Chapter IV: Part I

PHYSICAL FOUNDATIONS OF THE SCIENCE OF PROBABILITY. Chh. I-V.

CHAPTER I.

THE SERIES OF PROBABILITY.

§§ 1, 2. Distinction between the proportional propositions of Probability,
and the propositions of Logic.
3, 4. The former are best regarded as presenting a series of individuals,
5. Which may occur in any order of time,
6, 7. And which present themselves in groups.
8. Comparison of the above with the ordinary phraseology.
9, 10. These series ultimately fluctuate,
11. Especially in the case of moral and social phenomena,
12. Though in the case of games of chance the fluctuation is practically
inappreciable.
13, 14. In this latter case only can rigorous inferences be drawn.
15, 16. The Petersburg Problem.

CHAPTER II.

ARRANGEMENT AND FORMATION OF THE SERIES. LAWS OF ERROR.

§§ 1, 2. Indication of the nature of a Law of Error or Divergence.
3. Is there necessarily but one such law,
4. Applicable to widely distinct classes of things?
5, 6. This cannot be proved directly by statistics;
7, 8. _Which in certain cases show actual asymmetry._
9, 10. Nor deductively;
11. Nor by the Method of Least Squares.
12. Distinction between Laws of Error and the Method of Least
Squares.
13. Supposed existence of types.
14-16. Homogeneous and heterogeneous classes.
17, 18. _The type in the case of human stature, &c._
19, 20. The type in mental characteristics.
21, 22. Applications of the foregoing principles and results.

CHAPTER III.

ORIGIN OR PROCESS OF CAUSATION OF THE SERIES.

§ 1. The causes consist of (1) 'objects,'
2, 3. Which may or may not be distinguishable into natural kinds,
4-6. And (2) 'agencies.'
7. Requisites demanded in the above:
8, 9. Consequences of their absence.
10. Where are the required causes found?
11, 12. Not in the direct results of human will.
13-15. Examination of apparent exceptions.
16-18. _Further analysis of some natural causes._

CHAPTER IV.

HOW TO DISCOVER AND PROVE THE SERIES.

§ 1. The data of Probability are established by experience;
2. Though in practice most problems are solved deductively.
3-7. Mechanical instance to show the inadequacy of any à priori proof.
8. The Principle of Sufficient Reason inapplicable.
9. Evidence of actual experience.
10, 11. Further examination of the causes.
12, 13. Distinction between the succession of physical events and the
Doctrine of Combinations.
14, 15. Remarks of Laplace on this subject.
16. Bernoulli's Theorem;
17, 18. Its inapplicability to social phenomena.
19. Summation of preceding results.

CHAPTER V.

THE CONCEPTION OF RANDOMNESS.

§ 1. _General Indication._
2-5. _The postulate of ultimate uniform distribution at one stage or
another._
6. _This area of distribution must be finite:_
7, 8. _Geometrical illustrations in support:_
9. _Can we conceive any exception here?_
10, 11. _Experimental determination of the random character when the
events are many:_
12. _Corresponding determination when they are few._
13, 14. _Illustration from the constant π._
15, 16. _Conception of a line drawn at random._
17. _Graphical illustration._