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This study clarifies logical and scientific strength in epistemology, proposing a new interpretability-based definition for logical strength and viewing scientific strength as a specific instance. This framework aids in comparing logical systems and mathematical theories.

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Area of Science:

  • Epistemology of logic
  • Philosophy of science

Background:

  • The concept of 'strength' is central to current discussions on abductivism in the epistemology of logic.
  • Existing characterizations of logical and scientific strength have limitations.

Purpose of the Study:

  • To distinguish between logical and scientific strength.
  • To propose a novel framework for understanding logical strength in terms of interpretability.
  • To apply these concepts to compare logical systems and mathematical theories.

Main Methods:

  • Distinguishing logical and scientific strength based on existing literature.
  • Defining logical strength via interpretability.
  • Analyzing scientific strength as a specific case of logical strength.
  • Applying the refined notions to comparative analysis.

Main Results:

  • A clear distinction is drawn between logical and scientific strength.
  • Logical strength is redefined using interpretability.
  • Scientific strength is established as a specialized form of logical strength.
  • The framework is successfully applied to compare logics and mathematical theories.

Conclusions:

  • The proposed interpretability-based definition offers a more robust understanding of logical strength.
  • This framework provides novel insights into the relationship between logical systems and mathematical theories.
  • The study advances the epistemological analysis of logical and scientific strength.