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use of the word “ infinite ” in its application to the Most High. It is a fine, 
noble word, and I take it to mean the fulness, the fontal fulness, of all 
perfection ; and so regarded, we must apply it in a just sense, and in the 
only just and true sense, to the one Everlasting Supreme Being. As to 
Mr. Mill, we can hardly any of us undertake to criticise him lightly, although 
he has said that two and two in some inconceivable world may be equal to 
five. It appears to me that four means two and two — that it simply means 
so many units taken one after another ; and when you analyze four, which is 
fair according to Mr. Mill’s philosophy, and get at its meaning, you must 
come to two and two ; and that, by his own principle of analysis, you never 
can make four otherwise than equal to two and two. That is to say, 
if A is equal to A, four is equal to two and two, and five can never be 
equal to two and two. But Mr. Mill had the advantage in his argument 
with Dean Mansel, and, moreover, he is much more nearly allied to those 
who are transcendentalists than they are willing to imagine. He is an 
idealist, perfect and pure, as much as ever Berkeley and Hume were, and a 
nihilist as well as an idealist, if it be possible to conceive the combination ; 
but he is not the least in the world a materialist. He no more believes in 
matter outside of him than he believes in me as a unit apart from matter. I 
confess I think the real principle at stake has been indicated by Mr. Bow', 
and that is, that all is to be harmonized on the basis of induction. But I 
think Mr. Bow went too far in his endeavour to show how, in the philosophy 
of probabilities, reason and faith melt into each other. He tried to make us 
understand that demonstrative sciences were in part sciences of probabilities, 
and that therefore it should not be alleged against theology that it is simply 
a probable science. How, I should be disposed to invert that statement. I 
do not believe it can be pretended that the demonstrative sciences, properly so 
called, are based on probabilities. I believe that Euclid’s demonstrations are 
based on absolute axioms 
Mr. Bow. — I have referred in my paper to Euclid’s twelfth axiom as not 
being a pure intuition. 
Dr. Bigg. — Well, I only state my own opinion that Euclid’s elements are 
based on clear, absolute axioms. And I go further, and say that the physical 
sciences repose on axioms and on principles which are as clear and certain 
and axiomatic as any principles of mathematics ; and, just as in any mathe- 
matical problem you may have conditions uncertain and unresolved, and 
can only come to an approximate conclusion, so in physical sciences 
you may have more or less of your conditions that are uncertain, and 
which only enable you to come to approximate conclusions. My argument 
is this, that physical sciences repose on intuitive principles, and so do 
all sciences, whatsoever they may be ; and I reason in this way : You 
should harmonize faith and reason, not by making the demonstrative 
sciences appear to be merely probable, but by showing that metaphysical 
or moral science, no less than the demonstrative sciences, reposes on 
a basis of intuitive axioms and intuitive principles. The conclusion that I 
come to on the whole is this : that if we take the principle of induction, 
