Thesis - Probability
Todman (Theo)
Paper - Abstract

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Write-up2 (as at 12/08/2007 10:17:46): Probability

A requirement of great importance, therefore, is the ability to assign a probability to any statement about the world (or within a model), in accord with the likelihood of it being a true statement.
  1. Ideally3, we would like to assign a mathematical probability to any statement, ie. a real number in the range 0 to 1, with 0 representing impossibility & 1 representing certainty. As in the frequency theory of probability, the assigned number should represent the proportion of situations in which the statement is expected to turn out to be true.
  2. In practical4 life, where it is unreasonable to assign a numerical probability to an event, we do assign non-mathematical probabilities to statements and base our actions on them.
  3. It also makes sense to say that certain statements are more probable than others, even when they do not refer to the same domain5 of experience.
  4. It would seem to be possible to assign a priori6 probabilities to statements about the world, the probability being assigned a priori to that particular potential experience, by reference to other actual experiences, though not a priori to all experience.
  5. A statement with a low a priori probability may yet have a higher a posteriori probability because of the strength of actual testimony or experimental evidence.

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