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The correctness of reasoning, logical models, and the faithfulness problem

Bacelar Valente, Mario (2022) The correctness of reasoning, logical models, and the faithfulness problem. Principia: an international journal of epistemology, 26 (3). pp. 429-447.

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Abstract

When adopting a sound logical system, reasonings made within this system are correct. The situation with reasonings expressed, at least in part, with natural language is much more ambiguous. One way to be certain of the correctness of these reasonings is to provide a logical model of them. To conclude that a reasoning process is correct we need the logical model to be faithful to the reasoning. In this case, the reasoning inherits, so to speak, the correctness of the logical model. There is a weak link in this procedure, which we call the faithfulness problem: how do we decide that
the logical model is faithful to the reasoning that it is supposed to model? That is an issue external to logic, and we do not have rigorous formal methods to make the decision. The purpose of this paper is to expose the faithfulness problem (not to solve it). For that purpose, we will consider two examples, one from the geometrical reasoning in Euclid’s Elements and the other from a study on deductive reasoning in the psychology of reasoning.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Bacelar Valente, Mario
Keywords: Euclidean proof; formal proof; deductive reasoning; suppression task
Subjects: Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Proof
Specific Sciences > Psychology > Judgment and Decision Making
Specific Sciences > Mathematics
Specific Sciences > Psychology
Depositing User: mario bacelar valente
Date Deposited: 15 Dec 2022 18:32
Last Modified: 15 Dec 2022 18:32
Item ID: 21562
Journal or Publication Title: Principia: an international journal of epistemology
Subjects: Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Proof
Specific Sciences > Psychology > Judgment and Decision Making
Specific Sciences > Mathematics
Specific Sciences > Psychology
Date: 13 December 2022
Page Range: pp. 429-447
Volume: 26
Number: 3
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21562

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