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refute the man who denied the possibility of the resurrection ? It was by 
calling him a fool, and pointing out to him a grain which was sown in the 
ground, and which sprung up again to a new life. But I quite agree with 
one thing said by Mr. Warington, that not only is there a remarkable 
trinity to be found shadowed forth throughout nature, but there is also a 
wonderful duality, which may be taken as setting forth to us one of those 
deep analogies by means of which we can only faintly comprehend the union 
in our Lord and Saviour Jesus Christ of that marvellous duality of God and 
man. I am only sorry that I did not put in my pocket before I came here a 
remarkable paper, now out of print, and printed under a pseudonym by one 
of our members. It is a parallel between the Athanasian Creed and some of 
those things which mathematical students are willing to accept as truths, 
whether comprehensible or incomprehensible. The great objection made by 
unbelievers to the doctrine of the Trinity, as set forth in the Athanasian 
Creed, is that it requires a reasonable man to believe things which no reason- 
able man ought to be called on to believe. Now, Professor Byrne, who is one 
of the greatest mathematicians, has given the Athanasian Creed, and put side 
by side with it certain mathematical conclusions admitted by mathemati- 
cians. Every one of these mathematical parallels is as difficult of compre- 
hension, and demands as great an amount of faith, as the theological proposi- 
tions against which they are placed. No one but a first-rate mathematician 
like Professor Byrne could have found that parallel, and I confess I should 
like to see it printed at the end of this lecture. 
Mr. Reddie. — You propose to append Professor Byrne’s parallel between 
the Athanasian Creed and certain algebraical methods of demonstration ; but 
I think we should pause before agreeing to this ; as it should be borne in 
mind that Professor Byrne believes, and is actually on the point of publish- 
ing a book to prove, that many of those algebraical demonstrations are full 
of absurdities and irrational propositions, which want altogether to be cleared 
out from true mathematical proof. And if we were to appear to make our 
theology depend upon an analogy with the demonstrations of algebra, and 
afterwards to have the first mathematician of the day telling us that those 
demonstrations are irrational and unreliable, what would become of our 
theology ? Now, I am perfectly persuaded that there is such a thing as 
theological science, which can hold its ground rationally and logically, as well 
as, or better than, some of those other sciences which have been referred to. 
Many of the arguments which have been maintained by Mr. De La Mare, 
however, are not quite tenable. He says that the definition of parallel lines 
implies infinity, because they are two lines which continually produced shall 
never meet. But you may have a definition of parallel lines without im- 
plying infinity, as, for instance, two lines which cross a third line at precisely 
the same angle 
The Chairman. — I believe Mr. Reddie will find that none of the axioms 
or definitions of parallel lines substituted for that of Euclid have been found 
satisfactory. 
Mr. Reddie. — Neither is that in Euclid, and hence the existence of these 
