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

- "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.

- "Proposed Question in the Theory of Probabilities" (1851) Cambridge and Dublin Mathematical Journal
Volume 6 p. 286.

**Arthur Cayley**responded with a solution in a "Note on a Question in the Theory of Probabilities." This appeared in the Philosophical Magazine, Vol. 6 (October, 1853), p. 259 and may also be found in his Collected Mathematical Papers, Vol. 2, pages 103-104. See item 121 there as well as the notes on pages 594-598.

Boole now published his solution and argues that**Cayley**is incorrect. His objection lies on an absurd case.

- "Solution of a Question in the Theory of Probabilities" (January,
1853)
Philosophical Magazine Series 4
Volume 7 pp. 29-32.

At this time

Boole now replies in two letters and three papers published in the Philosophical Magazine:

- "Reply to some Observations by
**Mr. Wilbraham**on the Theory of Chances developed in Professor Boole's 'Laws of Thought' " (August, 1854) Philosophical Magazine Series 4 Volume 8 pp. 87-91.

- "On the Conditions by which the Solutions of Questions in the
Theory of Probabilities are Limited" (August, 1854) Philosophical Magazine Series 4
Volume 8 pp. 91-98.

- "Further Observations relating to the Theory of Probabilities in
Reply to Mr. Wilbraham," (September, 1854) Philosophical Magazine Series 4
Volume 8 pp. 175-176.

- "On the General Method in the Theory of Probabilities" (December, 1854) Philosophical Magazine Series 4 Volume 8 pp. 431-444.
- "On certain Propositions in Algebra connected with the Theory of Probabilities," (March, 1855) Philosophical Magazine Series 4 Volume 9 pp. 165-179.

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).