The name is absent

26

are behind in their moral conceptions can be shown, by an appeal to reason, that the more
advanced conceptions are better.

The above is, at best, only the barest outline of a theory. One would like to have a better
grasp of what the expressions “rudiments of morality” and “reason” mean. We have already
noted that the ability to apply recursive procedures is necessary in order to account for the
unboundedness of moral judgment. This should, then, be at least part of what we mean by
“reason” in referring to the application of reason to “rudiments of morality,” viz. the application
of recursive procedures to mental representations of social situations. Fiske’s relational models
are susceptible to recursion and composition, as shall be discussed shortly; but there seems to be
no room for the notion of progress in Fiske’s relational models account, no room for rational
convergence in people’s moral views toward a single ideal system, which is why his account of
moral diversity, unlike Kropotkin’s, is pluralist.

There are accounts of some types of cognition in which recursion is an engine of progress
without the relativity of parameter settings. To explore this sort of cognition, it is useful to turn
away from language and focus on mathematics. The world’s mathematical diversity is different
from its linguistic diversity. Languages, at least for many purposes, seem to be equivalent
variations on a common, underlying pattern. However, the difference between modern
mathematics and, say, ancient Greek mathematics is clearly progress. Recursion plays a role
here; mathematical progress requires new, subtle, and ingenious applications of recursive
procedures. By looking into the nature of mathematical cognition, we get an idea of how one
might put some flesh on the bare skeleton provided by Kropotkin, and thus begin to see an
alternative to Fiske’s pluralism. So let’s consider some recent work on mathematical cognition.

There is evidence for an innate number sense which humans share with other primates
(Dehaene, 1997). It is a modest endowment compared with the full range of human mathematical

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