The predicate of the current mathematical knowledge substantially increases the constructive mathematics what is impossible for any empirical science

Tyszka, Apoloniusz (2023) The predicate of the current mathematical knowledge substantially increases the constructive mathematics what is impossible for any empirical science. [Preprint]

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Official URL: http://applications-of-logic.uni.wroc.pl/XXV-Konfe...

Abstract

This is a shortened and revised version of the article: A. Tyszka, Statements and open problems on decidable sets X⊆N, Pi Mu Epsilon J. 15 (2023), no. 8, 493-504. The main results were presented at the 25th Conference Applications of Logic in Philosophy and the Foundations of Mathematics, see http://applications-of-logic.uni.wroc.pl/XXV-Konferencja-Zastosowania-Logiki-w-Filozofii-i-Podstawach-Matematyki. We assume that the current mathematical knowledge is a finite set of statements which is time-dependent. In every branch of mathematics, the set of all knowable truths is the set of all theorems. This set exists independently of our current scientific knowledge. Nicolas D. Goodman observed in Synthese that epistemic notions increase the understanding of mathematics without changing its content. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivial statements on decidable sets X⊆N that belong to constructive mathematics and refer to the current mathematical knowledge on X. This and the next sentence justify the article title. For any empirical science, we can identify the current knowledge with that science because truths from the empirical sciences are not necessary truths but working models of truth from a particular context.

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Item Type:

Preprint

Creators:

Creators	Email	ORCID
Tyszka, Apoloniusz	rttyszka@cyf-kr.edu.pl	0000-0002-2770-5495

Keywords:

composite numbers of the form 2^{2^n}+1, constructive algorithms, current mathematical knowledge, decidable sets X⊆N, epistemic notions, informal notions, known algorithms, known elements of N, primes of the form n^2+1, primes of the form n!+1, primes of the form 2^{2^n}+1

Subjects:

Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics

Depositing User:

Apoloniusz Tyszka

Date Deposited:

02 Aug 2023 15:19

Last Modified:

02 Aug 2023 15:19

Item ID:

22363

Official URL:

http://applications-of-logic.uni.wroc.pl/XXV-Konfe...