268 NATURE OF CAPITAL AND INCOME [Cmar. XVI 
ness of these elements is introduced into the problem, the 
observer unconsciously shifts his ground from the “long 
run” to the true theory of chance. 
Chance is, then, an affair of human knowledge or igno- 
rance. According to this — the ignorance — theory, chance 
is not objective, but subjective. Outside of the mind, 
chance has no place. If a man holds a coin in his hand and, 
without letting it be seen, asks his neighbor what the 
“real” chance is that heads are up, will not the latter reply 
one half? But as a matter of fact the position of the coin 
is absolutely determinate. Either heads are up, or tails 
are up; there is no ambiguity. Without changing the 
coin, the holder opens his hand. He sees that heads are 
up. Without disclosing this fact to his neighbor he re- 
peats the question, “What is the chance that heads are 
up?” Will not the latter still reply, “One half”? To 
him, in his ignorance about the coin, the chances are 
exactly even; but to the man who holds the coin and 
whose eye has seen it, there is no uncertainty. He knows 
that heads are up. For him the element of chance has 
vanished because the element of ignorance has vanished. 
Chance exists only so far as ignorance exists; varies with 
different persons according to their comparative ignorance 
of the matter under consideration ; and is in fact a measure 
of ignorance. 
Of course the actual statistical record may afford an im- 
portant and sometimes the only basis for our degree of 
knowledge and ignorance. Practically it therefore often 
happens that we derive our estimate of chances from the 
behavior of events “in the long run.” It is thus that the 
chances of fire, shipwreck, and death are estimated by the 
insurance companies. But while statistics supply data 
for the forming of subjective estimates of chances, they do 
not, themselves, constitute chances; and even when they 
enter into the problem the insurance examiner does not 
follow them blindly. He always examines the special