A CRITIQUE OF THE SCHOOLS OF THOUGHT IN PHILOSOPHY OF MATHEMATICS

Resumen

The discovery of paradoxes concerning certain mathematical assumptions in the wake of the twentieth century, posed a serious challenge to the objectivity and certainty of mathematical knowledge. This not only ushered in scepticism in the mathematical discipline, but also gave rise to the profound activity on meta-mathematics geared towards greater research on the foundations of mathematics. Several schools of thought in the Philosophy of mathematics emerging in the sequel, have sought to clarify the foundations and the nature of mathematical knowledge. This paper explores the positions of the five major such schools of thought in the philosophy of Mathematics, namely: Logicism, Intuitionism, Empiricism, Formalism, Psychologism. The paper argues that notwithstanding their relevant contributions in clarifying the foundations of mathematics, none of these schools meets the requirement of rational success in adequately addressing the challenge to the objectivity and certainty of mathematical knowledge, since each is nettled with some identified defects. The paper concludes with the conviction that greater research in this aspect of philosophy of mathematics will yield the required desideratum. The expository and analytic methods of research are adopted in the paper.