10, 11. Is any application of Probability to testimony valid?
CHAPTER XVII.
CREDIBILITY OF EXTRAORDINARY STORIES.
§ 1. Improbability before and after the event.
2, 3. Does the rejection of this lead to the conclusion that the credibility of a story is independent of its nature?
4. General and special credibility of a witness.
5–8. Distinction between alternative and open questions, and the usual rules for application of testimony to each of these.
9. Discussion of an objection.
10, 11. Testimony of worthless witnesses.
12–14. Common practical ways of regarding such problems.
15. Extraordinary stories not necessarily less probable.
16–18. Meaning of the term extraordinary, and its distinction from miraculous.
19, 20. Combination of testimony.
21, 22. Scientific meaning of a miracle.
23, 24. Two distinct prepossessions in regard to miracles, and the logical consequences of these.
25. Difficulty of discussing by our rules cases in which arbitrary interference can be postulated.
26, 27. Consequent inappropriateness of many arguments.
CHAPTER XVIII.
ON THE NATURE AND USE OF AN AVERAGE, AND ON THE DIFFERENT KINDS OF AVERAGE.
§:nbsp;1. Preliminary rude notion of an average,
2. More precise quantitative notion, yielding
(1) the Arithmetical Average,
3. (2) the Geometrical.
4. In asymmetrical curves of error the arithmetic average must be distinguished from,