Relative identity

Abstract

The work defends a theory of relative identity roughly similar to Geach's. It is held that statements of the form 'a is the same as b' are incomplete until a general noun is specified after 'same'; and that items which are identical with respect to one general noun may be distinct with respect to another. These theses are referred to respectively as (D) and (R). Chapter One contrasts the theory of absolute identity with theories of relative identity, places the latter in their historical context, and suggests why they have some initial plausibility despite the universal acceptance of the absolute theory. Chapters Two, Three, Four and Five concern the nature of the general nouns which may be used to complete identity statements. We are particularly concerned with general nouns which convey criteria by which identity claims may be judged and with the structure of the system of classes which these nouns name. Certain over-simple assumptions of Wiggins about this structure are rejected in Chapter Five. Chapters Six and Seven consider the thesis (D): in conjunction with (R) in Chapter Six, and independently in Chapter Seven Whilst {R) does not entail (D), as has often been supposed, it is convenient to accept both principles in a context free,(R )-relative identity theory in or1der to obtain a closer match with natural language identity statements than is possible for the absolute theory. In Chapter Seven it is argued that whilst Wiggins' theory, which excludes (R} but includes (D), cannot be proven false it represents no more than a new way of stating the absolute theory and can be made redundant by Perry's alternative theory which keeps the classical identity operator. In Chapter Eight various general objections to (R} are rejected: arguments which seek to show that relations which satisfy (R) fail certain conditions on identity relations. Forms of symmetry, transitivity and reflexivity and a non-Leibniz substitutivity principal are developed for (H)-relative identities. On the other hand, Geach's general argument in favour of (H)-relative identity as a means of keeping one's ontology minimal is rejected on familiar grounds. Chapters Nine and Ten deal with particular examples of (H). In Chapter Nine it is maintained that (R)-relative identity theory solves the problem of constitutivity and resolves its associated 'paradoxes' such as the ship of Theseus. It is demonstrated that arguments to show that the relation between an item and its constituents is not identity are based on absolutist principles. In Chapter Ten the standard absolutist treatment of examples of (H) is rejected as invalid.