Getting Rid of Derivational Redundancy or How to Solve Kuhn's Problem
Rens Bod
Abstract:
This paper deals with the problem of derivational redundancy in
scientific explanation, i.e. the problem that there can be extremely
many different explanatory derivations for a natural phenomenon while
students and experts mostly come up with one and the same derivation
for a phenomenon (modulo the order of applying laws). Given this
agreement among humans, we need to have a story of how to select from
the space of possible derivations of a phenomenon the derivation that
humans come up with. In this paper we argue that the problem of
derivational redundancy can be solved by a new notion of 'shortest
derivation', by which we mean the derivation that can be constructed
by the fewest (and therefore largest) partial derivations of
previously derived phenomena that function as 'exemplars'. We show how
the exemplar-based framework known as 'Data-Oriented Parsing' or 'DOP'
can be employed to select the shortest derivation in scientific
explanation. DOP's shortest derivation of a phenomenon maximizes what
is called the 'derivational similarity' between a phenomenon and a
corpus of exemplars. A preliminary investigation with exemplars from
classical and fluid mechanics shows that the shortest derivation
closely corresponds to the derivations that humans construct. Our
approach also proposes a concrete solution to Kuhn's problem of how we
know on which exemplar a phenomenon can be modeled. We argue that
humans model a phenomenon on the exemplar that is derivationally most
similar to the phenomenon, i.e. the exemplar from which the largest
subtree(s) can be used to derive the phenomenon.