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On the Interpretation and Transitivity of Non-standard Synchronisms

In the first section I discuss the interpretation of non-standard synchrony, and state the Principle of Committed Directionality (PCD) which is assumed in the balance of the paper. Section 2 provides a derivation of the general expression for E in three spatial dimensions, which agrees with one previously published for two spatial dimensions in the special case that E is symmetric about the x-axis. In an appendix, I illustrate the use of this expression by offering another proof of the intransitivity of nonstandard synchronisms amongst non-collinear points. In the third section I consider synchronisations in which E is a function of time. The final section examines the claims of Quinn that collinear synchrony can be intransitive and that there is a method of setting clocks which results in non-standard synchrony among non-collinear points being transitive, and finds that they fail, unless PCD is rejected.