A CRITICAL APPRAISAL OF INTUITIONIST FOUNDATIONS  OF MATHEMATICS

Etorobong Godwin  Akpan; Remigius Achinike  Obah

doi:10.17605/OSF.IO/7C5JW

Etorobong Godwin Akpan Department of Philosophy University of Port Harcourt, Port Harcourt, Rivers State, Nigeria
Remigius Achinike Obah Department of Philosophy University of Port Harcourt, Port Harcourt, Rivers State, Nigeria

DOI: https://doi.org/10.17605/OSF.IO/7C5JW

Keywords: Intuitionism, Finitism, Spread, Species, Continuum, Twoity

Abstract

The paper is a study of the intuitionist foundations of mathematic. It is work in the epistemology of mathematics. Hence, it is warranted by the need to ascertain the epistemic status of mathematical statements. Are they synthetic or a priori or synthetic a priori statements, as the case may be? The objective of the study is to evaluate the responses of intuitionist to these questions, so as to ascertain whether they could set to rest the controversies in the philosophy of mathematics. To achieve this objective, the method of content analysis has been adopted. This method is consistent with a qualitative research design. The major text selected for analysis are works of intuitionist mathematicians and other philosophers of mathematics. It has been submitted in the study, that although intuitionism is known for its proposal of the epistemology of subjective construction of mathematical entities, its system is inconsistent because of its dependence on ontological pluralism that leads to crude empiricism and the epistemological crisis of object absolutism.

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