Bacelar Valente, Mario
(0021)
Mathematical proof as (guided) intentional reasoning.
[Preprint]

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Abstract
In this paper, 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 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.
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