Redescribing language use records
John James Love · Minerva Access (University of Melbourne) · 2001
We develop a formal theory which is intended to serve as a tool to help investigate the process of radical interpretation. The theory is specifically intended to be used in the context of ongoing interpretation, which we call infinite interpretation. It is assumed that the investigation of such interpretation would take place by considering infinite interpretative scenarios in the finite context of academic consideration, on the assumption that the scenarios proposed appropriately represented the crucial features of actual infinite interpretative processes. And it is anticipated that this sort of investigation would result in establishing general principles of infinite interpretation which might in turn shed light on broader semantic concerns. However, in order to confine the scope of the project, we concentrate on developing the formal theory and discussing general philosophical concerns about this theory, rather than applying it to investigate interpretation or to discussing philosophical aspects of its application. The theory which we develop is expected to serve as a tool by way of establishing that certain proposed scenarios do not have the desirable property of being effectively describable. Of course, the value in applying the theory assumes that the result is not already determined, and so we would assume that a proposed scenario was only initially described to the extent required to ensure that certain semantic qualities were incorporated. We do not expect to develop a theory which will serve to exclude all those scenarios which can not be effectively described, though we do expect it to be a significant means of breaking into the problem. And the approach which we anticipate to be of value in this way is to consider proposed infinite interpretative scenarios which require access to records of object language use, whereby some of these records may not be directly accessible. By considering the indirect accessibility of these records, it is expected that restrictions on the possibility of effective description can be established. Moreover, effective description of a proposed scenario requires those records which can not be accessed directly to be effectively described as being accessed from object language use records which are directly accessible. Formally, we refer to such a description of indirect access as redescription, and so by proving that redescription is not possible, it can be shown that a proposed infinite interpretative scenario can not be effectively described. Furthermore, to aid this analysis, we assume that other aspects of a scenario can be effectively described, which is obviously acceptable given that failure to effectively describe some other aspect means that it must already the case that the scenario can not be effectively described. By viewing object language use records as encoded by natural numbers, the notion of redescription is formally analysed using recursion theory. The basic aim is to consider the factor which arises as having a significant bearing on the possibility of redescription, which is the comparison of the information content of all directly accessible records with the information content of all records to be indirectly accessed. Following this, we discuss general philosophical concerns about the theory.