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The Genesis of Set Theory Paradoxes

Categories: Logical Science
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About Course

Set theory was created to bring to mathematics the notion of a class. However, a set is not a class. A class is a singular entity without separable parts that represents a concept. A set is instead a collection of (often infinite) members that constitute its separable parts. For example, the tree class is a singular entity without separable parts but the tree set is an infinite collection of trees (including those that have existed in the past and would exist in the future). More precisely, a class is a mental entity that everyone can assimilate in finite time and store in finite space. A set is a physical entity that requires infinite time to assimilate and infinite space to store. Therefore, classes are not sets. However, if we try to reduce classes to sets, then we run into contradictions which are called Set Theory Paradoxes. These paradoxes illustrate that the reduction of a class to a set is false. In this course, we shall discuss the varied problems of such reduction.

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Course Content

The Logical Origins of Set Theory Paradoxes

  • The Problem of Logical Inversions
  • The Is vs. Has Distinction in Set Theory
  • Set Theoretic Reduction of Is to Has
  • The Creation of Set Theory Paradoxes

Understanding the Tripartite Nature of Concepts

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