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The Logic of Finite Order

This paper develops a formal system, consisting of a language and semantics, called serial logic ( SL ). In rough outline, SL permits quantiﬁcation over, and reference to, some ﬁnite number of things in an order , in an ordinary everyday sense of the word “order,” and superplural quantiﬁcation over things thus ordered. Before we discuss SL itself, some mention should be made of an issue in philosophical logic which provides the background to the development of SL , and with respect to which I wish to contend that the system permits progress.