On a form of intrinsic optimism in Set Theory
M. Mu\~noz P\'erez
TL;DR
This paper advocates for a form of intrinsic optimism in set theory, aiming to justify G"odel's phenomenological approach as a means to develop new axioms for ZFC to resolve independent problems like CH.
Contribution
It introduces a philosophical framework supporting the development of new axioms based on intrinsic set-theoretic optimism, aligning with G"odel's phenomenological methodology.
Findings
Supports G"odel's phenomenological approach for axiomatic development
Provides a philosophical basis for intrinsic optimism in set theory
Aims to justify new axioms to settle independent statements like CH
Abstract
In this paper we will try to provide a solid form of intrinsic set theoretical optimism. In other words, we will try to vindicate G\"odel's views on phenomenology as a method for arriving at new axioms of ZFC in order to decide independent statements such as CH.
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Taxonomy
TopicsPhilosophy and Theoretical Science · Mathematical and Theoretical Analysis · Free Will and Agency