Gödelian Platonism

Teppei Hayashi

The primary objective of this thesis is to clarify the philosophical view about mathematics of the great 20th century logician/mathematician Kurt G¨odel. G¨odel’s philosophical view of mathematics was well known during his lifetime. His view of mathematics is usually called mathematical realism or mathematical Platonism according to which mathematics is about objective existence. G¨odel’s view of mathematics — G¨odelian Platonism — had long been often regarded by many as na¨ıve and amateurish. However, the publication of G¨odel’s Collected Works (1986-2003) sheds new light on his thought. In this paper, based on new insights and documents which have become available through the publication of Collected Works, I will try to show that G¨odelian Platonism is not implausible, as some philosophers still think. To show this, I will concentrate on two principal characteristics of G¨odelian Platonism: conceptual realism and mathematical intuition. In the first chapter, I will review how G¨odelian Platonism has been interpreted. This will give readers a broad idea about G¨odelian Platonism and make clear the points which I will discuss in greater details in the later chapters. In the second chapter, I will deal with an important aspect of G¨odelian Platonism: conceptual realism. G¨odelian Platonism had long been thought as a kind of realism simpliciter, that is, the view that admits the objective existence of abstract objects like numbers, sets, and so forth. However, besides having believed in the existence of abstract objects themselves, G¨odel seems to have also believed in the existence of concepts of abstract objects. This conception of G¨odelian Platonism sheds lights on how we should understand G¨odel’s philosophy of mathematics. In the third chapter, I will discuss another important aspects of G¨odelian Platonism: intuition. This might be the most notorious aspect of G¨odelian Platonism because it had been thought of as a kind of perception through which we can directly access mathematical objects. I will try to demystify this aspect of G¨odelian Platonism.

Gödelian Platonism

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