The name is absent

27

accomplishment: A typical primate can represent number as an approximate magnitude,
discriminating quantities more accurately among small numbers and between numbers that are
further apart. In addition to this ability, the primate can also distinguish with precision quantities
of 1, 2, 3, and perhaps 4. These two capacities are shared by all primates, both infant and adult.

However, there is a crucial difference in a human child’s conception of mathematics
versus that of a non-human primate. By the time the human child has grasped the first three
integers, and possibly also the fourth, s/he realizes that each number has a successor. For a
chimpanzee, by contrast, even after years of training, there is no evidence that the chimp
understands the open-ended nature of the series of integers. Mathematical progress, beyond the
degree of knowledge innately shared by all primates, exhibits unbounded productivity and hence
requires the ability to apply recursive operations (Hauser et al., 2002).

There is also controlled empirical evidence suggesting that humans have recursive
abilities lacked by other primates. This may mean that humans are capable of types of recursion
alien to the minds of non-human primates, or it may simply mean that the human can apply
certain sophisticated types of recursion to a wider range of cognitive domains than can other
primates even though the other primates may be able to apply these same forms of recursion to
some more narrow range of domains. In either case, the evidence suggests a uniquely human
capacity. This capacity may tell us something about the nature of moral progress and support
absolutism. But before continuing the discussion of moral cognition, we need to say a bit about
different forms of recursion and the nature of language.

A very simple sort of recursive grammar is known as a “finite-state grammar” because
such a grammar can be realized in a certain sort of machine known as a “finite-state automaton.”
An example of a finite-state automaton is illustrated in Figure 1. Such a machine is capable of
entering into a finite number of states, represented in the figure by numbers. For each state that it

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