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\noindent{\bf John VENN}\\
b. 4 August 1834 - d. 4 April 1923
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\noindent{\bf Summary.} Venn is remembered largely for his writings on
logic and his compilation of data on alumni of Cambridge University, but
he also wrote a widely read text-book on probability theory.
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John Venn was born in Hull, England, in 1834, a son of a prominent divine. He spent his
entire career not only in one university but even one college, Gonville and
Caius, Cambridge. He is most generally remembered as an historian of his
college (of which he was President from 1903 until his death 20 years later),
and also aas a chronicler of all the graduates of the university in his
{\it Alumni Cantabrigienses} (1922-1954), a multi-volume work which was
continued after his death by his son. He was very active in the reform of
the Moral Science Tripos in the 1870s, and for many years he taught the
elementary logic course.
Partly in this connection, Venn wrote influential textbooks. The first one,
entitled {\it The Logic of Chance} and dealing with probability theory,
appeared in three editions between 1866 and 1888. He rehearsed many features
and practical applications of the theory, such as insurance, gambling and
the appraisal of testimony, although he deliberately eschewed most
mathematical details. Following R.L. Ellis (1817-1859), he adopted a
frequentist interpretation of probability, regarding as visciously
circular the assumption that we know which causes pertain to the effect
under study; only long runs could make them manifest in the first place.
Thus he rejected the view that statistical regularities could be
explained by causal mechanisms.
Venn applied his position to the St. Petersburg paradox, arguing that
the player faced with the joy of possibly infinite winnings should
appraise his requested investment in terms of an `average gain'
over some {\it finite} run of offers of reward. He also criticized
the estimation of random processes such as the births of boys and
girls as a function only of the occurrence of each event; he asserted
that the distribution of births in {it families} was sought, and
presented data on British families with 4,5 or 6 children.
Venn saw probability theory as a branch or offshoot of logic; for
example in `modality' where propositions such as `it is probable that
all $X$ is $Y$' is used in reasoning. He expanded his lecture course
on logic in his book {\it Symbolic Logic} (1888, 1894) (the origin
of that phrase, incidentally). He largely followed Boole's ideas on
the algebra of logic, with modifications to the interpretation of some
notations. His adherance to Boole made him rather pass\'e in the
development of algebraic logic (for example, he did not appreciate the
innovation of a logic of relations by De Morgan); but his book remains
a rich and valuable source of information. One of its virtues are the
many historical references, for which he drew on his own extensive library
(now kept in the Cambridge University Library).
Venn als introduced a diagrammatic representation of syllogisms; but the
name `Venn diagram' is a misnomer in that it normally designates the
representation introduced a century earlier by Euler, as Venn well knew.
His own diagrams used convex figures to represent each predicate in a
given case, drawn such that all possible intersections were illustrated;
then empty subclasses were shaded in. This kind of representation is more
general but more clumsy than Euler's and convex shapes can only work
for four predicates. Venn sought means for extending the diagrams for
more predicates; a systematic and general method was published in 1989 by
his Caius successor A.W.F. Edwards.
In {\it The Principles of Empirical or Inductive Logic} (1889, 1907), Venn
treated logic within the syllogistic tradition. Following a practice of logic
books of the 19th century later, he included applications which we might
construe as philosophy of science; for example causation, classification,
and the uniformity of nature. He comes over as a disaffected Millian,
especially with his cautious views of causation.
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\noindent{\bf References}
\noindent Collection of manuscripts, Gonville and Caius College Library,
Cambridge.
\noindent Kr\'uger, L. (1987). The slow rise of probabilism..., in Kr\'uger
et. al. (eds.), {\it The Probabilistic Revolution}, Vol. 1, MIT Press,
Cambridge, Mass., 59-89.
\noindent Shearman, A.T. (1906). {\it The Development of Symbolic Logic},
Williams and Norgate, London (repr. 1990, Thoemmes, Bristol). [Author
a student of Venn.]
\noindent Venn, J. (1866). {\it The Logic of Chance}, McMillan, London.
[2nd ed. 1876; 3rd ed. 1888, repr. 1962, Chelses, New York.]
\noindent Venn, J. (1889). {\it The Principles of Empirical or Inductive
Logic}, McMillan, London. [2nd ed. 1907.]
\noindent Venn, J. (1888). {\it Symbolic Logic}, McMillan, London. [2nd
ed. 1894, repr. 1970, Dover, New York.]
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\hfill{I. Grattan-Guinness}
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