Wednesday, March 11, 2009

MacLaurin, Clarke Velocities, and Powers

I've been reading various obscure sources recently as I investigate early interpretations of Newton and how they might have influenced Hume's understanding of space, time, body, souls, and scientific method. I came across this (to me) rather surprising passage from Colin MacLaurin's A Treatise of Fluxions in Two Books (1742). MacLaurin was a friend of Hume in Edinburgh, a key figure in the "Scottish Englightenment," and one of the premier mathematicians of his day. This passage comes from the book in which he attempts to explain recent developments in mathematics (especially in differential calculus) to an educated non-sophisticate.
It is indeed generally allowed, that if a body was to be left to itself from any term of the time of its motion, and was to be affected by no external influence after that term, it would proceed for ever with an uniform motion, describing always a certain space in a given time: and this seems to be a sufficient foundation for ascribing, in common language, the velocity to the body that moves, as a power. It is well known, that what is an effect in one respect, may be considered as a power or cause in another; and we know no cause in common philosophy, but what is itself to be considered as an effect: but this does not hinder us from judging of effects from such causes. However, if any dislike this expression, they may suppose any mover or cause of the motion they please, to which they may ascribe the power, considering the velocity as the action of this power, or as the adequate effect and measure of its exertion, while it is supposed to produce the motion at every term of the time. (Book 1, p. 54)
What interests me in this passage is his seeming indifference to whether something counts as a cause or an effect. On first reading, I thought MacLaurin was making the relatively uninteresting point that one thing (B) can be both an effect (of A) and a cause (of C). This is suggested when he says "what is an effect in one respect, may be considered as a power or cause in another." But his next sentence is more revealing. He offers that an unhappy reader may "suppose any mover or cause of the motion they please to which they may ascribe the power." This echoes his earlier line that the velocity of a moving body is "a power."
This is interesting because it is a break from a particularly influential reading of Newton that was popularized by Samuel Clarke. Clarke argued that since matter was incapable of self-motion, it had no power of its own. Therefore, to explain the introduction of motions into the world, we have to posit the existence of non-material souls. These souls can't be merely human, since motion shows up where humans aren't, so we have an argument for the existence of God (or at least other non-human souls; we get to God in needing to explain the existence of non-necessary matter). According to Clarke, Newton's world can't exist without God pushing matter around (or appointing lesser souls to do the pushing). (There is evidence to suggest that this was Newton's preferred hypothesis, when he felt like positing hypotheses.)
What MacLaurin is suggesting is quite radical in saying that one needn't invoke God to explain the power of motion. It's just as good from the perspective of Newtonian philosophy to refer to the powers of the bodies as it is to say that the bodies' motions are the effects of some other being. Whether velocity is the cause of the motion or the effect of the true cause of the motion makes no difference to studying velocity. This idea, which would not have been missed by Hume, not only does away with the need to posit "powers" in nature, it also does away with the need to invoke God to explain the Newtonian world. MacLaurin isn't suggesting here that one can do away with both of these hypotheses; he may have thought either one worked just fine, so he wouldn't push for either (in this place). It wouldn't be until Hume that we get a suggestion that one could do away with all these hypotheses and proceed in science and philosophy with mere regularity.
(Note: I'm not suggesting that it was Hume's reading of MacLaurin's Treatise of Fluxions that influenced his writings; Hume's Treatise, after all, was published first. But it is likely that MacLaurin was an important source of Hume's ideas about natural philosophy, if not while a student then at least in their friendship.)
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