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Relationalism

This article contributes to the debate of the meaning of relationalism and background independence, which has remained of interest in theoretical physics from Newton versus Leibniz through to foundational issues for today's leading candidate theories of quantum gravity. I contrast and compose the substantially different Leibniz--Mach--Barbour (LMB) and Rovelli--Crane (RC) uses of the word `relational'. Leibniz advocated primary timelessness and Mach that `time is to be abstracted from change'. I consider 3 distinct viewpoints on Machian time: Barbour's, Rovelli's and my own. I provide four expansions on Barbour's taking configuration space to be primary: to (perhaps a weakened notion of) phase space, categorizing, perspecting and propositioning. Categorizing means considering not only object spaces but also the corresponding morphisms and then functors between such pairs. Perspecting means considering the set of subsystem perspectives; this is an arena in which the LMB and Rovelli approaches make contact. By propositioning, I mean considering the set of propositions about a physical (sub)system. I argue against categorization being more than a formal pre-req