Sherlock Holmes and Probabilistic Induction

Uchii, Soshichi (1999) Sherlock Holmes and Probabilistic Induction.

Abstract

In this paper, (1) I argue that Sherlock Holmes was a good logician
according to the standard of his day, and (2) I try to show what his method of
reasoning was. Now, (2) is a harder task than (1), because we have to
identify the essential features of his method of reasoning. In order to
show this, I have not only to examine what Holmes says he is doing, but
also to look at the methods of scientific reasoning recommended by
several distinguished philosophers of science in the 19th century. I
want to examine Holmes's method of reasoning in a historical setting;
and this has something to do with the philosophy of science in the 19th
century, and hopefully with the philosophy of science today. I will
examine whether such methods are similar or dissimilar to Holmes's
method. Logicians and philosophers I wish to examine are, John
Herschel, John Stuart Mill, William Whewell, Augustus de Morgan, and
William Stanley Jevons; however, since the space is limited, I cannot do
justice to all of them.

My conclusion is this: Sherlock Holmes was distinctly different from
Herschel or Mill or Whewell who may be called a classical methodologist;
but he was very close to de Morgan or Jevons who were an advocate of the
new symbolic logic and the probabilistic theory of induction. But what
is the point of showing all this? The rise and development of
statistical method in the19th century had a great impact on the theories
of scientific reasoning, and de Morgan's or Jevons's theory is a newer
theory of induction in this century. And such a change of methodology
is clearly reflected in the popular stories of Sherlock Holmes, which
were written in the late 19th century and early 20th century.