# Contributions to the Formal Theory of Probability

@inproceedings{Popper1994ContributionsTT, title={Contributions to the Formal Theory of Probability}, author={Karl Raimund Sir Popper and David W. Miller}, year={1994} }

Popper (1959), Appendices *iv and *v) has given several axiom systems for probability that ensure, without further assumptions, that the domain of interpretation can be reduced to a Boolean algebra. This paper presents axiom systems for subtheories of probability theory that characterize in the same way lower semilattices (Section 1) and distributive lattices (Section 2). Section 1 gives a new (metamathematical) derivation of the laws of semilattices; and Section 2 one or two surprising… Expand

#### 7 Citations

Probabilistic Substitutivity at a Reduced Price

- Philosophy
- 2012

One of the many intriguing features of the axiomatic systems of probability investigated in Popper (1959), appendices _iv, _v, is the different status of the two arguments of the probability functor… Expand

More Triviality

- Computer Science
- J. Philos. Log.
- 1999

It is shown that even very weak axiom systems have only a very restricted set of models satisfying a natural generalisation of Adams' thesis, thereby casting severe doubt on the possibility of developing a non-Boolean semantics for conditionals consistent with it. Expand

Adams Conditionals and Non-Monotonic Probabilities

- Mathematics, Computer Science
- J. Log. Lang. Inf.
- 2006

This paper explores the possibility of accommodating Adams' thesis in systems of non-monotonic probability of varying strength, and shows that such systems impose many familiar lattice theoretic properties on their models as well as yielding interesting logics of conditionals, but that a standard complementation operation cannot be defined within them, on pain of collapsing probability into bivalence. Expand

Conditional Probability and Dutch Books

- Mathematics
- Philosophy of Science
- 2000

There is no set Δ of probability axioms that meets the following three desiderata: (1) Δ is vindicated by a Dutch book theorem; (2) Δ does not imply regularity (and thus allows, among other things,… Expand

Can Bayes' Rule be Justified by Cognitive Rationality Principles?

- Mathematics
- 2002

The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and… Expand

Can Quantum Mechanics be shown to be Incomplete in Principle

- Mathematics
- 2006

The paper presents an argument for the incompleteness in principle of quantum mechanics. I introduce four principles (P0–P3) concerning the interpretation of probability, in general and in quantum… Expand

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