Az 5D nem menti meg az S4 logikát

Absztrakt

S4 is a system of modal logical whose characteristic axiom states that whatever is necessary, is necessarily necessary. In standard possible world semantics the axiom is valid only if the accessibility relation between possible worlds is transitive. However, Hugh Chandler has presented a powerful argument against the axiom of S4. The argument is based on a sorites about the origin of material objects, such as, a bicycle. A bicycle could have originated from slightly different parts, but could not have originated from totally different parts. But we can construct a sequence of possible worlds in which the same bicycle has less and less original parts, until we reach a possible world where it originates from totally different parts. To block the inference Chandler rejects the transitivity of the accessibility relation, which makes the axiom of S4 invalid. In his recent paper Takashi Yagisawa offers a different solution in order to save S4. His solution is based on his five-dimensionalism (5D) which postulates that objects are modally extended. To block the inference Yagisawa uses overlapping five-dimensional objects and reference shifting names. In this paper I argue that Yagisawa fails to save S4 with 5D. My objection is that his device of reference shift allows us to generate true contradictions at possible worlds. I take this consequence to be far more negative than the theoretical advantages his theory may otherwise have. At the end I also consider a potential reply to my objection based on Yagisawa’s notion of modal centeredness, which I will eventually reject.