George Boole
b. 2 November 1815, Lincoln,
Lincolnshire, England
d. 8 December 1864, Ballintemple,
Cork, Ireland
Boole is the author of the 1854
work: An Investigation of the
Laws of Thought, on which are founded the mathematical theories of
logic and probabilities. A digital
copy of the original may be accessed or a reproduction downloaded
from Project Gutenberg.
Boole's papers on probability are reprinted in Studies in Logic and Probability,
Open Court Publishing Co., 1952.
John Michell wrote a memoir "An
Inquiry into the probable Parallax, and Magnitude of the fixed Stars,
from the Quantity of Light which they afford us, and the particular
Circumstances of their Situation," by the Rev. John Michell, B.D.
F.R.S published in Philosophical
Transactions Vol. LVII, Part 1 (1767), pp. 234-264. Many
years later a letter
by James Forbes regarding this paper to the editors of the Philosphical Magazine dated 13 July
1849 prompted Boole to contribute to this topic.
- "On the Theory of Probabilities, and in particular on Mitchell's
Problem of the Distribution of Fixed Stars" (Supplement, 1851) Philosophical Magazine, Series 4,
Vol. 1, pp. 521-530. A summary of the controversy is given by Barry
Gower, "Astronomy and Probability: Forbes versus Michell on the
Distribution of Stars," Annals of
Science, 39 (1982), 145-160.
- "Further Observations on the Theory of Probabilities" (1851) Philosophical Magazine, Series 4,
Vol. 2, pp. 96-101.
Boole next posed a problem in conditional probabilities which
ultimately caused him to re-examine his work. The difficulty lies in
some implicit assumptions made by Boole.
Boole also gives the solution in detail in Chapter XX, pages 321-326
of his An Investigation of the
Laws of Thought as Problem I.
At this time Henry Wilbraham publishes in the Philosophical Magazine Series 4
Volume 7, "On the Theory of Chances developed in Professor Boole's
'Laws of Thought,' " (Supplement, 1853), pages 465-476.
Boole now replies in two letters and three papers published in the Philosophical Magazine:
Richard Dedekind enters the discussion in defence of Cayley. He
contributes the memoir "Bemerkungen zu einer Aufgabe der
Wahrscheinlichkeitsrechnung," Crelle, Vol. L, (1855), pp.
268-271. This is translated as "Remarks
on a problem in the calculation
of a probability."
Cayley again is published on this same controversy in Philosophical Magazine, Series 4,
Vol. 23 (1862), pp. 361-365 & 470-471. The same may be found in
his Collected Mathematical Papers
Vol. V, pages 80-84 as Item 318. A short note, Item 319 accompanies
this on page 85.
Boole continued to be bedeviled by difficulties with the conjunction of
events and condition probabilties.
- [1857] G. Boole.
"On the application of the Theory of Probabilities to the Question of
the Combination of Testimonies or Judgments," (Keith Prize
Essay, 1857) Edinb. R.S. T. 21 pp. 597-653. See the Studies in Logic and Probability.
Appears as "On the application of the Theory of Probabilities to the Question
of the Combination of Testimonies," in
Proc. Roy. Soc. Edin. 3, 435-442.
- "On the Theory of Probabilities" (1862) Philosophical Transactions Vol.
152, pp. 225-252. [1862] G. Boole."On the Theory of Probabilities," Phil. Trans. 152, pp. 225-252.
Lastly, we note
A Treatise on the Calculus of Finite Differences. Cambridge & London:
Macmillan. (1860).