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Structural theories of truth struggle to express nonstratified defectiveness. Non-contractive theories also face this limitation, particularly when identifying defective sentences with those causing triviality under structural contraction.

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Area of Science:

  • Philosophy of language
  • Mathematical logic
  • Foundations of mathematics

Background:

  • Fully structural theories of truth are often considered limited in expressing nonstratified defectiveness.
  • Recent advancements include non-contractive theories of truth.

Purpose of the Study:

  • To investigate the expressive capabilities of non-contractive theories regarding nonstratified defectiveness.
  • To determine if non-contractive theories overcome limitations of previous structural theories.

Main Methods:

  • Analysis of non-contractive theories within the framework of structural theories of truth.
  • Examination of the consequences of identifying defective sentences with those yielding triviality under structural contraction.

Main Results:

  • Non-contractive theories share the expressive limitation of fully structural theories concerning nonstratified defectiveness.
  • This limitation persists under the condition that defective sentences lead to triviality when structural contraction is applied.

Conclusions:

  • Non-contractive theories, despite recent discussion, do not resolve the issue of expressing nonstratified defectiveness.
  • The expressive limitations are tied to the definition of defective sentences and the principle of structural contraction.