Loading your reading…

The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to StatisticsVenn, John

Philosophy

The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics

Name: The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics
Author: Venn, John

Venn, John

Chance; Logic, Symbolic and mathematical; Probabilities; Science -- Methodology

§  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,_
   5. (3) _the Maximum Ordinate average,_
   6. (4) _and the Median._
   7. _Diagram in illustration._
   8-10. _Average departure from the average, considered under the above
       heads, and under that of_
   11. (5) _The (average of) Mean Square of Error,_
   12-14. _The objects of taking averages._
   15. _Mr Galton's practical method of determining the average._
   16, 17. _No distinction between the average and the mean._
   18-20. _Distinction between what is necessary and what is experimental
       here._
   21, 22. _Theoretical defects in the determination of the 'errors'._
   23. _Practical escape from these._

(_Note about the units in the exponential equation and integral._)


CHAPTER XIX.

THE THEORY OF THE AVERAGE AS A MEANS OF APPROXIMATION TO THE TRUTH.

§§ 1-4. _General indication of the problem: i.e. an inverse one
    requiring the previous consideration of a direct one._

    [I. _The direct problem:--given the central value and law of
    dispersion of the single errors, to determine those of the
    averages._ §§ 6-20.]

   6. (i) _The law of dispersion may be determinable _à priori_,_
   7. (ii) _or experimentally, by statistics._
   8, 9. _Thence to determine the modulus of the error curve._
   10-14. _Numerical example to illustrate the nature and amount of
       the contraction of the modulus of the average-error curve._
   15. _This curve is of the same general kind as that of the single errors;_
   16. _Equally symmetrical,_
   17, 18. _And more heaped up towards the centre._
   19, 20. _Algebraic generalization of the foregoing results._

    [II. _The inverse problem:--given but a few of the errors to
    determine their centre and law, and thence to draw the above
    deductions._ §§ 21-25.]

   22, 23. _The actual calculations are the same as before,_
   24. _With the extra demand that we must determine how probable are the
       results._
   25. _Summary._

    [III. _Consideration of the same questions as applied to certain
    peculiar laws of error._ §§ 26-37.]

   26. (i) _All errors equally probable._
   27, 28. (ii) _Certain peculiar laws of error._
   29, 30. _Further analysis of the reasons for taking averages._
   31-35. _Illustrative examples._
   36, 37. _Curves with double centre and absence of symmetry._
   38, 39. _Conclusion._




THE LOGIC OF CHANCE.




CHAPTER I.


_ON CERTAIN KINDS OF GROUPS OR SERIES AS THE FOUNDATION OF PROBABILITY._

Public-domain text, read in full here on John Shaqi.

The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics

No reviews yet