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Implementing David Lewis' Principal Principle: A Program for Investigating the Relation between Credence and Chance

Stephen David John

Published Oct 6, 2020• 0 citations
OpenAlex

Abstract

In place of the just-so stories and intuition mongering of analytical metaphysicians, I offer a program for understanding the relationship between credence and chance in quantum physics and show how a version of the program can be implemented with some representation theorems.

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David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. This paper develops an account of how chance works in quantum theory that reveals a connection between credence and quantum chance quite unlike what is envisioned in the philosophical literature: as a theorem of quantum probability, updating a completely additive chance function on a knowledge of chance brings credence into line with chance. The account also suggests a way of construing the Humean supervenience of chance that has the virtue of dissolving some puzzles about the "undermining" of chances. A number of interpretative moves in quantum theory are needed to generate the account of quantum chance on offer here, and they can all be disputed. But engaging in these disputes is part and parcel of naturalized metaphysics, and as such it can be more productive than engaging in the battle of intuitions among analytical metaphysicians about how chance ought to work this and other possible worlds.

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David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. Given the generally accepted updating rule for quantum probabilities, there is a straight forward sense in which the Principal Principle is a theorem of quantum probability theory for any credence function satisfying a suitable additivity requirement. No additional principle of rationality is needed to bring credence into line with objective chance.

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David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. This paper develops an account of how chance works in quantum theory that reveals a connection between credence and quantum chance quite unlike what is envisioned in the philosophical literature: as a theorem of quantum probability, updating a completely additive chance function on a knowledge of chance brings credence into line with chance. The account also suggests a way of construing the Humean supervenience of chance that has the virtue of dissolving some puzzles about the "undermining" of chances. A number of interpretative moves in quantum theory are needed to generate the account of quantum chance on offer here, and they can all be disputed. But engaging in these disputes is part and parcel of naturalized metaphysics, and as such it can be more productive than engaging in the battle of intuitions among analytical metaphysicians about how chance ought to work this and other possible worlds.
David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. Given the generally accepted updating rule for quantum probabilities, there is a straight forward sense in which the Principal Principle is a theorem of quantum probability theory for any credence function satisfying a suitable additivity requirement. No additional principle of rationality is needed to bring credence into line with objective chance.
Abstract This chapter offers a theory of objective chance in the Everettian context, often seen as the main challenge facing EQM. By supplementing diverging EQM with quantum modal realist bridge principles connecting the physics of quantum mechanics with the metaphysics of modality, we obtain a package deal: Indexicalism. Indexicalist objective chance is an essentially self-locating phenomenon: chances are chances of self-location within the multiverse. I provide three arguments for Indexicalism: it establishes the right qualitative connections between chance and possibility, it establishes the right quantitative connection between chance and prediction, and it establishes the right epistemological story about how quantum mechanics is confirmed by empirical evidence. The resulting theory of chance is naturalistic and reductive; fundamental reality is deterministic, but chance arises at the non-fundamental level of Everett-worldbound perspectives. The theory provides unique resources for motivating an Everettian version of Lewis’s Principal Principle, helping to clarify at last the persistently mysterious connection between chance and rational credence.