On Hutcheson stopping Motion and a hidden, perhaps, polemic with Spinozism

This universal Benevolence toward all Men, we may compare to that Principle of Gravitation, which perhaps extends to all Bodys in the Universe; but like the Love of Benevolence, increases as the Distance is diminish’d, and is strongest when Bodys come to touch each other. Now this increase of Attraction upon nearer Approach, is as necessary to the Frame of the Universe, as that there should be any Attraction at all. For a general Attraction, equal in all Distances, would by the Contrariety of such multitudes of equal Forces, put an end to all Regularity of Motion, and perhaps stop it altogether.--Frances Hutcheson (1726) An Inquiry into the Original of Our Ideas of Beauty and Virtue.

In a lovely paper that he delivered in Ghent on Wednesday, Tamas Demeter made good use of the eminently quotable paragraph, with its seductive comparison between benevolence and Newtonian gravity, quoted above. Ignoring Newton's strictures, Hutcheson implies that attraction is governed by sympathy (see here). The image has a non-trivial after-life in Hutheson's student and astute critic, Adam Smith ("All the different members of it are bound together by the agreeable bands of love and affection, and are, as it were, drawn to one common centre of mutual good offices," [HT Ryan Hanley]) as well as in Smith's careful reader, Wollstonecraft ("private virtue becoming the cement of public happiness, an orderly whole is consolidated by the tendency of all the parts towards a common centre,") [recall this post].

But my eye rested on the final sentence of Hutcheson's paragraph which expresses a counterfactual about the impossibility of an alternative force-law. (Not all possible alternatives, of course.) When you start thinking about it, he seems he has packed quite a bit into the claim. Hutcheson really makes two counterfactual predictions about what would happen if there was uniform gravity (so not based on distance [presumably just based on masses]) in the universe: (a) motion would stop being regular or (b) motion would stop altogether. I focus on (b) first; this is really a kind of anti-cosmogeny. It claims that the world could not have evolved with such a force law.

In fact, Hutcheson's second (b) point ("a general Attraction, equal in all Distances, would by the Contrariety of such multitudes of equal Forces...stop [motion] altogether") sounds (recall this post) akin to a claim that Clarke makes against Spinoza: “because the determination of this self-existent motion must be every way at once, the effect of it could be nothing else but a perpetual rest; it's a an argument that I have long struggled with (see this paper). For the aficionados: I am pretty sure that the then also famous Bentley-Newton correspondence got started by a (now lost) question from Bentley to Newton to rule the possibility of the solar system evolving out of a homogeneous plenum (which the English think Spinoza ought to embrace) with Newtonian force laws. Hutcheson's (b) seems 'intuitive' because one can understand the idea that all forces can cancel each other out so that there is no motion.

But one thing Hutcheson's counterfactual thought experiment, (b), requires is that matter needs to be uniformly or symmetrically distributed (through the infinite universe). Otherwise there is no reason to think that all the possible forces would simply cancel each other out from the start, forever. (We leave aside Norton dome style thought experiments--from my Marij Van Strien's work we know these were familiar in the 19th century, but there is no evidence they were really understood at the start of the 18th century [NB the wikipedia page is weak on the history].) So, contrary to the argument of the General Scholium, Hutcheson is tacitly assuming something like a plenum here (at least as the starting point of cosmogeny). Why he would do so is odd, unless the paragraph originates in an earlier polemic against Spinozism (or the impious development of Cartesianism)? This is a plausible inference, given that Hutecheson is familiar with the polemics surrounding Spinoza and Toland (see here and here), and Hutcheson is often at pains at showing and/or assuming the existence of final causes.

I have to admit I am a bit stumped by Hutcheson's first claim that motion would stop being regular with a uniform universal attraction. I don't recall Newton modeling that force law. (Newton does model alternatives to the inverse square law.) So, I'll have to check the Principia. I would guess that (regardless of initial conditions), such a force law would result in a gigantic clump of matter in the middle of the universe. But I'll chew on this.*

 

 

*I thank Tamas Demeter, Maarten Van Dyck, and Daniel Schneider for discussion. I should be blamed for any blunders in this argument.

Comments

[Mark Behets]

1. I'm surprised that you agree with the b) argument of Hutcheson. If we can assume that his argument is based on Newtonian theory -and I see no reason to assume that it isn't-, than it confuses motion with accelaration. If all forces working on an object cancel each other, than it will not accelerate but continue its situation of rest or of motion in a straight line with a constant speed. (This is also true in Spinoza's physics -although Wim Klever is strongly denying this-: if there is no cause which can change the situation of a moving object, it continues its motion, driven by its conatus.)
2. The tacit assumption that matter is uniformily spread over the infinite universe is -according to my knowledge- also an assumption of Newton, which he needs to explain that the universe is static. If there was a point in the universe where matter was more concentrated than in the rest of the universe, all matter would be attracted to this point and move to it, which would imply that the position of the stars is not static (which Newton would not accept).
3. I see no possible explantion for the these a) of Hutcheson.

[David Wallace]

To Mark: I don't know the history here, but as a matter of physics, (a) the inverse-square-law form of Newtonian gravity isn't well defined in an infinite homogenous universe (the net force depends on the order in which the forces are summed) and (b) even in versions of Newtonian gravity that work around that problem, an infinite universe isn't static -it needs to be expanding or contracting.

[Eric Schliesser]

Mark, on your 1. David Wallace is right (and this was understood by Newton). And, moreover, the way the problem of forces canceling is standard-ly understood during the period is in the context of cosmogeny (or the origin of first motion) and the nature of matter. Mark on your 2. Newton explicitly denies that matter is uniformly spread over the universe. He solves the problem you discern by insisting that individual solar systems are so far apart that they won't fall in on each other. (Also, it is by no means obvious that Newton things the position of the stars is static.)
David, I don't think Newton thinks the universe is expanding or contracting, but I admit that I have not looked carefully at all his cosmological papers. (I should ask Chris Smeenk.)

[Mark Behets]

Thanks David and Eric for your clearing out Hutcheson's conclusion that motion would not start if gravity did not depend on distance.
As to the static universe: on the internet you can find a lot of references that Newton was convinced the Universe is static - even Einstein first intruduced a cosmologic constant in his general reltivity to make it compliant with a static universe. But the internet can be wrong of course.

[Mark Behets]

David and Eric, thanks for making it clear to me how Hutcheson came to his conclusion about the (non) start of motion.
The reason I thought Newton believed in a static universe where all starts hold each other in an (unstable), is following extract from one of his letters (Isaac Newton to Richard Bentley, dated 17 January 1692/3):
"The reason why matter eavenly scattered through a finite space would convene in the midst you conceive the same with me: but that there should be a Central particle so accurately placed in the middle as to be always equally attracted on all sides & thereby continue without motion, seems to me a supposition fully as hard as to make the sharpest needle stand upright on its point upon a lookingglass. {ffor} if the very mathematical center of the central particle be not accurately in the very mathematical center of the attractive power of the whole mass, the particle will not be attracted equally on all sides{.}

And much harder it is to suppose that all the particles in an infinite space should be so accurately poised one among another as to stand still in a perfect equilibrium. ffor I reccon this as hard as to make not one needle only but an infinite number of them (so many as there are particles in an infinite space) stand accurately poised upon their points. Yet I grant it possible, at least by a divine power; & if they were once so placed I agree with you that they would continue in that posture without motion for ever, unless put into new motion by the same power. When therefore I said that matter eavenly spread through all spaces would convene by its gravity into one or more great masses, I understand it of matter not resting in an accurate poise."

[Eric Schliesser]

Mark, the letter you quote is an answer to a hypothetical question that Bentley posed him (about, I suspect, what a Spinozistic cosmogeny would look like). In the General Scholium, Newton quite clearly denies that matter is evenly scattered through the universe.

[Eric Schliesser]

We have to be careful about the use of 'static.' Newton quite clearly thought that space and time were co-eternal/co-extensive with God or God's being and, thus, infinite in various senses. (He says as much in General Scholium.) But he tends to suggest that matter would have been created by God's free will. Newton was very coy about what this entailed for the future evolution of the universe.

[Mark Behets]

Eric, thanks for your answers. My knowledge about Newton is clearly too limited. However, I’m still confused about Newton stating that matter is not evenly scattered through the universe. As I see it, this would imply either of the following possibilities: i) either the non-evenly distribution of matter is exactly compensated by their position, in a way that Newton described in his letter above (“accurately poised one among another as to stand still in a perfect equilibrium”), ii) or there is no equilibrium, and although the stars are placed on immense distances from each other, they are moving. As I found the issue intriguing, I could not resist to digging further into it and to do some “finds” in the Principia, where I found in Book III, Proposition XIV, cor. 1:
“And since these stars are liable to no sensible parallax from the motion of the earth, they can have no force, because of their immense distance, to produce any sensible effect in our system. Not to mention that the fixed stars, everywhere promiscuously dispersed in the heavens, by their contrary attractions destroy their mutual actions.”
This seems to indicate that Newton’s position corresponds to possibility i) above. But as I do not have have knowledge of the full content of the principia, possibly I’m not understanding the correct context of this citation?

[Eric Schliesser]

First, Mark, you quote the Bentley correspondence out of context. (I already said that above.) He is answering a how-possible question by Bentley. Second, as Leibniz discerned, and Newton kind of acknowledges in the Queries to the Opticks there is no guarantee of equilibrium in Newton's understanding of either the solar system and at larger cosmological scales. (It is unclear if the active principles can guarantee it or if God who rewinds things is required.) Third, the passage you quote from the Principia says two main things:(i) that the various solar systems/stars are too far apart to have an effect on each other (something he repeats in the General Scholium where it is part of an argument to design)--that is orthogonal to homogeneity issue, although (ii) Newton's 'promiscuously dispersed' is a clear denial of homogeneity, too, (it means disorderly organized). (This, too, is repeated in the General scholium.) This is not to deny that he also seems to have thought that their actions cancel each other out, and it is unclear why he thinks he has evidence for that.