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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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, 493504. The main results were presented at the 25th Conference Applications of Logic in Philosophy and the Foundations of Mathematics, see http://applicationsoflogic.uni.wroc.pl/XXVKonferencjaZastosowaniaLogikiwFilozofiiiPodstawachMatematyki. We assume that the current mathematical knowledge is a finite set of statements which is timedependent. 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 nontrivial 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  

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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://applicationsoflogic.uni.wroc.pl/XXVKonfe...  
Subjects:  Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics 

Date:  2 August 2023  
URI:  https://philsciarchive.pitt.edu/id/eprint/22363 
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The predicate of the current mathematical knowledge increases the scope of mathematics what distinguishes mathematics from other fields of study. (deposited 21 Jul 2023 14:58)

The predicate of the current mathematical knowledge substantially increases the constructive mathematics what is impossible for the empirical sciences. (deposited 28 Jul 2023 17:55)
 The predicate of the current mathematical knowledge substantially increases the constructive mathematics what is impossible for any empirical science. (deposited 02 Aug 2023 15:19) [Currently Displayed]

The predicate of the current mathematical knowledge substantially increases the constructive mathematics what is impossible for the empirical sciences. (deposited 28 Jul 2023 17:55)
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