TL;DR
This paper clarifies the distinction between sets and proper classes by categorizing concepts and explains how misunderstandings of surveyability and definiteness lead to classical set-theoretic paradoxes.
Contribution
It introduces a categorization of concepts and attributes set-theoretic paradoxes to misinterpretations of surveyability versus definiteness.
Findings
Identifies categories of concepts: surveyable, definite, indefinite
Links paradoxes to failure in distinguishing surveyability from definiteness
Provides a framework to resolve classical set-theoretic paradoxes
Abstract
The central focus is on clarifying the distinction between sets and proper classes. To this end we identify several categories of concepts (surveyable, definite, indefinite), and we attribute the classical set theoretic paradoxes to a failure to appreciate the distinction between surveyability and definiteness.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Logic, Reasoning, and Knowledge · Philosophy and Theoretical Science