PhilSci Archive

Follow the Flow: sets, relations, and categories as special cases of functions with no domain

Sant'Anna, Adonai and Bueno, Otávio and de França, Márcio (2019) Follow the Flow: sets, relations, and categories as special cases of functions with no domain. UNSPECIFIED.

This is the latest version of this item.

[img]
Preview
Text
FlowComplete.pdf

Download (218kB) | Preview
[img]
Preview
Text
FlowComposition.pdf

Download (295kB) | Preview

Abstract

We introduce, develop, and apply a new approach for dealing with the intuitive notion of function, called Flow Theory. Within our framework all functions are monadic and none of them has any domain. Sets, proper classes, categories, functors, and even relations are special cases of functions. In this sense, functions in Flow are not equivalent to functions in ZFC. Nevertheless, we prove both ZFC and Category Theory are naturally immersed within Flow. Besides, our framework provides major advantages as a language for axiomatization of standard mathematical and physical theories. Russell's paradox is avoided without any equivalent to the Separation Scheme. Hierarchies of sets are obtained without any equivalent to the Power Set Axiom. And a clear principle of duality emerges from Flow, in a way which was not anticipated neither by Category Theory nor by standard set theories. Besides, there seems to be within Flow an identification not only with the common practice of doing mathematics (which is usually quite different from the ways proposed by logicians), but even with the common practice of teaching this formal science.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Other
Creators:
CreatorsEmailORCID
Sant'Anna, Adonaiadonai@ufpr.br0000-0003-3425-698X
Bueno, Otáviootaviobueno@me.com0000-0002-0251-3032
de França, Márciomarciopalmares@gmail.com0000-0003-1229-6825
Keywords: functions, set theory, category theory
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Depositing User: Adonai Sant'Anna
Date Deposited: 02 Dec 2019 23:15
Last Modified: 02 Dec 2019 23:15
Item ID: 16668
Official URL: https://quantuminternationalnet.com/
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Date: 16 December 2019
URI: http://philsci-archive.pitt.edu/id/eprint/16668

Available Versions of this Item

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item