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## A theory of physical probability

It is now common to hold that causes do not always (and perhaps never) determine their

effects, and indeed theories of "probabilistic causation" abound. The basic idea of these

theories is that C causes E just in case C and E both occur, and the chance of E would have

been lower than it is had C not occurred. The problems with these accounts are that (i) the

notion of chance remains primitive, and (ii) this account of causation does not coincide with the

intuitive notion of causation as ontological support.

Turning things around, I offer an analysis of chance in terms of causation, called the

causal theory of chance. The chance of an event E is the degree to which it is determined by its

causes. Thus chance events have full causal pedigrees, just like determined events; they are not

"events from nowhere". I hold that, for stochastic as well as for deterministic processes, the

actual history of a system is caused by its dynamical properties (represented by the lagrangian)

and the boundary condition. A system is stochastic if (a description of) the actual history is not

fully determined by maximal knowledge of these causes, i.e. it is not logically entailed by them.

If chance involves partial determination, and determination is logical entailment, then

there must be such a thing as partial entailment, or logical probability. To make the notion of

logical probability plausible, in the face of current opposition to it, I offer a new account of

logical probability which meets objections levelled at the previous accounts of Keynes and

Carnap.

The causal theory of chance, unlike its competitors, satisfies all of the following criteria:

(i) Chance is defined for single events.

(ii) Chance supervenes on the physical properties of the system in question.

(iii) Chance is a probability function, i.e. a normalised measure.

(iv) Knowledge of the chance of an event warrants a numerically equal degree of belief, i.e.

Miller's Principle can be derived within the theory.

(v) Chance is empirically accessible, within any given range of error, by measuring relative

frequencies.

(vi) With an additional assumption, the theory entails Reichenbach's Common Cause Principle

(CCP).

(vii) The theory enables us to make sense of probabilities in quantum mechanics.

The assumption used to prove the CCP is that the state of a system represents complete

information, so that the state of a composite system "factorises" into a logical conjunction of

states for the sub-systems. To make sense of quantum mechanics, particularly the EPR

experiment, we drop this assumption. In this case, the EPR criterion of reality is false. It states

that if an event E is predictable, and locally caused, then it is locally predictable. This fails

when maximal information about a pair of systems does not factorise, leading to a non-locality

of knowledge. / Arts, Faculty of / Philosophy, Department of / Graduate

Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/9890 |

Date | 05 1900 |

Creators | Johns, Richard |

Source Sets | University of British Columbia |

Language | English |

Detected Language | English |

Type | Text, Thesis/Dissertation |

Format | 14961361 bytes, application/pdf |

Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |

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