# A Philosophical Treatise of Universal Induction

@article{Rathmanner2011APT, title={A Philosophical Treatise of Universal Induction}, author={Samuel Rathmanner and Marcus Hutter}, journal={Entropy}, year={2011}, volume={13}, pages={1076-1136} }

Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework… Expand

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#### References

SHOWING 1-10 OF 71 REFERENCES

Probability theory: the logic of science

- 2005

This is a remarkable book by a remarkable scientist. E. T. Jaynes was a physicist, principally theoretical, who found himself driven to spend much of his life advocating, defending and developing a… Expand

An Introduction to Kolmogorov Complexity and Its Applications

- Computer Science, Psychology
- Texts and Monographs in Computer Science
- 1993

The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. Expand

Dutch Bookies and Money Pumps

- Philosophy
- 1986

C ONCLUSIVE arguments in philosophy are rare, so any such argument we find we prize. If it is not only conclusive but clever, all the better for it. The Dutch book arguments of the theory of… Expand

Open Problems in Universal Induction & Intelligence

- Computer Science, Mathematics
- Algorithms
- 2009

The state of the art in universal induction and its extension to universal intelligence is described and the state-of-the-art is described only in passing and the reader is referred to the literature. Expand

Universal Intelligence: A Definition of Machine Intelligence

- Computer Science
- Minds and Machines
- 2007

A number of well known informal definitions of human intelligence are taken, and mathematically formalised to produce a general measure of intelligence for arbitrary machines that formally captures the concept of machine intelligence in the broadest reasonable sense. Expand

The theory that would not die

- Mathematics
- 2012

In the early 1730sThomas Bayes (1701?–1761)was appointed minister at the Presbyterian Meeting House on Mount Sion, Tunbridge Wells, a town that had developed around the restorative chalybeate spring… Expand

Contemporary debates in philosophy of science

- Sociology
- 2004

Notes on Contributors.Preface.Introduction: What is the Philosophy of Science?.Part I: Do Thought Experiments Transcend Empiricism?.1. Why Thought Experiments Transcend Empiricism: James Robert Brown… Expand

On Universal Prediction and Bayesian Confirmation

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2007

It is shown that Solomonoff’s model possesses many desirable properties: strong total and future bounds, and weak instantaneous limits, and, in contrast to most classical continuous prior densities, it has no zero p(oste)rior problem. Expand

A Complete Theory of Everything (Will Be Subjective)

- Computer Science, Physics
- Algorithms
- 2010

The suggested principle is extended to morepractical (partial, approximate, probabilistic, parametric) world models (rather than theories of everything) and provided a justiﬁcation of Ockham’s razor, and criticize the anthropic principle, the doomsday argument, the no free lunch theorem, and the falsi ﬁability dogma. Expand

A Computer Scientist's View of Life, the Universe, and Everything

- 1997

Is the universe computable? If so, it may be much cheaper in terms of information requirements to compute all computable universes instead of just ours. I apply basic concepts of Kolmogorov… Expand