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member of the famous ‘Vienna Circle’, ran a preparatory seminar on ‘Algebra and logic’ while
Newman was in Vienna.^25 ,26 Hahn was not only a specialist in the topology of curves and in
real-variable mathematical analysis but also regarded formal logic as an important topic, both
for research and teaching. In later years, Hahn held two full seminar courses on Whitehead and
R u s s e l l ’s Principia Mathematica, one of the earliest major publications in modern mathematical
logic. Russell’s approach to philosophy and logic strongly influenced the Vienna Circle. Hahn
also supervised the young Kurt Gödel, a doctoral student in Vienna.
After Vienna
Newman became a pioneer of topology in Britain, with a serious interest in logic and logic
education, and also in Russell’s philosophy. One surely sees strong Viennese influence here,
especially from Hans Hahn.
Newman applied for a College Fellowship at St John’s in 1923, a year that saw him publishing
in the traditional area of mathematical analysis (in particular, on avoiding the axiom of choice
in the theory of functions of real variables), and also writing a long unpublished essay in the
philosophy of science, entitled ‘The foundations of mathematics from the standpoint of physics’.
This could well have originated in a Viennese conversation. Maybe he even wrote some of it in
Vienna.^27 In the essay, Newman contrasted the world of idealized objects customarily adopted
in applied mathematics (smooth bodies, light strings, and so on) with the world ‘of real physical
objects’. He distinguished the two worlds by the different logics that they used. The idealizers
would draw on classical two-valued logic, for which he cited a recent metamathematical paper
by Hilbert as a source,^28 but those interested in real life, he said, would go to constructive logic,
on which he cited recent papers by Brouwer and Hermann Weyl.^29 This readiness to embrace
logical pluralism and to put logics at the centre of his analysis of a problem was most unusual for
a mathematician, and far more a product of Vienna than Cambridge.^30 ,^31
An occasion for Newman to exercise his logical and philosophical talents arose when he
attended a series of philosophical lectures that Russell gave in Trinity College Cambridge in
- These lectures were the basis for Russell’s book The Analysis of Matter.^32 Newman helped
Russell to write two chapters, and, when the book appeared in 1928, he criticized its philo-
sophical basis most acutely.^33 ,^34 Russell accepted the criticisms, which stimulated Newman to
write Russell two long letters on logic and on topology, featuring some ideas from his 1923
philosophical essay.^35 Newman continued to pioneer both topology and logic at Cambridge
and, doubtless with topology in mind, Hardy successfully proposed Newman as a Fellow of the
Royal Society, with J. E. Littlewood as seconder—even though Newman was no analyst in the
Hardy–Littlewood tradition.
Newman used the Royal Society to support the cause of logic. In 1950, he proposed Turing
as a Fellow, seconded by Russell, and Turing was duly elected in 1951. Just five years later, in
1955, Newman wrote Turing’s Royal Society obituary.^36 In 1966 Newman proposed Gödel as a
Foreign Member, and again Russell seconded; Gödel was elected to the society two years later.^37
When Russell died in 1970, Newman agreed to write the society’s obituary of Russell, together
with the philosopher Freddie Ayer, but failing health prevented him from fulfilling his obliga-
tion. He died in 1984.