"In physics sense and experience which reach only to apparent effects hold sway; in mechanics the abstract notions of mathematicians are admitted. In first philosophy or metaphysics we are concerned with incorporeal things, with causes, truth, and the existence of things. The physicist studies the series or successions of sensible things, noting by what laws they are connected." (Berkeley, De Motu 71, [Translated by Luce].)
Yesterday, I mentioned that aspects of Hume's Treatise belong to eighteenth century anti-mathematics without explaining what I meant by the term. By "anti-mathematics" I mean expressed reservations about the authority and utility of (Newtonian) mathematical sciences, especially the application of mathematics in inquiry into nature. (I have done posts on this theme before, recall these posts on Mandeville here and here; and on Adam Smith here). I distinguish between two general strategies (although in practices the strategies may be blended): (i) "the devaluation" strategy," which tries to undermine the epistemic status (recall my post on Hume) or epistemic reach of the mathematical sciences; and (ii) what I call a "containment" strategy, which grants the success of Newtonian science, but insists that there are domains of natural inquiry in which applying mathematics lacks utility or is inappropriate (see, for example, Mary Domski's beautiful paper on Locke). While in my story anti-mathematics originates in Spinoza ("Letter on the Infinite"; I quoted a crucial passage here), the strategies get developed in response to efforts to use the authority of Newtonian natural philosophy to settle debates within philosophy (something I call "Newton's Challenge to Philosophy").
This doctrine is a frontal attack on the Newtonian program, which aimed to establish “the motions that result from any forces whatever and of the
forces that are required for any motions whatever” (Newton, Principia, preface to the reader; see here a link to a 1728 translation). Newton's definitions had offered (mathematical) theory-mediated measures for such various forces. And Newton's "rules of reasoning" are explicitly directed at causal ascription (see the first two rules here). More important, the fourth rule argues that the results of Newton's experimental philosophy should be taken as "accurately, or very nearly true;" now, in one sense this is (as George Smith has emphasized) an articulation of Newton's fallibilism, but Newton also does not leave room for some, alternative higher science to settle the truth of the causes.
Before I turn to the status of gravity or action at a distance, it is worth reiterating this last point; forces cause changes in motion (see the second law). Universal gravity is just one of these forces. Now because Newton had admitted that he does not know the cause of gravity, he left himself to an instrumentalist reading (one, in fact, advocated by his follower Clarke as Andrew Janiak nicely shows). But Newton thought that one could accept gravity as a genuine cause without knowing its physical instantiation/mechanism. After all, otherwise any causal explanation would be open to an infinite regress of demands of having the causes of causes demonstrated before they could be accepted.
Now, early Berkeley is often associated with instrumentalism about forces (see this nuanced piece by Lisa Downing). But in a sense this understates what he is up to when it comes to gravity, Berkeley insists that "since the cause of the fall of heavy bodies is unseen and unknown, gravity...cannot properly be styled a sensible quality. It is, therefore, an occult quality." (De Motu, 4.) That is to say, there is nothing that needs to be provisionally accepted, and, therefore, nothing that calls out to be explained. Any claims on behalf of gravity that understand it as a really existing cause land the Newtonians with the commonly despised scholastics.