PhilSci Archive

Informal and formal proofs, metalogic, and the groundedness problem

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

[img]
Preview
Text
Informal and formal proofs, metalogic, and the groundedness problem.pdf

Download (288kB) | Preview

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.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Creators:
CreatorsEmailORCID
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: http://philsci-archive.pitt.edu/id/eprint/17994

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item