Karl Pearson 
3 
to ordinary dressings is logically more legitimate than to either alone. The only 
argument must be that in some way a wrong distribution of the a ■priori chance of 
blood poisoning is more likely to correct itself if applied for comparative than for 
absolute purposes. Dr Venn does not show, however, that any distribution, right 
or wrong, would lead in the comparative case to the same result. I cannot help 
fencying that had Dr Venn come across the problem as a bag of balls problem he 
would have rejected the equal distribution of ignorance solution. But when he 
meets the same problem in a vital problem of conduct, he realises that some 
solution is essential, there is a wide experience in man of the stability of statistical 
ratios, and for practical purposes he needs to apply this even to small samples of 
new experiences. What he demands and rightly demands is a measure of the faith 
he is to put — as a guide to immediate conduct — in small experience, and Bayes' 
hypothesis gives him a rule, which if rough, corresponds not wholly badly with his 
sum total of small experiences. The mathematicians in their customary manner 
first stated an hypothesis which simplified their analysis without questioning 
whether it had any foundation in experience. But Maxwell's brilliant paradox — 
that the theory of probabilities is the only logic for the practical man — means more 
than it superficially conveys. The practical man is always working by comparative 
probabilities even if he has not reduced his appreciations to numbers. He would 
certainly scoff at the idea that a first sample should not influence his judgment of 
what a second sample or what the bulk would be like. For such an idea would render 
most actions in life impossible. If science cannot measure the degree of probability 
involved — so much the worse for science. The practical man will stick to his 
appreciative methods until it does, or will accept the results of inverse probability 
of the Bayes-Laplace brand till better are forthcoming. 
Now let us see exactly where we stand. Notwithstanding the criticisms of Boole 
and Venn all branches of science have adopted the theory of " probable errors " : 
they have applied past experience of limited samples to predict what deviations are 
likely to occur from this past experience in future experience, and mankind acts in 
accordance with a firm conviction in the relative stability of statistical ratios. But 
any numerical appreciation of the reasonableness of this conduct is apparently 
based on the " equal distribution of ignorance " or ultimately on such a quaint idea 
as that of Bayes that his balls might roll anywhere on the table with equal 
probability. 
Edgeworth has done all that is feasible to transfer our faith in inverse prob- 
abilities from purely mathematical to more sound observational foundations. He 
wrote in 1884*, "The ridicule which has been heaped upon Bayes' theorem and 
the inverse method will be found only applicable to the pretence here deprecated 
of eliciting knowledge out of ignorance, something out of nothing. The most 
formidable objection is that which was made by Boole and is repeated by Mr Venn, 
Mr Pierce and others with approbation. Our procedure in treating one value as 
a priori not less likely than another is, it is said, of a quite arbitrary character, and 
* Mind, Vol. ix. p. 230. 
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