- LOGIC 543
proudly proclaimed that "Not only... will 'no knowledge of mathematics beyond
the simple rules of Arithmetic' be required to understand these pages, but it is not
intended that any such knowledge should be acquired by the process of reading
them." Venn was particularly exercised about the attempts to apply probability
theory in jurisprudence. Referring to Laplace, Quetelet, and the others, he wrote:When they have searched for illustrations drawn from the practical
business of life, they have very generally, but unfortunately, hit
upon just the sort of instances which, as I shall endeavour to show
hereafter, are among the very worst that could be chosen for the
purpose. It is scarcely possible for any unprejudiced person to
read what has been written about the credibility of witnesses by
eminent writers, without his experiencing an invincible distrust of
the principles which they adopt.He went on to say that, although probability may require considerable mathe-
matical knowledge, "the discussion of the fundamental principles on which the rules
are based does not necessarily require any such qualification." Moreover,The opinion that Probability, instead of being a branch of the
general science of evidence which happens to make much use of
mathematics, is a portion of mathematics, erroneous as it is, has
yet been very disadvantageous to the science in several ways.As one might expect, he took a dim view of the writings of de Morgan and
Boole, saying that de Morgan had "given an investigation into the foundations of
Probability as conceived by him, and nothing can be more complete and precise
than his statement of principles and his deductions from them. If I could at all agree
with these principles there would have been no necessity for the following essay." As
for Boole, "Owing to his peculiar treatment of the subject, I have scarely anywhere
come into contact with any of his expressed opinions," a subtle, but acerbic way of
saying that Boole had failed to convince anyone.
In Venn's view, expressed at the beginning of his fourth chapter, the practical
application of probability in such matters as insurance was simply one more aspect
of induction, the extrapolation of past experience into the future:We cannot tell how many persons will be born or die in a year, or
how many houses will be burnt or ships wrecked, without actually
counting them. When we thus speak of "experience," we mean to
employ the term in its widest signification; we mean experience
supplemented by all the aids which inductive or deductive logic
can afford. When, for instance, we have found the series which
comprises the numbers of persons of any assigned class who die in
successive years, we have no hesitation in extending it some way
into the future as well as into the past. The justification of such a
procedure must be sought in the ordinary canons of Induction.Venn thus proclaimed himself a frequentist. The justification for applied proba-
bility and statistics was to be induction. But how firm a foundation was induction?
The skeptical Scot David Hume (1711-1776) had leveled a devastating criticism