experience, translation is a merging between two networks. Quine’s argument, that
there is a multiplicity of different possible translations among languages, may well
not be applicable to mathematical translations, for reasons that will become
apparent.
- If we do not in fact arrive at the same total, we assume that someone has made a
mistake, has carried out the operation wrongly; this is to say that we did not both
follow the convention.
- The comparative sociology of networks casts light on how this conception of
mathematics arose. Plato’s faction within the Greek networks was an alliance
between mathematicians and philosophers, whose creativity came from tension
with opposing factions of empiricists, materialists, and skeptical relativists. Sub-
sequent Platonic and Neoplatonic religions made mutually supporting arguments
out of the conception of a transcendent God, a hierarchy of degrees of universality,
and mathematical Platonism. This combination of concepts was later taken over
by the mainstream of Christian, Islamic, and Jewish philosophers, and has re-
mained available as a tradition for philosophy of mathematics into the secularizing
period of European thought. In India and China no such mathematical Platonism
arose, even with the prevalence of Idealist philosophy in India in the post-Buddhist
period. This is due to the fact (documented in Chapter 10) that the networks of
mathematics and of philosophers had very few overlaps in China and India, unlike
in Greece and the West.
- Since mathematics is also a genealogy of techniques, which took off in its own
rapid-discovery revolution in the generations between Tartaglia and Descartes, the
development of mathematical-experimental paradigms in modern science has been
yet another kind of hybridization among genealogies of techniques. The lineages
of mathematics have branched and recombined among themselves, giving rise to
a rich ecology of mathematical “species” which have cross-bred in various ways
with the similarly cross-breeding “species” of research equipment genealogies.
- That is, since the telegraph (first in 1837), and subsequently electric motors,
telephones, lighting, and so on made it part of banal reality. Electricity had had a
more restricted laboratory reality for researchers since the Leiden jar was invented
in the 1740s, and especially since the voltaic cell (1799), which produced a reliable
continuous current. During the intervening period before laboratory equipment
was widely exported into everyday life, there were many popular interpretations
of the reality of electricity (e.g., Mesmer’s, as well as religious interpretations),
which lacked the sense of banal normalcy electricity was later to acquire.
- There is a family continuity between one generation of such concepts and the next,
although just what constitutes such continuity does not appear to be specifiable in
general and in advance. Kuhn (1961) has argued that even in the massive concep-
tual shifts which he calls paradigm revolutions, the mathematics is preserved. As
we have seen in the previous section, mathematics should be regarded as a practical
technique for making discoveries about formal intellectual operations; this means
that once again what is preserved across the generations is not the ideas per se but
the continuity of yet another genealogy of research “equipment.” Mathematical
continuity and groundedness of scientific entities is another case of the continuity
Notes to Pages 867–873^ •^1033
