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.
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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.
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Item Type: | Other | ||||||||||||
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Keywords: | functions, set theory, category theory | ||||||||||||
Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic |
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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 |
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Date: | 16 December 2019 | ||||||||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/16668 |
Available Versions of this Item
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Follow the Flow: sets, relations, and categories as special cases of functions with no domain. (deposited 04 Nov 2019 19:56)
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Follow the Flow: sets, relations, and categories as special cases of functions with no domain. (deposited 04 Dec 2019 17:08)
- Follow the Flow: sets, relations, and categories as special cases of functions with no domain. (deposited 02 Dec 2019 23:15) [Currently Displayed]
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Follow the Flow: sets, relations, and categories as special cases of functions with no domain. (deposited 04 Dec 2019 17:08)
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