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that was so influenced by it and other Marxist theory has enshrined as axiomatic the
need to bracket our own contemporary absolutes to prevent them from engendering
contaminating assumptions about different times and places; if such biases cannot be
limited entirely, then we are obliged to be openly cognizant of them in the process of
interpretation. Williams's argument is primarily addressed to the case of literature, but
the conclusions he draws are clearly relevant to any discourse we might choose to study
from a cultural point of view, including mathematics:
We cannot separate literature and art from other kinds of social practice, in such a way
as to make them subject to quite special and distinct laws. They might have quite
specii c features as practices, but they cannot be separated from the general social
process. . . . When we read much literature, over the whole range, without the
sleight-of-hand of calling Literature only that which we have already selected as
embodying certain meanings and values at a certain scale of intensity, we are bound to
recognize that . . . this activity takes place in all areas of the culture.
19
Since the purpose of resurrecting early modern arithmetic might be to provide it with
an instrumental role in economic systems that
are
historically contingent, it would be
highly dubious to assume that mathematics itself is untouched by history. Williams
argues that though we may be drawn to the “irreducible individuality [of works], we
should i nd ourselves attending i rst to the reality of their practice and the conditions
of the practice as it was then executed.”
20
He continues to emphasize that this will
require us to ask dif erent kinds of questions, but the larger point is that we must
remember to ask both kinds of questions, and not allow a bias toward one kind of ques-
tion and its answers to lead to neglect of the other. In analogy with literature that is
unwarrantably coni ned to “Literature,” mathematics may suf er the similar fate of
becoming “ Mathematics. ” There are several “ meanings and values ” of Mathematics —
which also happen to be recognizable as absolutes of our own culture—to guard against.
First, there is the truth that contemporary mathematics, both simple and advanced,
underpins every area of contemporary economic activity. It does not follow that math-
ematics was developed, either in the early modern period or in any other, solely to
promote our current economic systems. Second, the contemporary stereotype that
mathematics and its practitioners are cold, impersonal, remote, and unsociable could
be disproved for our time and for many others.
21
That such characteristics are organi-
cally related to the role mathematics may or may not have played in the rise of “deper-
sonalized” economic systems is equally dubious.
