1903.] STONEY—UNIVERSE OF REAL EXISTENCES. 107 
ties are called the humanities. Explorers of nature, investigators 
of the work done or being done: which is not man’s work, stand a 
better chance of success than those whose thoughts mainly travel 
within the narrower range: and on several accounts; first, because 
they find less difficulty in freeing themselves from the limitations of 
the human standpoint, which we may liken to the Ptolemaic point 
of view, and in grasping the wider resources of a more Copernican 
survey ; largely, too, because they more easily ‘become expert in 
using such symbols as words in a generalized or otherwise modified 
sense when it becomes necessary to do so; but perhaps most of all 
because they are already familiar with the contrast between the two 
kinds of supposition which those physicists who use language care- 
fully distinguish as ¢heortes and hypotheses. As some readers of the 
papers I have already written on these subjects have found here their 
chief difficulty, it appears desirable ‘to devote a chapter of this essay 
to its elucidation. This, indeed, is almost necessary; inasmuch as 
sound progress in the task before us is not even possible unless this 
distinction is clearly grasped, and unless a facility has been acquired 
in handling both hypotheses and theories without risk of the confu- 
sion between them which has been too often made. 
CHAPTER 2. OF THEORIES AND HYPOTHESES. 
‘Both theories and hypotheses are suppositions—a theory means a 
supposition which we hope to be true, a hypothesis is a supposition 
which we expect to be useful. Theories accordingly are either cor- 
rect or incorrect, true or false, quite irrespectively of whether we, 
men, can make much, or little, or any use of them. Zhe merit 
of a theory ts simply to be true. It often, indeed usually, happens 
that the true theory is also useful; but it by no means need be 
so. Accordingly, the question whether a particular theory is of 
any use is irrelevant. 
On the other hand a hypothesis is a supposition which aims at 
being useful, and which ts legitimate if useful. A hypothesis may 
be a theory—in other words, a supposition which we make expect- 
ing it to help us forward in our investigation, may also be the sup- 
position which we think to be true: but it by no means need be so; 
and in fact the best, z.c., the most useful, hypotheses are often of 
the kind that make no pretense to being true. For example, all 
applications of mathematics to the investigation of nature are de- 
