Mathematical proofs and metareasoning

Bacelar Valente, Mario (2022) Mathematical proofs and metareasoning. [Preprint]

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Abstract

In this paper, informal mathematical proofs are conceived as a form of (guided) intentional reasoning. In a proof, we start with a sentence – the premise; this sentence is followed by another, the conclusion of an inferential step. Guided by the text, we produce an autonomous reasoning process that enables us to arrive at the conclusion from the premise. That reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling of correctness, which makes us feel-know that the reasoning is correct. Guided by the proof, we go through small inferential steps, one at a time. In each of these cycles, we produce an autonomous reasoning process that “links” the premise to the conclusion. This enables, due to our metareasoning, to associate to the verbal conclusion a feeling of correctness. In each step/cycle of the proof, as a (guided) intentional reasoning process, we have a feeling of correctness. Overall, we reach a feeling of correctness for the whole proof. The main purpose of this work is to suggest that this approach allows us to address the issues of how does a proof functions, for us, as an enabler to ascertain the correctness of its argument, and how do we ascertain this correctness.

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Item Type: Preprint
Creators:
CreatorsEmailORCID
Bacelar Valente, Mario
Keywords: mathematical proof; intentional reasoning; metareasoning; feeling of correctness
Subjects: Specific Sciences > Cognitive Science
Specific Sciences > Mathematics
Depositing User: mario bacelar valente
Date Deposited: 06 Mar 2022 20:25
Item ID: 20236
Subjects: Specific Sciences > Cognitive Science
Specific Sciences > Mathematics
Date: 22 February 2022
URI: https://philsci-archive.pitt.edu/id/eprint/20236