Petrification in Contemporary Set Theory: The Multiverse and the Later Wittgenstein

Area of Science:

• Philosophy of Mathematics
• Set Theory

Background:

• Wittgenstein's concept of petrification offers a novel lens for mathematical phenomena.
• Existing mathematical philosophies like formalism have limitations, particularly with basic examples.
• Disagreements persist regarding the absolute undecidability of the Continuum Hypothesis (CH).

Purpose of the Study:

• To apply Wittgenstein's petrification concept to advanced mathematics, potentially surpassing current theories.
• To analyze the absolute undecidability of CH using petrification and hinge epistemology.
• To re-evaluate Joel David Hamkins' arguments on set theory disagreements.

Main Methods:

• Applying Wittgenstein's petrification concept to advanced mathematical phenomena.
• Analyzing the Continuum Hypothesis (CH) undecidability through petrification and hinge epistemology.
• Examining normative practices and disagreements within contemporary set theory.

Main Results:

• Wittgenstein's petrification provides a valuable framework for understanding advanced mathematical concepts.
• The construction of models for the Continuum Hypothesis (CH) has become a normative demand for undecidability.
• Disagreements in set theory stem from non-universal normative hinges, refining existing arguments.

Conclusions:

• Petrification offers a powerful explanatory tool in the philosophy of mathematics.
• The normative force of model-construction practices in set theory contributes to the perceived undecidability of CH.
• Understanding normative hinges is crucial for resolving disagreements in contemporary set theory.