Bacelar Valente, Mario (2020) On the formal justification of informal proofs. [Preprint]
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Abstract
When modeling the informal proofs of Euclid’s Elements using the sound logical system E, we go from proofs seen as somewhat nonrigorous – even having gaps to be filled – to rigorous proofs. According to the ‘standard view’, the correctness of an informal proof is underwritten by the existence of a corresponding formal derivation. However, metalogic grounds the soundness of the logical system E, and proofs in metalogic are not like formal proofs and look suspiciously like informal proofs. In our view, they are informal proofs. This brings about what we are calling here the groundedness problem: how can we show with certainty that our metalogical proofs are correct and sustain our logical system? According to the ‘standard view’, we cannot. In this way, we would have to doubt the soundness of the formal system E. This in turn might lead us to doubt the justification of Euclidean informal proofs in terms of the corresponding formal proofs in E.
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| Item Type: | Preprint | ||||||
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| Keywords: | Euclidean proof; metalogic; formal proof; informal proof; mathematical proof; metatheorems | ||||||
| Subjects: | Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics |
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| Depositing User: | mario bacelar valente | ||||||
| Date Deposited: | 12 May 2021 16:38 | ||||||
| Last Modified: | 12 May 2021 16:38 | ||||||
| Item ID: | 19031 | ||||||
| Subjects: | Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics |
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| Date: | 2020 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/19031 |
Available Versions of this Item
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Informal and formal proofs, metalogic, and the groundedness problem. (deposited 17 Aug 2020 14:12)
- On the formal justification of informal proofs. (deposited 12 May 2021 16:38) [Currently Displayed]
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