(Text as at 12/08/2007 10:17:46)

**We must note that beliefs are not held in isolation, but form a network of interconnected beliefs commonly called a world view. **

- Any world view must be self-consistent. That is, all its statements must be simultaneously relatively true. For a world view to be absolutely true, all its component beliefs must simultaneously be true of the world.
- Any world view may be condensed into an irreducible set of propositions, none of which duplicates any of the contents of another & which collectively cover the world view. Since, however, there may be difficulty in ensuring the independence of the propositions, we may have to be satisfied with a non-disjoint covering set (as in topology).
- Let us suppose that a world view is composed of a set of irreducible propositions {pi} enumerated by the index set
**I**and let each of these propositions have probability**P**(pi). Then, the probability of the world view is (or is closely related to) the product, over I, of these probabilities, ie. Pie**I**(**P**(pi)). - Naively, we can deduce two consequences from the above, given below.
- Firstly, no sophisticated world view can have a high probability of being true in all its parts, because the number of irreducible propositions it contains will be be large while their probabilities will often be low. To take a trivial example, let us suppose our world view consists of an irreducible set of 20 propositions, each of which we take to be 90% certain; then, we have only the right to be 12% certain of the truth of our world view.
- Secondly, the greater the number of irreducible propositions in a world view, the lower the probability of that world view. Hence the force and importance of Occam's Razor, of which more will be said later.

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12/08/2007 10:17:46 | 222 (World Views) | Certainty |

Certainty |

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Adams (Ernest) | The Logic of Conditionals: An Application of Probability to Deductive Logic | Book |

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