Bacelar Valente, Mario (2020) Informal and formal proofs, metalogic, and the groundedness problem. [Preprint]

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Abstract

When modeling informal proofs like that of Euclid’s Elements using a sound logical system, we go from proofs seen as somewhat unrigorous – even having gaps to be filled – to rigorous proofs. However, metalogic grounds the soundness of our logical system, and proofs in metalogic are not like formal proofs and look suspiciously like the informal proofs. This brings about what I am calling here the groundedness problem: how can we decide with certainty that our metalogical proofs are rigorous and sustain our logical system? In this paper, I will expose this problem. I will not try to solve it here.

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Item Type:	Preprint
Creators:	Creators Email ORCID Bacelar Valente, Mario
Keywords:	logic, metalogic, proof of soundness, Euclid, Elements, Euclidean proof
Subjects:	Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Proof Specific Sciences > Psychology > Judgment and Decision Making Specific Sciences > Psychology
Depositing User:	mario bacelar valente
Date Deposited:	17 Aug 2020 14:12
Last Modified:	17 Aug 2020 14:12
Item ID:	17994
Subjects:	Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Proof Specific Sciences > Psychology > Judgment and Decision Making Specific Sciences > Psychology
Date:	15 August 2020
URI:	https://philsci-archive.pitt.edu/id/eprint/17994

Available Versions of this Item

• Informal and formal proofs, metalogic, and the groundedness problem. (deposited 17 Aug 2020 14:12) [Currently Displayed]
  • On the formal justification of informal proofs. (deposited 12 May 2021 16:38)

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