Split identity: intransitive judgments of the identity of objects.

Identity is a transitive relation, according to all standard accounts. Necessarily, if x=y and y=z, then x=z. However, people sometimes say that two objects, x and z, are the same as a third, y, even when x and z have different properties (thus, x=y and y=z, but x≠z). In the present experiments, participants read stories about an iceberg that breaks into two icebergs, one to the east and the other to the west. Many participants (32-54%, in baseline conditions across experiments) decided that both successors were the original iceberg, despite the different spatial locations of the successors. Experiment 1 shows that this tendency is not due to participants failing to understand both to mean both are simultaneously the original. Similarly, Experiment 2 demonstrates that the tendency is not solely due to their interpreting the question to be about properties of the icebergs rather than about the icebergs themselves. Experiments 3 and 4 suggest, instead, that participants may understand Which is the original? to mean Which, in its own right, is entitled to be the original? Emphasizing entitlement increases the number of seemingly intransitive responses, whereas emphasizing the formal properties of identity decreases them.