From Conceptions of Space and Time by Akhundov (p. 115)
The nonphysical character of action-at-a-distance disturbed even Newton, who attempted to develop a short-range theory of gravitation. The crux of the matter, however, is that action-at-a-distance is connected not with gravitation but with the conception of space and time. As Kuznetsov notes:
In Newton’s physics, forces were distributed rectilinearly over infinite distances. These Newtonian forces—the instantaneous, extratemporal interactions of bodies—were the physical framework of Newtonian space, which existed independently of time.
Here there is also a certain paradox that in general inevitably accompanies absoluteness (absoluteness is internally paradoxical). Thus action-at-a-distance, which was incorporated in Newton’s system to substantiate absolute space and time, repudiates the very idea of space and time. Acceptance of action-at-a-distance denies the continuity of absolute space and time, introducing into them absolute disruption.
The extratemporality of forces acting at a distance is intrinsic to their instantaneous essence. Emile Meyerson has also discussed their extraspatiality:
The hypothesis of action at a distance consists in supposing that one phenomenon is the condition of another and that nothing happens in intermediary space. Assuredly it will be affirmed that intermediary space is traversed by force. But the two phenomenon being simultaneous, force does not cross space; it leaps over it, if we dare express it thus.
This leads Meyerson to conclude that the idea of instantaneous action-at-a-distance is destructive of the concept of space.