Abstract

I consider exactly what is involved in a solution to the probability problem of the Everett interpretation, in the light of recent work on applying considerations from decision theory to that problem. I suggest an overall framework for understanding probability in a physical theory, and conclude that this framework, when applied to the Everett interpretation, yields the result that that interpretation satisfactorily solves the measurement problem.

  1. Introduction

  2. What is probability?

    2.1Objective probability and the Principal Principle

    2.2Three ways of satisfying the functional definition

    2.3Cautious functionalism

    2.4Is the functional definition complete?

  3. The Everett interpretation and subjective uncertainty

    3.1Interpreting quantum mechanics

    3.2The need for subjective uncertainty

    3.3Saunders' argument for subjective uncertainty

    3.4Objections to Saunders' argument

    3.5Subjective uncertainty again: arguments from interpretative charity

    3.6Quantum weights and the functional definition of probability

  4. Rejecting subjective uncertainty

    4.1The fission program

    4.2Against the fission program

  5. Justifying the axioms of decision theory

    5.1The primitive status of the decision-theoretic axioms

    5.2Holistic scepticism

    5.3The role of an explanation of decision theory

  6. Conclusion

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