The historical context of the Descartes-More correspondence shows Descartes defending reciprocity precisely to resist absolute space, not primarily to rebut Scholastic property theories.
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Scholastic(describes the philosophical tradition being discussed)
A style of philosophy developed in medieval Europe that tried to combine Christian theology with the logical methods of ancient Greek philosophers.
absolute space(Newtonian mechanics, critiqued by Einstein and Mach)
Newton's concept of a fixed, unobservable spatial framework with respect to which true motions are defined; the reference frame to which Foucault's pendulum was said to remain aligned
reciprocity(Condition for full intersubjective communion in disponibilité.)
The mutual presence of availability in both parties of an intersubjective relationship, necessary for the relationship to fully realize itself though it cannot be demanded.