13 
instrument of human reason, and not merely a medium for the 
expression of thought.* The general result is this : The 
materials of knowledge are worked up into strictly scientific 
forms by the belief in uniformity and by the operations of the 
understanding. These operations — viz., the logical processes, 
considered in connection with other canons of belief, are used by 
Boole in his theory of probabilities. 
10. In saying that space and time determine the present 
sphere of our knowledge, Boole may be taken to assign “ the 
conditioned in space and time” as that sphere. But I think that 
he affords no support to the theory called “ The Philosophy of 
the Conditioned.” His remark that a progression adinfinituru is 
impossible to finite powers, does not fully disclose his views. On 
turning to a previous page (194) we find him observing that 
the “ impossibility of infinite succession” has commonly been 
assumed as a fundamental principle of metaphysics, and extended 
to other questions than that of causation ; that Aristotle applies 
it to establish the necessity of first principles of demonstration ; 
of an end (the good) in human actions, &c. ; that there is, perhaps, 
no principle more frequently referred to in his writings ; that by 
the schoolmen it was similarly applied to prove the impossibility 
of an infinite subordination of genera and species, and hence 
the necessary existence of universals. Boole’s remark on this 
seems to indicate that he was not satisfied with the principle. 
Apparently, he says, the impossibility of our forming a definite 
and complete conception of an infinite series, i,e. y of com- 
prehending it as a whole , has been confounded with a 
logical inconsistency, or contradiction in the idea itself. The 
question of infinity must, I think, be left to mathematicians, 
and, fortunately, it has undergone a careful discussion at the 
hands of one who, like Boole, was famed in the scientific world, 
and who, in his f memoir “ On Infinity,” &c., has treated the 
subject critically, historically, and philosophically. Perhaps 
Boole and De Morgan substantially agreed even in their views 
as to the basis of geometry, for Boole (see p. 404 and compare p. 
419) says, that although the perfect triangle, or square, or circle 
exists not in nature, eludes all our power of representative 
conception, and is presented to us- in thought only, as the 
limit of an indefinite process of abstraction, yet by a wonderful 
faculty of the understanding, it may be made the subject of 
propositions which are absolutely true, and that the domain of 
reason is thus revealed to us as larger than that of imagination. 
Disputes about infinity seem to arise from a neglect to 
distinguish between imaged and unimaged concepts. De Morgan 
observes that all our senses have their images ; we can image 
a cry of fire, and the inmates of the house rousing up in alarm. 
* Boole, “ Laws of Thought,” chap, ii., art. 1, page 24. 
f “ On Infinity ; and on the Sign of Equality,” by Augustus de Morgan. 
Printed in the transactions of the Cambridge Philosophical Society, vol. xi. 
part 1. 
