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Certainty in mathematics: is there a problem? (English)
Philos. Math. Educ. J. 28, 22 p., electronic only (2014).
Summary: Two independent questions about the certainty in mathematics are posed. Is mathematical knowledge known with certainty? Why is the belief in the certainty of mathematical knowledge so widespread and where does it come from? Absolutist claims of the certainty of mathematical knowledge are articulated and critiqued. The contrasting view that mathematical knowledge is known with a certainty circumscribed by the limits of human knowing is proposed, elaborated and defended. In explaining the reasons for beliefs in the certainty of mathematics both cultural historical and individual psychological factors are identified. The cultural historical development of mathematics contributes four factors: 1, the invariance and conservation of number and the reliability of calculation; 2, the emergence of numbers as abstract entities with apparently independent existence; 3, the emergence of proof with its goal of convincing readers of the certainty of mathematical propositions; 4, the engulfment and neutralisation of historically emergent contradictions and uncertainties and their incorporation into the mathematical narrative of certainty. The second source of the beliefs in the certainty of mathematics is the individual development of learners who internalize ideas of invariance, reliability and certainty through their classroom experiences and exposure to cultural factors including these four.
Classification: E20 D20 E50 A30
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