228 
PROFESSOE BOOLE ON THE THEORY OF PROBABILITIES. 
properties in the actual urn is the same as it is conceived to be in the ideal urn of free 
balls, but the hypothesis that it is so, involves an equal distribution of our actual 
knowledge, and enables us to construct the problem from ultimate hypotheses which 
reduce it to a calculation of combinations. 
I pass from the particular and material to the general problem. In the form to which 
this is brought by the Calculus of Logic, the probabilities are those of events of which 
certain combinations are, as a logical consequence of the original definitions of those 
events, impossible. It might, at first sight, appear that this establishes a fundamental 
difference between this problem and that of the urn, in which certain combinations are 
prevented from issuing by a material hindrance. In the one case the restriction appears 
as logically necessary, in the other as only actual. 
Upon this I remark, that the data of the problem in its ultimate reduced form might 
result from the same kind of dependence as in the actual data ; that they, in fact, would 
thus result if the mind of the observer were capable of contemplating, and were in a 
position to contemplate, each of the events in this ultimate translated form simply as a 
whole, and of recording, through an approximately infinite series of observations, what 
combinations of those wholes come into being, and what do not, in the actual universe. 
What appears as necessary in the translated data would now appear as actual—as a 
result of observation ; what is impossible would be received as non-existent. The ques- 
tion is, then, whether the difference between the conception of what is impossible from 
involving a logical contradiction, and the conception of what in the actual constitution 
of things never exists, is of a kind to afiect expectation. I do not hesitate to say that it 
is not. We are concerned with events in so far as they are capable of happening or not 
happening, of combining or not combining ; but w^e are not concerned with the reasons 
in vu’tue of which they happen or do not happen, combine or do not combine. If we 
went beyond this, we should enter upon a metaphysical question to which I presume 
that no answer can, upon rational grounds, be given, viz. upon the question whether, 
when two things or events are in the actual constitution of things incapable of happen- 
ing together, it would, if our knowledge were sufiiciently extended, be found that the 
resulting conceptions of them were logically inconsistent. 
I have but one further observation on Principle II. to make. It is that in the general 
problem we are not called upon to interpret the ideal events. The whole procedure is, 
like every other procedure of abstract thought, formal. We do not say that the ideal 
events exist, but that the events in the translated form of the actual problem are to be 
considered to have such relations with respect to happening or not happening as a 
certain system of ideal events would have if conceived first as free, and then subjected, 
without their freedom being otherwise affected, to relations formally agreeing with those 
to which the events in the translated problem are snbject. 
tion through arbitrary hypotheses, coupled with the assumption that any result thus obtained is necessarily 
the true one. The application of the principle employed in the text, and founded upon the general theorem 
of development in Logic, I hold to be not arbitrary. 
