by Scott Soames
In this scenario the water recedes from the center and ascends the sides of the bucket because the water is spinning. But spinning relative to what? Not the bucket, since when the system reaches equilibrium, water and bucket spin at the same rate and so are at rest relative to each other. Yet the surface of the water remains concave, with some of it high on the sides of the bucket, while the center is depressed because a force is acting on the water, driving it from the center.
Bucket before and after spinning.
Forces acting on water in the spinning bucket.
According to Newton’s first law, this means the water must be moving and changing direction. Since its position relative to the spinning bucket isn’t changing, its position in absolute space must be changing.21 Since, according to Newton’s laws, this change could only be the result of forces causing quantities of water to climb the sides of the bucket, stating physical laws in terms of absolute space and time allowed him to explain an observed empirical phenomenon that might otherwise have resisted explanation. So absolute space and time are not gratuitous constructs in his system.
Newton was, of course, an inspiration to many of the scientists and philosophers of his day. One of them, Robert Boyle (1627–1691), who discovered Boyle’s law of gases, invented a barometer, and espoused a natural philosophy in which physical phenomena are explained by laws of matter in motion, saw himself as following Francis Bacon and Descartes. John Locke’s scientific mentor at Oxford, Boyle was a founding member of the Royal Society of London, which published Newton’s Principia and claimed both Locke and the great physicist as members. Locke posthumously edited and published Boyle’s The General History of the Air in 1692.22
At Oxford, Locke (1632–1704), who was eventually to become one of the greatest British philosophers of all time, studied chemistry, physics, and medicine. Reading Boyle led him to the natural philosophy of Descartes and the project of determining the scope of human knowledge and understanding. Active in the tumultuous public life of his day, Locke took nearly twenty years to complete his Essay Concerning Human Understanding, which was published in 1689. Having read Newton and other scientists, he modestly compares his work to theirs.
The commonwealth of learning is not at this time without master-builders, whose mighty designs, in advancing the sciences, will leave lasting monuments to the admiration of posterity; but everyone must not hope to be a Boyle or a Sydenham [with whom Locke studied medicine]; and in an age that produces such masters as Huygens and the incomparable Mr. Newton … it is ambition enough to be employed as an under-labourer in clearing the ground a little, and in removing some of the rubbish that lies in the way to knowledge.23
Locke’s Essay develops a simple empirical psychology and empiricist epistemology. For him, all our ideas arise from mental operations—association, comparison, combination, and abstraction—on simple ideas cognized in sense perception and introspection. Genuine knowledge comes from ideas that are properly grounded in these sources. Some ideas—of size, shape, mass, and motion—directly represent, or resemble, the primary qualities for which they stand, while others stand for secondary qualities like color and sweetness, which are powers of producing sensations in us. Physical substances, about which he took us to have knowledge, were combinations of qualities inhering a mysterious substratum, supposedly known to us by a cognitive process of abstraction. In short, the real properties of material things were those recognized by Newton, plus the powers of producing appearances—i.e., sensations—in us.
Although this satisfied Locke, the way he achieved his bifurcation of primary and secondary properties was suspect. So was his attempt to explain the empiricist origin of our idea of the underlying substratum of material objects, and his effort to ground our idea of causal power in the awareness of our own will. These became fair game for his empiricist successors, the philosophers George Berkeley and David Hume. Nevertheless, the lasting virtue of the Essay was its attempt to initiate a science and natural philosophy of the mind to complement the maturing science of the physical world that Locke and the philosophers of his day were both involved with and deeply impressed by.
Whereas Locke sought to extend Newtonian naturalism to the study of the mind, the German philosopher G. W. Leibniz (1646–1716) sought to harmonize Newtonian physics with a speculative metaphysics purporting to describe reality at a more basic level. A mathematician who independently invented the calculus, he was also a historian and philosophical logician who was well versed in Aristotelian and scholastic philosophy, as well as the works of modern thinkers like Descartes, Kepler, and Galileo.
His metaphysical system featured a version of the ontological argument plus other purported proofs of a morally perfect, necessarily existing God as creator of a system of reality described by four theses of Leibniz’s philosophical logic.
(i) All propositions are reducible to subject-predicate propositions, which are true just in case the subject has the property predicated of it.
(ii) An object x has a property just in case it is included in (the essence of) what x is.
(iii) Every property P that x has is included in its essence, because if x has P, then necessarily anything that doesn’t have P isn’t x. Since x can’t fail to be x, it is impossible for x to lack P.24
(iv) For any object y and property P that y has, there is a relational property P-similar—of being like y in possessing P; there is also a relational property P-different—of being unlike y in not possessing P. If y were to come to lack P, then every object that now possesses P-similar would come to lack it and every object that now has P-different would come to lack it. So any change in the properties of one object would lead to a change in the properties of all objects.
It follows from (iv) that if we knew all the properties of any object, we would know every property of every object. It also follows that any change in the properties of one object would lead to corresponding changes in the properties of every object. Although this sounds pretty dramatic, it wouldn’t be objectionable if it weren’t combined with (iii). Combining it with (iii) gives us the result that any change in one object would result in the nonexistence of every object, and its replacement by another object. In short, reality is seen as a harmony of essentially interconnected objects any change in which would result in an entirely new system of different objects.25
Another consequence of the system is that every true proposition p is necessary and knowable a priori by one who completely understands it. The reason for this, according to Leibniz, is that p’s subject already contains the property predicated of it—in the way that the concept square already contains having equal sides in the proposition A square has equal sides. But since complete analyses of propositions about existing things are always infinite, only God knows them a priori. For us, they are contingent truths knowable only by experience and observation.26
Leibniz applied this abstract scheme to an idealist version of metaphysical atomism in which the atoms are noncorporeal monads, which are simple, enduring substances without parts, shape, or spatial extension. They are spiritual because, for Leibniz, conceptions of matter in terms of spatial extension render it inert, and so incapable of explaining movement and change. It’s not that there aren’t things properly called bodies, which move and change in accord with Newtonian laws; there are. The point is that we can’t explain the forces initiating motion and change unless such bodies are seen as vast complexes of more fundamental change agents. Since, for Leibniz, the ultimate forces of change are perceptions and purposes, this means that the ultimate agents of change, God and the created monads, must be spiritual. This combination of natural theology, putative logical analysis, and Aristotelian teleology was not an attempt to contribute to natural science. It was one of the last great systems of speculative metaphysics, which hoped to survive by interpreting natural science, without competing with it.
That said, Leibniz did reject the Newtonian conception of space as made up of infinitely man
y spatial points, taken to be fundamental constituents of reality in terms of which spatial relations between objects or events are defined. Reversing explanatory priorities, Leibniz took the relations to be fundamental, while regarding spatial points as constructions abstracted from them. To do otherwise, he thought, would only give rise to unanswerable questions: Where is the earth, not in relation to the solar system (which we know), but in absolute space? Where is the solar system, not in relation to the Milky Way (which we also know), but in absolute space? Where is the universe as a whole? Not only can we not answer these questions, we can’t even formulate what answers might be possible. After all, points in absolute space don’t come with their own unique addresses.
One can ask similar questions about the velocities of things—the earth, the sun, the galaxies, and the like. We can, of course, answer questions about their relative velocities; and we can even formulate possible answers, of the form, e.g., n miles per minute, some of which must be correct, if space really is absolute. We can do this despite the fact that we have no idea how to go about determining which of those possible answers is correct. In light of this, one can’t help but wonder, “Does it really make sense to assume one such answer must be correct?”
Because he rejected as obviously nonsensical the unanswerable questions of precisely where the universe is located and how fast it is moving in the limitless Newtonian spatial domain, Leibniz rejected absolute space.27 What he didn’t make clear is how to think of the relative spatial relations between Newtonian bodies as somehow grounded in “perceptions” and “purposes” of nonspatial, spiritual monads. Nevertheless, this appeal to subjectivity did not go unnoticed, but rather became one of the chief influences on Kant’s later subjective view of space and time.
Another philosopher who, for the most part, sought to interpret, rather than directly quarrel with, Newton was the Anglican bishop George Berkeley (1685–1753). Berkeley espoused a purified version of Locke’s empiricism that led him to reject matter and to characterize the universe as consisting only of God, finite spirits, and their “ideas.” The “matter” he reasonably rejected was Locke’s imperceptible underlying substratum in which primary and secondary qualities supposedly inhered. With nothing to “support” them, these qualities disappeared in Berkeley’s philosophy, leaving only “ideas” imprinted on our minds by God. Although Newton’s laws remained (as descriptions of ideas God implants in us), Berkeley rejected Newton’s natural philosophy, which spoke of what Berkeley took to be the “occult” force of gravitation as a “cause” of motion (despite its not being a genuine power). It seems not to have occurred to him that genuine causal explanation might not require anything beyond general regularities of the sort Newton provided.
Although his criticisms of Locke’s conceptions of primary and secondary qualities, of causation, and of underlying matter as a kind of featureless glue holding bundles of properties together, revealed genuine problems with earlier philosophical systems, Berkeley’s fantastic worldview found few adherents. Like Locke, he took the objects of immediate perception—vision, hearing, taste, and touch—to be sense impressions (ideas). This, arguably, was the fundamental mistake on which all empiricist attempts to construct a psychology of perception and representational cognitive states foundered. Our sense experiences are not mental things we see, hear, taste, touch, or otherwise cognize; rather they are mental things—cognitive processes really—by which, in normal cases, we see, hear, taste, and touch real, nonmental things—a view whose leading proponent at the time was an important figure in the Scottish Enlightenment, the philosopher Thomas Reid (1710–1796).
Berkeley’s failure to see this didn’t stop him from tackling real problems. For example, his theory of vision attempted to explain our judgments of the magnitude of objects and their distance from us. Noting that we don’t see distance or magnitude themselves (in the way that we see trees and mountains), he rejected the Cartesian theory that we unconsciously judge distance by calculating the angle between an object and our eyes. Instead, he thought, we have kinesthetic sensations of focusing our eyes on the object, which increase as it comes closer, and which are associated with blurred vision when it is very close. For Berkeley, our judgments of distance and magnitude arise from these sensations plus the faintness or vividness of our perception. As with Locke and Descartes, the important point wasn’t the correctness of the attempted cognitive theory, but the fact that it was offered at all.
Regarded by many to be the greatest British philosopher of all time, David Hume (1711–1776) was Britain’s last great empiricist. His aim was, by observation and “the experimental method,” to lay the foundations of “the science of human understanding.” Being unable to derive any notion of substance—material or spiritual—from simple qualitative sense impressions, he rejected Lockean physical and mental substance. He also argued that neither the existence of physical objects—capable of existing unperceived—nor one’s own existence—as one who thinks, perceives, and endures through connected experiences—can be validly derived from true premises about the sensory and introspective contents of our minds. He didn’t, of course, cease to believe in physical objects and conscious beings. Like everyone else, he retained these beliefs, which he took to be true and justified in any reasonable sense in which empirical beliefs can be justified. But their justification didn’t come from reason, as he conceived it; it came from habit and human nature, which were the centers of his natural philosophy.
His treatment of causation was similar. Arguing that we have no reason to believe in any power or necessity by which causes produce effects, he nevertheless tried to explain how causal claims can be known to be true, and why we are wrongly disposed to think that causes somehow make it impossible for their effects not to occur. For Hume, to say that event x causes event y is (very roughly) to say that for some event types A and B, x is of type A, y is of type B, and events of type A are always followed by those of type B. In short, causation is constant conjunction of events of specified types. But there is more to the story. After observing many cases of events of type A being followed by those of type B, an idea of A becomes mentally associated with an idea of B. Because of this, whenever we judge an event to be an A we immediately expect it to be followed by an event of type B. This associative principle was, for Hume, a fundamental law of our mental life—analogous to Newton’s law of gravitation governing the physical world. Due to its operation, the expectation that an event, x, observed to be of type A, will be followed by an event, y, of type B, arises in us independently of our will, being felt as an inevitable necessity. This inevitable occurrence of the idea of B following the idea of A leads us, uncritically, to think of the event y as being made necessary by the event x.
It was, Hume thought, one of the chief virtues of his theory of mind that it dispelled this illusion. According to his deflationary analysis of causation, both physical events and mental events do standardly have causes; indeed the primary task of his Treatise was to discover the laws of mental causation. But there is never any necessary connection between cause and effect. Nor is the claim that all events have causes either a necessary truth or one that can be deduced from any principles of which we can be absolutely certain. For Hume, all necessary, a priori certainties express “relations of ideas” as opposed to “matters of fact.” Taking the denials of these truths to be self-contradictory, he, in effect, assimilated them to tautologies—like No unmarried man is married—or those that can be reduced to tautologies by verbal definitions—like No bachelor is unmarried. Truths such as these, Hume believed, don’t state facts, and so don’t entail the existence of anything. Thus, he insisted that pure a priori reasoning alone, unaided by sensory observation, can never yield knowledge of the world. Empirical knowledge must always be grounded in observation and experiment.
Like Hume, the great German philosopher Immanuel Kant (1724–1804) saw philosophy as doing for the mind what Newton did for the physical world. Having been introduced to Newton’s t
hought in college at the University of Königsberg, along with the work of the major British and European thinkers and philosophers of his era, Kant taught philosophy at Königsberg for four decades. He agreed with Hume that premises that merely describe contents of our ideas and sensations are insufficient to derive the conclusions that all events have causes, that physical space is Euclidean, or even that enduring objects “presented in space and time”—planets, animals, human bodies, and our own “egos”—really exist. However, unlike Hume, who believed that all genuine knowledge of matters of fact are based on the testimony of our senses, Kant looked to features of our minds to supply the extra ingredients he took to be needed for such knowledge. These, he thought, included space and time themselves, which, he maintained, our minds impose on perceptual experience, and causality, which he took us to impose on the world in attempting to understand it. Because these conceptual additions to the experienced world are knowable preconditions required by our own understanding, he took himself to have recovered our knowledge of many widely believed and seemingly fundamental truths—including the proposition that every empirical event has a cause, and the proposition that the space containing empirical objects we experience is Euclidean.
Despite this, he faced a dilemma. He had to hold either (i) that the planets, animals, mountains, and the like, about which we take ourselves to have knowledge, are independent of us, or (ii) that they are constituted in part by the mental categories our minds impose on experience. Neither option served his purpose. Since the skepticism he wished to refute concerned knowledge of independent things, taking them to be partially constituted by us threatened to drain his refutation of significance. Since there is no guarantee that independent things must conform to how we must think of them, even a successful explanation of why we (must?) think of them in certain ways would be open to skeptical challenge. In time, this dilemma was to be vividly illustrated by the inclusion of non-Euclidean elements in twentieth-century physical theories of space-time, contradicting the Kantian claim that we know a priori that physical space is Euclidian.