special constructions always stay within logicism? Whitehead was as pat as Russell in
his lecture: 'The whole of mathematics is here.', he announced confidently, 'it is
mathematics, neither more nor less'.66 But he gave no explicit description of this
mathematics which the 'analytic stage' would deliver, so that the trivialisation of
logicism is not definitively avoided.
rather unfortunate line of influence from
the philosophy of mathematics from that time to ours has become largely a cottage
industry which in fact deals only with logic(s), set theory(ies), transfinite arithmetic
and small pieces of other branches of mathematics. While extremely interesting
material occurs within its own range, it comfortably avoids practically all mathema-
tics that mathematicians do, and gives a highly distorted.view of the
tions which can be raised in the philosophy of mat he ma tic^.^' I am most perplexed by
the reactions I receive from philosophers of mathematics to this criticism: the answer
is either the pat and mathematically unproven 'it's all sets!', or the pat and philoso-
phically uninteresting 'the point is philosophically uninteresting'. But with it left
unanswered, "philosophy of mathematics" stays in its own little coiner and so
remains as mathematics for philosophers and philosophy for mathematicians-as
saw at the start of this paper.
The paper is based on lectures delivered to the 'Problemgeschichte der Mathe-
matik' seminar held at Oberwolfach, West Germany, in May 1984, and at the confer-
ence on 'Russell's early technical philosophy' which took place the following month
at the University of Toronto. I am grateful to the organisers of the Toronto confer-
ence for allowing this published version to appear here. It benefited from points
made at both meetings, and especially from discussions with K.M. Blackwell, N.
Griffin, J. King and
Lewis of McMaster University. For permission to publish
manuscripts by Russell and to reproduce the folio as Figure 1, I am indebted to the
University's instrument Res.-Lib. Ltd.
1985) and to the Bertrand Russell Estate.
A.N. Whitehead, 'Presidential address; the organisation of thought',
Reports of the British Associa-
tion for the Advancement of Science.
(1916: pb. 1917), 355-363; reprinted in
Proceedings of the Arb-
(1916- 1917). 58-76;
The organisation of thought
(1917, London), ch. 6; and
Theoims of education and other ways
(1929, London). ch. 8. My disclaimer of footnote 4 to attempt
to discuss Whitehead's full views on mathematics are not infringed here, for in this lecture he dealt
only with logicism.