40 
finite intelligence,” of which the rigorous law is intended to 
be laid down; but of “any intelligence,” finite or not. 
In mathematics, in which the infinite presents itself in its 
least sacred and most intelligible form, no definite proposition 
about the infinite is permitted, nor can such a proposition ever 
be a premiss in any argument. When such a proposition pre- 
sents itself, the thread of reasoning is snapped, and no conclu- 
sion whatever is possible. All our principles break down, and 
our trustiest axioms are shipwrecked, if we attempt to cross 
that gulf impassable. To build a theory on a definite pro- 
position about the infinite is the most unscientific procedure 
in the world. 
Although the review of a book is something out of place in 
this Society, yet remarks may be listened to on what professes 
to be a series of demonstrations. Mr. Kirkman thinks that 
the only novelty in these Institutes is the manipulation of the 
word contradictory. Professor Ferriers has discovered a new 
predicament, that of the contradictory, which has nothing to 
do with contradictions. It is neither contra nor dietary ; it 
is not that which is expressible in propositions ; but it is ex- 
pressed by terms without propositions. (Ontology, Prop. I. 
p. 460.) This is the balloon whereby he soars out of the 
epistemology into the ontology : this is his bridge over the 
gulf between the finite and the infinite. An amusing example 
of his management of this new and convenient middle term 
may be seen (Theory of Knowing, Prop. IV. p. 138) in his 
attempt to connect it with respectable old contradictions. 
“ Matter per se is a contradictory thing, just as much as a 
circle without a centre is a contradictory thing.” The cen- 
treless circle will hardly allow this claim of relationship : it 
will say to matter per se, “ I am contradictory to my defini- 
tion ; but what right have you to be contradictory at all?” 
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