Humans routinely generalize universal relationships to unfamiliar instances
. If we are told "if glork then frum," and "glork," we can infer "frum"; an
y name that serves as the subject of a sentence can appear as the object of
a sentence. These universals are pervasive in language and reasoning. One
account of how they are generalized holds that humans possess mechanisms th
at manipulate symbols and variables; an alternative account holds that symb
ol-manipulation can be eliminated from scientific theories in favor of desc
riptions couched in terms of networks of interconnected nodes. Can these "e
liminative" connectionist models offer a genuine alternative? This article
shows that eliminative connectionist models cannot account for how we exten
d universals to arbitrary items. The argument runs as follows. First, if th
ese models, as currently conceived, were to extend universals to arbitrary
instances, they would have to generalize outside the space of training exam
ples. Next, it is shown that the class of eliminative connectionist models
that is currently popular cannot learn to extend universals outside the tra
ining space. This limitation might be avoided through the use of an archite
cture that implements symbol manipulation. (C) 1998 Academic Press.