﻿ Note: Christian Tractatus (Theo Todman's Web Page)

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## Christian Tractatus

(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.

1. 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.
2. 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).
3. 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. PieI(P(pi)).
4. 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.

Note last updated Reference for this Topic Parent Topic
12/08/2007 10:17:46 222 (World Views) Certainty

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### Authors, Books & Papers Citing this Note

 Author Title Medium Extra Links Read? Adams (Ernest) The Logic of Conditionals: An Application of Probability to Deductive Logic Book

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