 We cannot avoid the difficulties associated with sequences by appealing to the Kuratowski definition of sequences in terms of unordered sets (where, e.g., \(\langle x, y\rangle = \{\{x\}, \{x, y\}\}\)) (or Bergmann’s Kuratowski inspired account of order in terms of ‘diads’, see his 1981: 147). There are indefinitely many other set-theoretic constructions upon which we may rely to model sequences, e.g., Wiener’s, hence the familiar objection that we cannot legitimately fix upon any one such construction as revelatory of the nature of sequences (see Kitcher (1978: 125–6) generalising upon a point originally made by Benacerraf (1965: 54–62)). But there is also the less familiar objection that the Kuratowski definition cannot be used to analyse the order inherent in the sequence \(\langle x, y\rangle\). Compare: we cannot analyse personal identity in terms of memory because it’s built into the what we mean by memory that you can only remember your own experiences, i.e., the very notion that we set out to explain, viz. personal identity, is presupposed by our analysans. Similarly \(\{\{x\}, \{x, y\}\}\) only serves as a model of \(\langle x, y\rangle\) relative to the assumption that the thing that belongs to a singleton member, namely \(\{x\}\), of the first class comes first in the pair \(\langle x, y\rangle\), so the notion of order is presupposed (Hochberg 1981, 2001: 176–7).