Archive for June, 2017

In the first two editions of the Principia, Newton makes two pronouncements about the scope of natural philosophy that appear to be in tension with one another. In the first (1687) edition Preface to the Reader, Newton writes, “the basic problem of [natural] philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces” (Janiak 60). In the famous General Scholium added to the second (1713) edition, Newton writes, “to treat of God from the phenomena is certainly a part of natural philosophy” (Janiak 113). We know from Newton’s correspondence that this was a late addition to the text (Janiak 158).

These two pronouncements are not inconsistent, for the first claims that a certain class of questions constitutes “the basic problem of [natural] philosophy,” while the second claims that a different, apparently disconnected, class of questions is “a part of natural philosophy.” Nevertheless, there seems to me to be a tension, for if natural philosophy is a unified enterprise then one would expect all of the questions it asks and answers to be tightly connected with its “basic problem” and unless one thinks (as perhaps Descartes does?) that force is divine action or something, then it is unclear that this further question is tightly connected in this way. Perhaps Newton thinks that a legitimate but peripheral question for natural philosophy is why God has created the specific forces that exist, rather than other forces, or perhaps he simply doesn’t think of natural philosophy as a tightly unified enterprise organized around “the basic problem”. This is not spelled out in the General Scholium, and indeed the paragraphs on God have the appearance of an irrelevant digression.

What I want to suggest is that Berkeley’s De Motu (1721) can be seen in part as a defense of rigorous adherence to Newton’s position in the first edition preface (reinterpreted in light of Berkeley’s own account of force) as against Newton’s remark in the General Scholium.

In the Principles (1710), Berkeley refers to natural philosophers as “Those men who frame general rules from the phenomena, and afterwards derive the phenomena from those rules” (§108). This appears to be an echo of Newton’s first edition Preface. Curiously, though, Berkeley omits all mention of force, which is the central concept in Newton’s physics. More generally, in the Principles, Berkeley shows very little concern about the nature or status of force, and it is unclear whether he even really recognizes its importance to Newton. This oversight is rectified in De Motu.*

In De Motu Berkeley writes:

in mechanics, notions are initially established—that is, definitions and first general statements about motion—from which more remote and less general conclusions are subsequently deduced by a mathematical method. And just as the magnitudes of particular bodies are measured by applying geometrical theorems, so likewise the motions of any parts of the system of the world, and the phenomena that depend on them, become known and determined by applying the universal theorems of mechanics. That is all that a physicist should aim to realize.

Just as geometers, for the sake of their discipline, invent many things which they themselves cannot describe nor find in the nature of things, for exactly similar reasons a student of mechanics employs certain abstract and general terms and feigns in bodies a force, an action, an attraction or solicitation, etc. which are extremely useful in theories and propositions, as also in calculations of motion, even though it would be as vain to seek them in the very truth of things, or in bodies that actually exist, as it would be to seek the things that geometers invent by mathematical abstraction (§§38-39, tr. Clarke, boldface added).

The comparison of physics to geometry in §38 is Newton’s (see Janiak 59-60), but §39 takes this in a distinctively Berkeleian direction, arguing that forces are no more to be found “in the very truth of things” than length without breadth or other geometrical abstractions. The key point, though, is Berkeley’s assertion that this “is all that a physicist should aim to realize.”

Berkeley’s position here, as in the Principles, is that “mechanical explanation” is a matter of subsumption under general laws (De Motu §37). What is new here is the recognition that these laws cannot be formulated without certain “general and abstract terms” (§7; NB: abstract terms, not ideas), like ‘force’. However, although Newton defines ‘impressed force’ as “the action exerted on a body” by another body (Janiak 80) and Berkeley concedes that “this way of speaking is appropriate for mechanical demonstrations” (De Motu §28), nevertheless Berkeley denies that force involves genuine action, in any metaphysically robust sense. It follows from this picture that “it is the responsibility of the physicist or mechanist to provide only the rules, and not the efficient causes, of impulses or attractions and, in a word, the laws of motion; and once these are established properly, to assign the solution of a particular phenomenon” (De Motu §35). Thus, in a passage that can be read as a commentary on Newton’s discussion of God in the General Scholium, Berkeley writes:

One may conclude from this that the cause of motion and rest is identical with that of the existence of bodies [i.e., God] … To discuss God, however, and the greatest and best creator and conserver of all things, and to demonstrate how all things depend on the highest and true being, although it is the most excellent part of human knowledge, appears to belong to first philosophy or metaphysics and theology rather than to natural philosophy, which today is almost completely restricted to experiments and mechanics. Therefore natural philosophy either presupposes knowledge of God, or it borrows it from some superior science. Nevertheless it is very true that the investigation of nature provides the higher sciences in every way with excellent arguments to show and prove the wisdom, goodness, and power of God (De Motu §34).

Berkeley concludes his book as follows:

In physics, we rely on sensation and experience, which extend only to effects that are perceivable; in mechanics, the abstract notions of mathematics are accepted. In first philosophy or metaphysics, one discusses incorporeal things and the causes, truth, and existence of things … Causes that are truly active can be known to some extent only by reflection and reasoning … The discussion of these causes, however, is reserved for first philosophy or metaphysics. If each science is given the scope that properly belongs to it and its limits are assigned, and if the principles and objects that belong to each one are carefully distinguished, it will be possible to treat each one with greater facility and clarity (De Motu §§71-72).

In other words, Newton ought to have stuck to his original project of “discover[ing] the forces of nature from the phenomena of motions and … demonstrat[ing] the other phenomena from these forces,” since “to treat of God from the phenomena” is not part of natural philosophy (physics or mechanics). True causes, such as God, are the province of metaphysics, a distinct enterprise with distinct methods and tools and, importantly, an enterprise in which the employment of ‘mathematical hypotheses’ like force is illegitimate.

(Cross-posted at blog.kennypearce.net.)

  • I don’t have the book in front of me, but if memory serves this point is made by Lisa Downing.

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One of the problems for the traditional ‘Rationalists and Empiricists’ story of early modern philosophy is that it is surprisingly difficult to define ‘rationalism’ and ’empiricism’ appropriately (see here for a previous discussion). One traditional way of drawing the distinction, derived from Locke, is over the existence of innate ideas. This distinction, however, does not capture what is of importance to many other early modern philosophers, and oddly excludes Malebranche and his followers from the rationalist camp. (Since Malebranche holds that no ideas are ever in the human mind—they are all in God—he holds that no ideas are innate to the human mind.) Another traditional way of drawing the distinction, derived from Kant, is over the existence of a priori knowledge. This is perhaps somewhat more promising, for Locke’s critique of innate ideas is presented as a component of a broader critique of innate knowledge. However, most of the philosophers usually classified as empiricists accept at least some a priori knowledge: for instance, in mathematics. Kant would say that the rationalists accept synthetic knowledge a priori, but the analytic/synthetic distinction is a Kantian innovation with no precise parallel in earlier modern philosophers.

An approach which is perhaps more promising, in terms of its ability to connect to explicit subjects of debate in the period is the definition of rationalism in terms of ratio, i.e., reason. The rationalist, on this telling, distinguishes between the faculty of sense/imagination and the faculty of pure reason/intellect. The empiricist collapses them. On this way of drawing the distinction, Cartesianism turns out to be a paradigmatic form of rationalism (good), and Malebrancheans get to be rationalists for the same reason other Cartesians do (also good). Further, Hobbes and Gassendi offer explicit arguments in favor of empiricism in this sense, and Berkeley and Hume appear to presuppose such an empiricism. Still, there are some odd consequences. The question whether Locke is an empiricist turns out, on this approach, to be a difficult interpretive question rather than a straightforward textual one, though Locke does strongly suggest empiricism (in this sense) by his intentional collapse of the distinction between ‘species’ and ‘notions’ (EHU §1.1.8). A stranger consequence (which perhaps suggests that this account should not be pushed back before the mid-17th century) is that the traditional Aristotelian/Thomistic picture turns out to be a form of rationalism, despite holding that “there is nothing in the intellect which is not first in the senses,” since it does affirm a distinction between sensory and intellectual representations.

One more curious feature of this approach (which is the reason I am thinking about it today) is that it turns out that Newton offers an explicit argument for this kind of rationalism in De Gravitatione:*

If anyone now objects that we cannot imagine extension to be infinite, I agree. But at the same time I contend that we can understand it. We can imagine a greater extension, and then a greater one, but we can understand that there exists an extension greater than we can imagine. And here, incidentally, the faculty of understanding is clearly distinguished from imagination (Janiak 38).

Now, in a way this is not surprising. In Descartes (and Plato), as in Newton here, there is considerable evidence that the affirmation of rationalism (in this sense) arises from reflection on the phenomenology of mathematics: many people who have a great deal of experience in mathematics report the experience of encountering an object not revealed by the senses, hence one supposes that there is a faculty of understanding that has objects of its own, distinct from the objects of the senses. Perhaps these objects may be somehow derived from the senses, in a manner consistent with the Aristotelian dictum (“nothing in the intellect that was not first in the senses”) as the Aristotelians interpreted it, or perhaps not. Nevertheless, the idea/notion of extension contemplated by the intellect is unlike anything known by the senses, for the senses know only particular images of extension, all of which are finite.

Hobbes, Berkeley (at least on my reading), and Hume all hold, on the contrary, that this mathematical activity, which may be somehow and in some sense about infinite extension, nevertheless employs, as the mind’s immediate object, only finite determinate sense images. These images, which according to Descartes and his followers are the objects of the faculty of sense/imagination and are not even properly called ‘ideas’, are in fact all the ideas there are. It can be seen now why Locke’s empiricism is somewhat ambiguous: although he rejects the species/notion distinction, whether his abstract ideas are imagistic in this way is highly controversial. One can also see here that Newton’s rationalism (in this sense) is part of a broader tension in the development of physics, which to some degree continues to this day. Galileo, Leibniz, and Newton all insist that a proper approach to physics must be both mathematical and experimental, but math itself is, of course, precisely not experimental. For Newton (at least in De Gravitatione), just as much as for Descartes, many of the fundamental concepts of physics (most notably, in both cases, extension) are mathematical concepts attained by the pure intellect and differing radically from anything perceived by the senses. Yet (against Descartes, in agreement with Galileo and Leibniz) Newton holds that the laws of physics, employing those concepts, must be derived from sensory experience. And of course even Descartes holds that the laws ought to be applicable to what we experience by means of the senses. So there is no obvious contradiction between Newton’s rationalism and his empirical/experimental methodology, but there is an apparent tension, or at least a collection of difficult philosophical questions (which are, again, still very much alive) concerning the very concept of (what we now call) applied math. Though these sorts of questions are by no means absent from (e.g.) Plato, the mathematization of physics through the 17th century suddenly places them among the most important questions in natural philosophy, a role they had not previously occupied.

(Cross-posted at blog.kennypearce.net.)

  • I should note at the outset of this discussion that I am not a Newton specialist and, other than looking at the introduction on the Google preview this morning, have not read this important book on the subject I am about to discuss. I am aware that the relationship of De Gravitatione to Newton’s published works is a vexed question. Blog posts are not journal papers.

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In Colin Maclaurin’s four-volume An Account of Sir Issac Newton’s Philosophical Discoveries, published posthumously by his wife Anne, he responds in a footnote to Spinoza’s “Epistle 15,” the so-called “worm in the blood” letter. In Spinoza’s letter he considers how a small animal living in a bloodstream would consider particles to be wholes that the animal whose blood it is would consider to be parts. Spinoza raises a number of interesting conclusions from this, which I won’t go into here.

Maclaurin, a mathematician and philosopher deeply influenced by Newton, denies that human beings can be usefully and correctly compared to such minute animals. Humans, according to Maclaurin’s footnote (Book 1, page 18), “must be allowed to be the first being that pertains to this globe, which, for any thing we know, may be as considerable (not in magnitude, but in more valuable respects) as any in the solar system, which is itself, perhaps, not inferior to any other system in these parts of the vast expanse.” Although with respect to magnitude this planet and its “first being” are not considerable in magnitude, it is appropriate that humans have the particular situation that they do. If they were “occupying a lower place in nature,” they could better understand other minute things but “would have been in no condition to institute an analysis of nature, in that case.” (Maclaurin here seems to conflate being smaller in magnitude with being in a “lower place in nature,” which seems to be the very problem that he justly rejected in the previous two sentences.) On the other side, if we were larger we might have “access to the distant parts of the system,” but this would lead us to “too great attention on” these distant parts. By indulging in a “correspondence with the planets” and then the fixed stars and ultimately infinite space, a person would fail in the duties “incumbent upon him, as a member of society.” Humans are thus properly suited by their magnitude not to fall too easily into investigations of the very small or very large; attempting comprehensive knowledge of either would be detrimental to human society, according to Maclaurin. The trade-off is that we fall short of comprehensive knowledge of the minute and “the distant parts of the system,” but we are able to carry out an “analysis of nature.”

Maclaurin’s footnote is an elaboration and defense of his claim that “tracing the chain of causes is the most noble pursuit of philosophy.” This task begins with what is sensible to us, and those things that are sensible to us are “those things which are proportioned to sense.” He wants to go further, though, and claim that there is something special about our situation such that we are well positioned to carry out this investigation–so well positioned that we can infer a divine appointment. However, Maclaurin’s response to Spinoza is suspicious, seemingly a “just-so” story about our place in a divinely ordained order. Can anything be said on his behalf that doesn’t assume a number of contentious claims about a divine first cause that ordered the universe and situated us just so? In other words, why can’t there be a noble philosophy for the “animalcules in the blood discovered by Microscopes”?


Full text of the footnote (in context at this link):

If we were to examine more particularly the situation of man in nature we should find reason to conclude perhaps that it is well adapted to one of his faculties and inclinations for extending his knowledge in such a manner as might be consistent with other duties incumbent upon him and that they have not judged rightly who have compared him in this respect (Spinoz. Epist. 15) with the animalcules in the blood discovered by Microscopes. He must be allowed to be the first being that pertains to this globe which for any thing we know may be as considerable not in magnitude but in more valuable respects as any in the solar system which is itself perhaps not inferior to any other system in these parts of the vast expanse. By occupying a lower place in rature man might have more easily seen what passes amongst the minute particles of matter but he would have lost more than he could have gained by this advantage. He would have been in no condition to institute an analysis of nature in that case. On the other hand we doubt not but there are excellent reasons why he should not have access to the distant parts of the system and must be contented at present with a very imperfect knowledge of them. The duties incumbent upon him as a member of society might have suffered by too great an attention to them or communication with them. Had he been indulged in a correspondence with the planets, he next would have desired to pry into the state of the fixed stars, and at length to comprehend infinite space.

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