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 categorytheoretic asset stresses the fact that the scope of scientific knowledge is to build ‘meaningful connections’ (i.e. wellbehaved 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 selfduality of the bicategory of profunctors accounts for the fact that theoretical and observational terms can exchange their rôle without substantial changes in the resulting predictivedescriptive 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  

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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:  http://philsciarchive.pitt.edu/id/eprint/18519 
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