PRESIDENT’S ADDRESS — SECTION A. 
15 
faculty ” are equally applicable to all human reasoning and emotion. 
It is, perhaps, only the mathematician or the musician who can fully 
appreciate how all his specialised work merges into his everyday ideas. 
But, says one haughty mathematician, our reasoning has more 
validity than the metaphysicians’, in that it is based upon a rock. It 
may be, but without any doubt that rock is essentially metaphysical. 
Another says it is the process and not the foundation that makes all 
the difference. How comes it then that to those most skilled, 
unfamiliar mathematical processes and unfamiliar physical reasoning 
(like Faraday’s, as viewed by his contemporaries) of the most advanced 
type, based on the thoughts and labours of multitudes of previous 
natural philosophers — how comes it that these processes above all seem 
to smack of metaphysics ? 
Let us examine a stone or two of those rocky foundations. If 
two and two do not always make four, a very considerable part of 
modern mathematical and physical ideas must vanish like a dream 
that is forgotten. And yet can any mathematician prove that two and 
two do without exception make four? Your mathematician will smile 
a contemptuous smile, and will whisper — Is he mad ? Your metaphy- 
sician, on the other hand, will say — Here is a concatenation of words 
that apparently forms a rational question. In the first place is it 
rational — i.e., is it other than nonsense ? He examines the words 
on this side and on that, and he concludes that the question is not 
nonsensical. He does not say that he can conceive an order of things 
in which two and two do not make four, but he does say that an 
order is conceivable in which both the assertion and its negation are 
nonsense. He says: Conceive three bags — one containing white balls, 
one black balls, and the third empty. Now take out a white and black 
ball, and put them in the third bag ; then take out another white and 
black ball, and put them in the third bag. Continue the operation till 
the white or black balls are exhausted. Suppose that both are exhausted 
simultaneously. Now separate the black balls from the white, and 
repeat the process. Have we any reasons for supposing that again 
the white and black balls will be exhausted simultaneously ? 
Undoubtedly we have, but it is merely that the same sort of thing has 
repeatedly occurred to us, not to say to our forefathers before. We 
cannot prove that because the phenomenon occurred on the first trial 
it will occur on the second. There is no law of thought involved — 
merely experience. Now, says the metaphysician, I can conceive an 
order of things in which this experience had no place. In such an 
order our labels one, two, three , four , &c., would have no meaning, and 
the statement that two and two made four would be a sick man’s 
fancy. 
Whether you consider such questions as belonging to the 
mathematician’s or the metaphysician’s domain, you must acknow- 
ledge that the mathematician is reduced to treating his question 
metaphysically, or the metaphysician to treating it mathematically. 
The processes in such cases merge into one another. 
It is more than likely that both the average mathematician and the 
average metaphysician would alike regard these speculations as to the last 
degree frivolous, both hurrying off in different directions to more con- 
genial pastures ; but that wonderful mathematician and metaphysician, 
Clifford, did not so regard them. How was it that the arch-enemy of 
