12 
8. If the study of the laws of thought avails us neither to 
determine the actual constitution of things, nor to explain its 
perplexities, still less, according to Boole, does it enable us to 
rise above the present conditions of our being, or lend its sanc- 
tion to the doctrine which affirms the possibility of an intuitive 
knowledge of the infinite, and the unconditioned , whether such 
knowledge be sought for in the realm of nature, or above that 
realm. We can never be said to comprehend that which is 
represented to thought as the limit of an indefinite process of 
abstraction. A progression ad infinitum is impossible to finite 
powers. But though we cannot comprehend the infinite, there 
may be even scientific grounds for believing thaj; human nature 
is constituted in some relation to the infinite. We cannot 
perfectly express the laws of thought, or establish in the most 
general sense the methods of which they form the basis without 
at least the implication of elements which ordinary language 
expresses by the terms “ Universe” and “ Eternity.” As in the 
pure abstractions of Geometry, so in the domain of Logic it is 
seen, that the empire of Truth is, in a certain sense, larger than 
that of Imagination. Thus the theory of the mental processes, 
as applied only to finite objects, seems to involve the recognition 
of a sphere of thought from which all limits are withdrawn. 
9. I believe the foregoing to be a substantially correct 
representation of Boole’s views on the constitution of those 
faculties of the mind which are exercised in science. He speaks 
of the confidence with which young children connect events 
whose association they have once perceived, and of their reference 
of every kind of sequence to that of cause and effect. He 
speaks of the uniformity of nature as pre- supposed in the theory 
of probability, and of the necessary sequence of states and con- 
ditions in the inorganic world.* I venture to make a distinc- 
tion between understanding and intellect which is not 
made* by Boole, who seems to use the words understanding 
intellect, and reason, interchangeably. By intellect, I mean 
the intellect proper, the noetic faculty, the source of the notions 
of space and time ; and, if that source be held to be the exercise 
of the utmost possible degree of abstraction on things or events, 
then I should call such an exercise of the mind an exercise of 
intellect. With Hamilton, I use the term understanding for the 
dianoetic or discursive faculty, for the faculty of relations or 
comparison + ; treating it as admitted, that language is an 
* Boole, op. cit., p. 361, footnote. Since my last address, another 
illustration of the instinctive tendency to regard antecedent and subsequent 
as antecedent and consequent, or, as cause and effect, has come under my 
notice. A little girl disturbed at an unusual hour asked a question to this 
effect : “ If I go to bed, when will it grow light again ? ” I forget whether 
day had dawned or not, and my only doubt is, whether the words sleep and 
dark ought not to be substituted for “ bed ” and “ light ” respectively. Next, 
see Boole, p.p. 14 and 407. 
t “ Discussions,” &c., hy Sir William Hamilton, Bart., second edition 
London, 1853. See p.p. 4, 7, and 13 $ see also p.p. 17 and 27. 
