On the Constructions of Pure Numbers: An Epistemic-Constructivist Analysis

Date

2023-3-15

Author

Birgül, Osman Gazi

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The dissertation aims at explaining the set-theoretical construction processes of pure numbers by laying out the epistemological, cognitive, and linguistic aspects of the constructions from the perspective of epistemic constructivism. To achieve its aim, the dissertation consists of two main chapters. The first main chapter sheds light on Cantor’s notion of set and the membership relation. Explaining the reasons why human reason is vulnerable to paradoxes, the chapter shows that the epistemic-constructivist analysis eliminates the logical and semantic paradoxes. The chapter further identifies sets with a special type of concept and elaborates on the extensional identity of sets and of concepts. The second main chapter applies the analyses of the first main chapter to the explanation of the set-theoretical constructions of pure numbers, beginning with an explanation on the construction of 0 by analyzing the empty set axiom in Zermelo-Fraenkel model of set theory. The chapter further provides explanations for the constructions of 1, 2, and the higher numbers by appealing to linguistic tools such as mention and use. The chapter finally explains the constructions of the transfinite ordinal and cardinal numbers by appealing to some abilities such as higher-order thinking and associative abilities. The dissertation concludes that the set-theoretical constructions of pure numbers can be explained in a paradox-free way and on epistemological, cognitive, and linguistic grounds, where there is no distinction between the knowledge of the construct-how and the knowledge of the construct-that of pure numbers.

Subject Keywords

Epistemic Constructivism, Pure Numbers, Set Theory, Cantor, Transfinite Numbers

URI

https://hdl.handle.net/11511/103098

Collections

Graduate School of Social Sciences, Thesis