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Meaning and reference from a probabilistic point of view.

Jacob Feldman1, Lee-Sun Choi2

  • 1Dept. of Psychology, Center for Cognitive Science, Rutgers University, United States.

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Bayesian models of cognition require probabilistic interpretations of reality. This study introduces translation uncertainty to quantify model discrepancies, linking observer concordance to this uncertainty for a probabilistic semantics.

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Bayesian cognitive scienceInformation theoryKullback-Leibler divergenceMeaningReference

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Area of Science:

  • Cognitive Science
  • Epistemology
  • Metaphysics

Background:

  • Bayesian models of cognition necessitate reframing epistemological and metaphysical questions probabilistically.
  • Subjective probability assumes distinct observers hold unique, potentially non-true, probabilistic world models.

Purpose of the Study:

  • To reframe traditional epistemological and metaphysical questions within a subjective Bayesian framework.
  • To define the meaning, reference, and truth conditions of terms in probabilistic theories.
  • To introduce information-theoretic tools for analyzing observer model discrepancies.

Main Methods:

  • Utilizing a subjective (Bayesian) conception of probability.
  • Employing information theory to analyze observer models.
  • Introducing 'translation uncertainty' as a generalized Kullback-Leibler divergence.

Main Results:

  • Derived information-theoretic relationships between Bayesian observers.
  • Demonstrated that observer model concordance depends on translation uncertainty.
  • Established a quantitative link between model discrepancy and shared understanding.

Conclusions:

  • The proposed framework offers a pathway to a semantics for a probabilistic language of thought.
  • Translation uncertainty quantifies discrepancies between subjective probabilistic models.
  • This approach provides a rigorous method for comparing and understanding differing observer perspectives.