Proof<i>vs</i>Truth in Mathematics

Murawski, Roman

doi:10.2478/sh-2020-0025

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…Defining some representation of truth is important to our understanding of complexity, though this has been a question mathematics and philosophy have struggled with for some time [5].…”

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confidence: 99%

Comment in Reply to "On the complexity of extending the convergence region for Traub’s method"

Williams¹

2021

Preprint

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This comment is in reply to the paper “On the complexity of extending the convergence region for Traub’s method” [1]. In complexity science, from the mathematical perspective, discussions of complexity often concern algorithmic complexity such as in the paper responded to here [2]. But this is only one of the kinds of complexity that exists even in the mathematical domain. There is also the complexity in the behavior of a system of equations; there is the complexity of the reasoning or algorithm required to understand a system of equations (“understand” interpreted here as defining the problem needing to be solved); and, as mentioned, there is the complexity of the reasoning or algorithm required to solve a system of equations.

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“…Defining some representation of truth is important to our understanding of complexity, though this has been a question mathematics and philosophy have struggled with for some time [5].…”

mentioning

confidence: 99%

Comment in Reply to "On the complexity of extending the convergence region for Traub’s method"

Williams¹

2021

Preprint

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The Provability-Truth Relation in Formal Languages in Terms of Gödel's Incompleteness Theorems

TAŞTAN

2022

MetaZihin: Yapay Zeka Ve Zihin Felsefesi Dergisi

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In this article, we try to show the limits of formalism based on Gödel's incompleteness theorems. The most fundamental debate at the our work is shaped by the tension between provability and truth. The studies that started with Frege's project to reduce arithmetic to logic and continued with Hilbert's formalism project aimed to establish a solid foundation for mathematics. But when Gödel proved that some propositions cannot be decided formally, the containment of Hilbert's formalism project took a hit. On the other hand, Gödel's theorems started the discussion of provability and truth, as it showed that there were propositions whose proof could not be given, but whose truth was mentioned. In our study, we aim to illuminate the argument between provability and truth in a formal language based on Gödel's theorems.

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ProofvsTruth in Mathematics

Cited by 2 publications

References 21 publications

Comment in Reply to "On the complexity of extending the convergence region for Traub’s method"

Comment in Reply to "On the complexity of extending the convergence region for Traub’s method"

The Provability-Truth Relation in Formal Languages in Terms of Gödel's Incompleteness Theorems

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