Related papers: Objective and Subjective Solomonoff Probabilities …
We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
A "geometric" intepretation of probability is proposed, modelled on the treatment of tense in 4-dimensional spacetime. It is applied to Everett's approach to quantum mechanics, as formulated in terms of consistent histories. Standard…
The problem of interpreting quantum theory on a large (e.g. cosmological) scale has been commonly conceived as a search for objective reality in a framework that is fundamentally probabilistic. The Everett programme attempts to evade the…
Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…
The concept of probability was prominent in the original foundations of quantum mechanics, and continues to be so today. Indeed, the controversies regarding objective and subjective interpretations of probability have again become active. I…
We review the Consistent Amplitude approach to Quantum Theory and argue that quantum probabilities are explicitly Bayesian. In this approach amplitudes are tools for inference. They codify objective information about how complicated…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
QBism is currently one of the most widely discussed 'subjective' interpretations of quantum mechanics. Its key move is to say that quantum probabilities are personalist Bayesian probabilities and that the quantum state represents subjective…
Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett's seminal idea is that all possible definite futures on the pointer…
It is often objected that the Everett interpretation of QM cannot make sense of quantum probabilities, in one or both of two ways: either it can't make sense of probability at all, or it can't explain why probability should be governed by…
This paper presents formulae that can solve various seemingly hopeless philosophical conundrums. We discuss the simulation argument, teleportation, mind-uploading, the rationality of utilitarianism, and the ethics of exploiting artificial…
An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented…
Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical…
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…
Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several…
We reminisce and discuss applications of algorithmic probability to a wide range of problems in artificial intelligence, philosophy and technological society. We propose that Solomonoff has effectively axiomatized the field of artificial…
In this paper we attempt to analyze the concept of quantum probability within quantum computation and quantum computational logic. While the subjectivist interpretation of quantum probability explains it as a reliable predictive tool for an…
We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…