Psychological Validity of Schematic Proofs
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.
KeywordsRecursive Function Logical Theory Mathematical Induction Schematic Argument Correct Proof
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- 3.Sundholm, B.: A Survey of the Omega Rule. PhD thesis, University of Oxford, Oxford, UK (1983)Google Scholar
- 4.Penrose, R.: Mathematical intelligence. In: Khalfa, J. (ed.) What is Intelligence?, Cambridge, UK, The Darwin College Lectures, pp. 107–136. Cambridge University Press, Cambridge (1994)Google Scholar
- 7.Gamow, G.: One two three.. infinity: Facts & Speculations of Science. Dover Publications, New York (1988)Google Scholar
- 10.Hilbert, D.: Grundlagen der Geometrie. Teubner, Stuttgart (1899); English translation ’Foundations of Geometry’ published in 1902, by Open Court, ChicagoGoogle Scholar