Danish Yearbook of , Vol. 30 (1995), 7-36

THE PROBLEM OF TRANSWORLD IDENTITY

LARS GUNDERSEN Dep. of & , University of St. Andrews & Filosofisk Institut, Arhus Universitet

Introduction

Since Arthur Prior published his Past, Present and Fufure, it has been widely assumed among modal that there is some kind of connection between time and modality. One route leading to this insight - the route sketched in the present essay - is a thorough treatment of the problem of trans• world identity. The narrow scope of this essay is, thus, the problem of trans-world identity. Not the epistemological problem of how an object can be identified as the same in other possible worlds, but the metaphysical problem of how it is pos• sible, in the first place, for an object to exist in more than one world. A rather dull problem, you might think. For although a strange subject-matter, philoso• phy is, as opposed to theology, at least usually concerned with this-worldly problems. Well, it is a dull problem. But its significance becomes apparent when reflecting on how great a prevalence the so-called possible world frame• work has won in discussions of a great variety of philosophical topics. In the section following shortly it is pointed out how these various dis• courses depend for their plausibility on a satisfactory solution to the problem of trans-world identity. Furthermore it is elaborated what the exact nature of the problem of trans-world identity is and which principal difficulties any at• tempted solution will have to encounter. In the second and last section the classical solutions of and Da• vid Lewis are expounded. It is argued, however, that none of these are fully ad• equate. Kripke's suggestion - that trans-world identity is a stipulated, and hence primitive notion not to be constrained by any kind of criteria - invites relativism or/and mysticism; and Lewis' suggestion - that we can dispense with trans-world identity altogether and put qualitative determined counter• part-relations in its place - fails to do justice to basic pre-philosophical intui• tions about identity and existence. The broad scope of the essay is thus a demonstration that the problem of transworld identity cannot be solved within a classical, non-temporal dis- 8 LARS GUNDERSEN course. This does not mean, however, that the problem is impossible to solve. Rather it means that the non-temporal modal presuppositions of Kripke and Lewis are false. A feasible solution to the problem is, in short, that two objects are trans-world identical in virtue of their trans-temporal identity to a common historical ancestor. Two object's trans-world identity supervenes, thus, on trans-temporal identity relations in a branching world. There is only one such world, so the problem of trans-world identity can be brought back where it be• longs: to the class of this-worldly problems. I would have liked to elaborate further on such a solution within a temporal modal discourse but space and time have forced me to leave this constructive part of the discussion as a topic for another occasion.

1. Possible World Frameworks and the Problem of Transworld Identity. Most philosophers agree that there are other ways the world could have been, and that these alternative ways constitute the touchstone for determining the -value of sentences from modal discourses. In philosophical vocabulary these alternative ways have come to be known as 'possible worlds' and, partic• ularly in the last thirty years, many philosophical research programmes have in one way or another been centred around the challenge of giving a systematic account of how possible worlds semantics influences a number of traditional philosophical problems. In this section I shall, firstly, indicate the crucial role a possible world framework plays in a great range of intentional discourse, and secondly, present the problem which concerns the remainder of this essay, that is the problem of trans-world identity (PT!, for short) and demonstrate how the plausibility of a possible world framework depends on a satisfactory solution to PTI.

Semantics for The most obvious example of a discourse that has benefited from the possible world frameworks is of course modal logic, in particular the question of which modal inferences are to count as valid. Aristotle in his De Interpretatione at• tempted to give a systematic overview of which forms of modal inferences are sound; an attempt that has been developed and improved by many of the great medieval logicians, and in modern times with important contributions from philosophers such as c.1. Lewis. It was not until axiomatized systems were