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

Preview

Text philsci-erkennen.pdf Download (661kB) | Preview

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.

---

Export/Citation:

EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL

Social Networking:

Share |

---

Item Type:	Preprint
Creators:	Creators Email ORCID Dentamaro, Dario dario.dentamaro@stud.unifi.it Loregian, Fosco fosco.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.pitt.edu/id/eprint/18519

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item