (2020) Functorial Erkennen. [Preprint]

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Abstract

We outline a ‘formal theory of scientific theories’ rooted in the theory of profunctors; the category-theoretic asset stresses the fact that the scope of scientific knowledge is to build ‘meaningful connections’ (i.e. well-behaved adjunctions) between a linguistic object (a ‘theoretical category’ T ) and the world W said language ought to describe. Such a world is often unfathomable, and thus we can only resort to a smaller fragment of it in our analysis: this is the ‘observational category’ O ⊆ W. From this we build the category [O op , Set] of all possible displacements of observational terms O. The self-duality of the bicategory of profunctors accounts for the fact that theoretical and observational terms can exchange their rôle without substantial changes in the resulting predictive-descriptive theory; this provides evidence for the idea that their separation is a mere linguistic convention; to every profunctor R linking T and O one can associate an object O ] R T obtained glueing together the two categories and accounting for the mutual relations subsumed by R. Under mild assumptions, such an arrangement of functors, profunctors, and gluings provides a categorical interpretation for the ‘Ramseyfication’ operation, in a very explicit sense: in a scientific theory, if a computation entails a certain behaviour for the system the theory describes, then saturating its theoretical variables with actual observed terms, we obtain the entailment in the world.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Dentamaro, Dariodario.dentamaro@stud.unifi.it
Loregian, Foscofosco.loregian@taltech.ee
Keywords: profunctor, science, hermeneutics
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Depositing User: Dr. Fosco Loregian
Date Deposited: 15 Dec 2020 18:31
Last Modified: 15 Dec 2020 18:31
Item ID: 18519
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Date: 15 December 2020
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/18519

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