598 PROFESSOR BOOLE ON THE COMBINATION 
Iregard the elements of a problem relating to probability as logical, when its data 
and its queesitum are the probabilities of events. The reason for this appellation 
will shortly be seen. In expression, events may be distinguished as simple or com- 
pound. A simple event, 7.¢., an event simple in expression, is one which is expressed 
by a single term or predication; a compound event, one which is formed by 
combining the expressions of simple events. “It rains,”—“ it thunders,” would 
be simple events; “it rains and thunders,”—“ it either rains or thunders,” &c., 
would be compound events. The constructions by which such combinations are 
expressed, although they belong to language, have their foundations in Logic. 
Thus the conjunctions and, either, or, &c., express merely certain operations of 
the faculty of Conception, the entire theory of which belongs to the science of 
Logic. The calculus of Logic, to which I shall have occasion to refer, is a deve- 
lopment of that science in mathematical forms, in which letters represent things, 
or events, as subjects of Conception, and signs connecting those letters represent the 
operations of that faculty, the laws of the signs being the expressed laws of the 
operations signified. It is simply a mistake to regard that calculus as an attempt 
to reduce the ideas of Logic under the dominion of number. Such are the grounds 
upon which the class of problems to which I have referred are said to involve 
logical elements. The description is, however, not entirely appropriate, for the 
problems, as they are concerned with probabilities, in the mathematical accepta- 
tion of that term, involve numerical as well as logical elements; but it is by the 
latter that they are distinguished, and of them only is account taken in the no- 
menclature. 
Thus, as an illustration of what has been said, that problem would be com- 
posed of logical elements, which, assigning for its numerical data the probabilities 
of the throwing an ace or six with each single die, should propose to determine the 
probability that the issue of a throw with two dice should be two aces, or that it 
should be an ace and a six, or that it should be either two aces or an ace and a 
six; and so on for any conceivable throw with any number of dice. 
3. In the above example, the events whose numerical probabilities are given are 
simple events, of which the event whose probability is sought is a logical combina- 
tion. But it might happen that the former events were themselves combinations 
of simple events. For instance, the data might be the probabilities that certain 
meteorological phenomena, as rain, thunder, hail, &c., would occur in certain de- 
finite combinations, and the object sought might be the probability that they 
would occur in certain other combinations; all these combinations being, such 
as it is within the province of language to express by means of conjunctions, 
and of the adverb not. Now this would still be a problem whose elements are 
logical. 
4, But there are questions universally recognised as belonging to the theory 
of probabilities, whose elements cannot, in their direct significance, be regarded 
