On the interaction between bodies and abstract Mathematical quantities; on Newton's Vis Insita as Inherent, Innate, and essential

Def. 11 12.  The force of a body or inherent and innate to a  body The _Ùinherent, innate, and essential force [vis insita, innata, et essentialis]_Ù of a body is the power by which it endeavors to perseveres in its state of rest or of moving uniformly in a straight line.  It is proportional to the quantity of the body, and is in fact exercised proportionally to the change of bearing [allatae] state, _Ùand in so far as it is exercised it can be said to be the exercised force of the body endeavoring and struggling against [conatus et reluctatio]   Of this kind  , of which one kind is the centrifugal force of rotating [bodies] [gyrantium]_Ù.--Isaac Newton "De Motu Corpurum in mediis regulariter cedentibus," translated by George Smith. 

The quoted passage is from one of the sequence of manuscripts that Newton wrote between Halley's famous visit to Cambridge and the Principia. It caught my eye while I was editing one of George's entries forthcoming in The Oxford Handbook of Isaac Newton. In his biography of Newton, Richard Westfall mentions the first sentence, in passing, as part of a "struggle" to clarify the relation between inherent and impressed force. And, in fact, since we are dealing with a conceptualization of inertial motion, what Newton means by vis insita or inherent forces is of central importance to understanding the Principia. So, for example, in his classic (2006) article, on the subject of inherent and centrifugal forces, Domenico Bertoloni Meli also quotes the passage. But the fact that Newton couples this vis insita with innateness and essence goes unremarked. I mention Westfall, Smith, and Bertoloni Meli as exemplars of a certain kind of reticence among leading Newton scholars to analyze some of Newton's metaphysics while he was developing the Principia. More surprisingly, Alan Gabbey, who -- together with the two giants of Newton's metaphysics, Howard Stein and Ted McGuire -- has never exhibited such reticence, also quotes the passage (back in 1971), but does not explore its meaning.

Recently, George, in a recent paper devoted to confirming Stein's conjecture "that Newton's conception of forces of nature as forces of interaction “was actually developed by Newton at the same time that he was discovering the law of gravitation,”" (Smith quoting Stein) notes, while commenting on a disagreement between Stein and me "about metaphysics of Newtonian gravity," "I have no objections to anyone's citing passages from Newton's writings in an effort to extract his “metaphysical” thinking, for where else can one turn to. I question, however, how much weight can be put on Article 21 [that appeared posthumously]. As already noted, nothing remotely akin to it appears in any edition of the Principia, nor for that matter in any other publication or extant manuscript."* Smith is right about that. (The implicature of his comment puzzles me: on the first two pages of my paper, I had, in fact, asserted three times that I was attributing a view to Newton that he held when he was drafting/writing the Principia, but no more than that.) But even metaphysical ephemera can be interesting, even illuminating.

This post makes no claim about the wider significance in Newton's thought of the passage quoted above. The first thing to notice about the first sentence is that the power of a body by which it  perseveres in its state of rest or of moving uniformly in a straight line is not treated as a property or quality, but as a force of that body. Descartes' first two laws of motion do not such thing.+ 

So, there are three questions worth asking: first, what is a force of a body? Second, what makes a force inherent, innate, and essential.' Third, why, in the Principia, did Newton drop the claim that this force is 'innate and essential.' For (on this third question), when in the Principia, he returns to something very much like the idea of definition 12 (quoted above), is to be found in definition 3 (of the Principia): "Inherent force of matter is the power of resisting by which every body, so far as it is able, perseveres in its state either of resting or of moving uniformly straight forward." And in the very next sentence, Newton adds "This force is always proportional to the body and does not differ in any way from the inertia of the mass except in the manner in which it is conceived."  Of course, in comparison to the quoted passage above, in the Principia, Newton adds the very striking claim that vis insita is identical to the inertia of the mass, except (and this is no less striking) in the manner of conceiving them. 

As it happens, for independent reasons scholars have argued (and agreed, I think) that in the Principia, Newton treats forces are abstract mathematical quantities (this is pretty clear from the corollaries to the laws.)  Of course, it is not entirely clear what to make of the claim that a body's force just is an abstract mathematical quantity. Earlier Newton has explained that when he uses 'mass' he just means the "quantity of matter" which "is a measure of matter that arises from its density and volume jointly." (This is definition 1 of the Principia.) So, while it is tempting to treat inertia as a property of body, it too, is a feature of mass, which is a quantity, and in turn, a measure of two physical parameters (density and volume). So, that vis insita is identical to the inertia of the mass just is to say that two abstract mathematical quantities related to bodies are alike. (Newton's conception of mass is an abstract feature shared by all bodies.)

Because it is common since the advent of relativity theory and the quantum revolution to present Newton's ontology as kind of commonsensical (with modest allowance for the strangeness of the possibility of action at a distance), that it is sometimes forgotten or underestimated that even the building blocks of Newton's physics are, from an ontological perspective, quite unusual. That Newton was innovating helps explain that, as Zvi Biener and Chris Smeenk have shown in an eye-opening article, that there are tensions lurking here between a geometric conception of body and what they call dynamic conception of body (looking forward to Boscovitch), as a collection of forces.** 

This generates a hypotheses about why Newton dropped the very idea of inertia as "an innate and essential force" from the Principia. Once one starts treating forces as abstract mathematical quantities that can be measured (mediated by theory, perhaps) and that are (interpreted as) causes of motion, it is unclear what is gained by treated them as innate or essential or not.  (And one can discern an interest in measurement behind the idea of 'exercised proportionally.') That's just the kind of metaphysics that, say, George Smith finds irrelevant to the evidential practice (and something similar seems to lie behind Parker's comment quoted in the note).* Fair enough.**

Be that as it may, as it happens, in Rule 3 of the Principia, Newton explicitly claims that vis insita is "immutable." In addition, he is explicit that vis insita is a means to establish that movability and perseverance are universal properties in bodies given the third rule that encourages us to make an inductive leap from the finding of particular properties of bodies without exception to the commitment that these "be taken as qualities of all bodies universally." And Newton then suggests that there is a contrast between universal and essential qualities of matter. The third rule is a means toward the former not the latter. Interestingly, it is quite natural to read Newton in the third rule as claiming that while gravity is merely universal and not an essential quality of matter, vis insita is not just universal and an essential quality of matter (as evinced by its immutability). This would be an echo then of definition 12 in the passage quoted from De Motu at the top of this post.

At this point, I need to make a modest detour. The trio, 'inherent, innate, and essential,' has a notorious afterlife because, in a famous letter to Bentley, of february 1693 (it's been frequently cited by physicists and scholars), Newton denies "that gravity should be innate, inherent, and essential to matter." In the previous sentence, Newton had asserted that 'it is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation in the sense of Epicurus, be essential and inherent in it." In earlier letters Newton had complained that Bentley had attributed to him the idea that gravity is inherent and essential to matter. Presumably, Bentley had sent Newton the sermon he had preached (the seventh of the Boyle lecturers), on November 7, 1692, and which he was preparing for publication, for comments to Newton.

As an aside, in the published (1693) version of Bentley's sermons, Bentley continued to tie Newton's theory to Epicurus', but limited the similarity to the claim "that the weight of all Bodies around the Earth is ever proportional to the quantity of their Matter." (Bentley, a famous classicist, adds a footnote to Lucretius.) Bentley goes on to add that Newton and the Epicureans also agree on the existence of a vast vacuum of empty space in the universe. He then draws a distinction between two kinds of atheist cosmogonies (one he labels epicurean, and another which is more crypto-Spinozist, of a sort later defended more explicitly by Toland.) He then insists that both will be refuted on the assumption that "mutual gravitation or spontaneous attraction can neither be inherent and eſſential to Matter; nor even supervene to it, unless impressed and infused into it by a divine power." This superaddition of gravity thesis has been recently defended (not by me, but) by John Henry as indeed Newton's own view (in part on the basis of Newton's letter to Bentley.)

What Newton has meant by his rejection that gravity is 'inherent, innate, and essential' quality of matter has been subject of much scholarly controversy (and I have been one of the partisans). But because of that debate, it seems to be agreed that by an 'essential quality' of matter Newton means it is a quality, or necessary condition, required for the existence of matter. And so understood one can see why Newton would have been tempted in De Motu to call vis insita essential, because it is the feature that is required for (to speak anachronistically) the physics he is pursuing. Without the power by which a body "perseveres in its state of rest or of moving uniformly in a straight line" it wouldn't be the kind of entity Newton is studying.++ 

Now, in the previous paragraph I moved from ontology to epistemology. That's partially because the Rules for the Study of Natural Philosophy in the Principia themselves seem to give the reader, as Zvi Biener and I argued, at most the ontology apt for the epistemic attitude to be taken in the context of natural philosophical research. And this ontology is, thus, more provisional than talk of 'essential' qualities seem to suggest.

Andrew Janiak has suggested, that for a quality to be “innate”  is to think of it as due to no other physical process, entity, or medium between material bodies.*** So, an innate quality is to be a kind of contrast to a relational quality (which generates from, say, an interaction). To the best of my knowledge Newton calls no quality or power innate in the Principia.

That Newton dropped the claim that vis insita is an innate quality of body can then be readily explained I think. Between the draft quoted at the top of the post, Newton came to think of natural forces as forces of interaction. This is, in fact, the very point of Smith's recent article on Stein I quoted above (and was assumed by me under the influence of Stein).+++ And, evidentially, these forces are manifested in and measured by interactions (in part, as 'struggle' against change, etc.) And, in the Principia, Newton is explicit that these forces are both causes and effects of the interactions of bodies.

Famously, Descartes' metaphysics floundered on the mysterious interaction between bodies and souls. It is worth noting that in Newton there is an interaction between bodies and abstract mathematical quantities. If we focus on the measurement practice this is not mysterious at all and it generates, as Smith shows in his majestic "Closing the Loop" ever more stringent evidence. But if we step back, and ask ourselves how to conceive of the interaction between bodies and abstract mathematical quantities, one is left somewhat speechless.

 

*In a very fine, recent prize-winning paper, Adwait Parker mentions my position as "a metaphysical reading of Newtonian force reconciling the published English edition of Liber secundus (i.e., A Treatise of the System of the World) with Principia."  

+“that each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move”; “all movement is, of itself, along straight line." 

**Parker, however, very nicely distinguished two "kinds of mass by the measurement procedures available to Newton." 

++Newton scholars will recognize echoes of Katherine Brading's law-constitutive interpretation of Newton on body here.

***See p. xxiv the introduction to his edition/translation of Newton's Philosophical Writings. Janiak treats inherent and innate qualities as synonyms.  I am not sure that is right. 

+++Since Smith and Stein were my teachers this should not surprise.

Comments

[Alan Nelson]

Very interesting!

A small footnote. To say that mass is a quantity "arising" from density and volume, does not imply that density is a property rather than another quantity. For *density of a body* must be defined as: .

The trouble in getting the metaphysics to bottom out pushes one toward an epistemological outlook.

[Marius]

Another small footnote. I took feel like Alan, broadly. The epistemology must drive the metaphysics, not the other way around -- at least as far as the later Newton is concerned.

From that vantage point, I don't understand the difference between 'essential' and 'merely universal' properties of body. There's only one generic pattern of evidential reasoning, in Newton: deduction from phenomena. Ipse dixit. How is the essential/universal distinction to be drawn, if we infer to them by the same logic?

Answer: essential properties are explanatory; or explanatorily more basic than just universal traits. Objection: Newton doesn't have a theory of (scientific) explanation. He has a logic of evidence/confirmation theory, but that's it.

So...

[Eric Schliesser]

Good point, Alan. I tried to finesse the issue by using 'parameter'

[Eric Schliesser]

Ah, Marius, two remarks: (i) the later Newton is an achievement, and I'd like to help explain how he got there. (ii) As Zvi and I note in our (relatively recent, but ignored) paper on Newton's laws, we really distinguish between two perspectives in Newton: the epistemological one that predominates within the study of nature, and another, a kind of psychological condition of possibility that is more speculative and metaphysical that we find on the margins, in the notes, and -- crucially the scholia and queries.

[Marius]

Thanks, Eric. This helps.
(I don't ignore your paper, for the record. I've been discussing it just recently, with a fellow Newtonian who's writing on the same topic.)

And, yes, it is fascinating to see how Newton moves from the probing, conjectural register to the but-here's-what-the-evidence-allows-us-to-claim stance. I think it's becoming the new trend in Newton historiography, at least in the circles I frequent. Reconstructing the inferential paths that start in the notes and deleted drafts, and end with the considered views. Hard work, but rewarding and useful.