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Indeterminism in physics and intuitionistic mathematics.

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Summary
This summary is machine-generated.

Standard mathematics may limit physics theories by excluding indeterminism and the passage of time. Intuitionistic mathematics offers a potential solution for a more dynamic, information-creating scientific worldview.

Keywords:
Foundation of mathematicsIndeterminismIntuitionism

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Area of Science:

  • Physics
  • Philosophy of Science
  • Mathematical Logic

Background:

  • Most physical theories are deterministic, contrasting with quantum mechanics and its measurement problem.
  • The limitations of standard mathematics in representing indeterminism and temporal information flow are highlighted.
  • Scientific determinism might be an artifact of timeless mathematical frameworks.

Purpose of the Study:

  • To explore the hypothesis that standard mathematical language limits scientific theories by excluding indeterminism.
  • To investigate the development of an alternative mathematical language compatible with indeterminism and the passage of time.
  • To propose intuitionistic mathematics as a suitable framework for a dynamic, information-generating worldview.

Main Methods:

  • Conceptual analysis of determinism in physics and limitations of standard mathematics.
  • Exploration of intuitionistic mathematics as an alternative formal system.
  • Illustrative examples demonstrating the application of intuitionistic mathematics in simple terms.

Main Results:

  • Identified a potential link between the timeless nature of standard mathematics and perceived scientific determinism.
  • Proposed intuitionistic mathematics as a viable alternative for modeling indeterministic processes.
  • Demonstrated the potential of intuitionistic mathematics to incorporate the creation of new information over time.

Conclusions:

  • The inability of standard mathematics to represent indeterminism may contribute to the measurement problem in quantum mechanics.
  • Intuitionistic mathematics offers a powerful and compatible alternative for describing a universe where new information is continuously created.
  • Adopting intuitionistic mathematics could lead to a more accurate representation of physical reality, including temporal dynamics and quantum phenomena.