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 THE PHILOSOPHY OF CHANCE. 225 In the more complicated beliefs not even this degree of pre- cision is possible ; however, even in such cases there may well be important quantitative, although not numerical, estimates. Mr. Venn next objects " Should we find this average to be of the amount assigned by theory " ? The answer is, as before, supplied by the doctrine of averages. The required conformity between our experienced feeling and the theoretic rule holds on an average. Mr. Venn tells us of the undue confidence of the gambler. But is there no such thing as undue diffidence ? or may not the over-confidence of one party be balanced by that of another? Peter and Paul betting against each other about an event, the chance of which is really even, are each ready to give odds. Upon an average their opposite errors counterbalance each other. (3) But, continues Mr. Venn, even supposing that quan- tification of belief is, and is according to standard scale, what security hae we that it is as it ought to be ? The instinc- tive is not always right. Resentment is an instinctive prin- ciple ; yet it is right to subdue it. It may be replied that the comparison should be, not with resentment, but with those superior principles, as Butler calls them, rational self-love or benevolence, in virtue of which resentment is subdued. These principles, as Mill and others have observed, do not admit of proof in the ordinary sense. Somehow or other we make up our mind what canon of conduct to adopt. The first principle of belief is similarly self-balanced, and rests upon nothing. Accordingly, the position that belief ougM not always to be what it is, or tends to be normally, if I may say so, finds its ethical analogue, not in the suppression of a secondary principle like resentment, but (as on the intellec- tual side we have to deal with no such hierarchy of prin- ciples) with that self-limitation of a supreme principle which has been so well illustrated by Butler and Mr. Sidgwick. And no doubt the self-limitation of belief in the interest of truth is conceivable, and has been defended. A certain de- gree of superstition is favourable to the imagination ; a cer- tain power of imagination is necessary to the perception of higher truth. Still this method of drugging the intellectual nature must be employed with great caution. Truth in the inward parts should be the rule ; the " lie within the soul," the doubtful and dangerous exception. (4) Again Mr. Venn objects that the selection of statisti- cally measured belief, out of all other cases of belief, is arbi- trary. The answer is that other important sciences are arbi- trarily defined. Political economy is an arbitrarily selected