In both syntax and phonology, it has long been observed that significant restrictions exist on displacement. One such restriction ensures that displacement leads to sequences of elements which are in some sense contiguous, formalised in syntax in the concept of Feature Geometry-based Relativised Minimality by Starke (2001) and Contiguous Agree by Nevins (2007), and in Autosegmental Phonology by the Line-Crossing Prohibition (originating in the Well-formedness Condition in Goldsmith 1976).

I argue that effects of this type, which have been called Contiguity Effects, are best captured by taking displacement to involve total weak orders of elements in the sense of Order Theory. Building on work taking the LCA to hold throughout the derivation, I argue that precedence relations may be the basis of phrase structure, though without claiming that linearisation is necessary for LF (as for example suggested in Kayne 2013). I then develop this approach to show that Order Theory provides useful axioms for both phrase structure and displacement, and that the existence of displacement is expected given the use of Order Theory.