In principle determination of generic priors

TL;DR

This paper extends probability theory using propositional logic and symmetry principles to allow for the determination of any probability, removing the need for the principle of indifference and enabling flexible assumptions about possibility spaces.

Contribution

It introduces a method to determine generic priors through propositional logic and symmetry, eliminating the principle of indifference and accommodating unknown possibility space sizes.

Findings

Probability can be determined using propositional logic and symmetry.

The principle of indifference becomes combinatoric, not fundamental.

Assumptions about possibility spaces can be made without specifying their size.

Abstract

Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry from propositional logic. It is shown how the notions of `possibility' and `property' may be suffciently represented in propositional logic such that 1) the principle of indifference drops out and becomes essentially combinatoric in nature and 2) one may appropriately represent assumptions where one assumes there is a space of possibilities but does not assume the size of the space.