Psychological Validity of Schematic Proofs

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Schematic proofs are functions which can produce a proof of a proposition for each value of their parameters. A schematic proof can be constructed by abstracting a general pattern of proof from several examples of a family of proofs. In this paper we examine several interesting aspects of the use of schematic proofs in mathematics. Furthermore, we pose several conjectures about the psychological validity of the use of schematic proofs in mathematics. These conjectures need testing, hence we propose an empirical study which would either support or refute our conjectures. Ultimately, we suggest that schematic proofs are worthy of a closer and more detailed study and investigation.