"Except, however, in such cases as games of chance, where the very 
purpose in view requires ignorance instead of knowledge, I can 
conceive no case in which we ought to be satisfied with such an 
estimate of chances as this; an estimate founded on the absolute 
minimum of knowledge respecting the subject. It is plain that, in the 
case of the coloured balls, a very slight ground of surmise that the 
white balls were really more numerous than either of the other 
colours, would suffice to ^/d/ 
<http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=246&chapter=39870&layout=html#lf0223-07_footnote_nt_2760> 
vitiate the whole of the calculations made in our previous state of 
indifference. It would place us in that position of more advanced 
knowledge, in which the probabilities, to us, would be different from 
what they were before; and in estimating these new probabilities we 
should have to proceed on a totally different set of data, furnished 
no longer by mere counting of possible suppositions, but by specific 
knowledge of facts. Such data it should always be our endeavour to 
obtain; and in all inquiries, unless on subjects equally beyond the 
range of our means of knowledge and our practical uses, they may be 
obtained, if not good, at least better than none at all.^* 
<http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=246&chapter=39870&layout=html#lf0223-07_footnote_nt_2761>

It is obvious, too, that even when the probabilities are derived from 
observation and experiment, a very slight improvement in the data, by 
better observations, or by taking into fuller consideration the 
special circumstances of the case, is of more use than the most 
elaborate application of the calculus to probabilities founded on the 
data in their previous state of inferiority. The neglect of this 
obvious reflection has given rise to misapplications of the calculus 
of probabilities which have made it the real opprobrium of mathematics."

 From John Stuart Mill's "A System of Logic: Ratiocinative and Inductive."

http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=246&chapter=39870&layout=html


Pat Gunning