This is the final paper written for my first independent research. As usual, I only post the introduction and the conclusion here. Please feel free to contact me via email (refer to the Home page) if you would like to read some of my arguments in detail or offer any critic.
This paper explores the idea of infinity as both a mathematical concept and a metaphysical concept while seeking unity between the two aspects of infinity under Platonist realism. While addressing relevant substitutes of the classical Platonist view of infinity and considering the contemporary revival of Platonism argued by Kurt Gödel alongside recent developments in Mathematical Logic pioneered by Georg Cantor, this paper rationalises the enduring charm of Platonist realism and argues for its unrivalled elegance in explaining the concept of infinity.
In this paper, I explain the mathematical and metaphysical aspects of infinity and how they may conflict at times. Unifying the two aspects of infinity has been a serious academic interest among mathematicians and philosophers in ages. While this essay does not cover all past unifying accounts at all, it demonstrates several failed accounts and how Platonism, or in particular, Gödel’s version of Platonism can possibly unify the two aspects of infinity and resolve the Zeno paradox.
The myth of infinity remains a growing interest among modern mathematicians, philosophers and theologians. With the development of transfinite mathematics pioneered by Cantor, the concept of infinity has become more intriguing and independent of other branches of mathematics. Meanwhile, Platonism, albeit a very old school of thought in philosophy of mathematics, remains very popular among mathematicians today. Although classical Platonism falls short of demonstrating mathematical infinity, its elegance in its metaphysical commitment is unrivalled. In the recent revival of Platonism, Gödel appeals to human mathematical intuitions in pursuit of mathematical truth and makes up for the shortcomings of classical Platonic realism. He proposes an alternative way of constructing mathematical knowledge besides axiomatisation. With Gödel’s insight, Platonism remains a promising solution to the myth of infinity and, in some sense, pave the stairs to God’ throne.
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