MOTION

Motion (Gr. κίνησις, Lat. motus ) can be taken in a wide and in a strict sense. In the wide sense it stands for any change, for any transition from one state or condition to another. In a strict sense it means successive and continuous change, usually spoken of as movement. Aristotle held that it is unnecessary to prove the existence of motion, since the fact is evident. This notwithstanding, motion constitutes the first and enduring problem of philosophy, and through the study of it philosophers come to significant insights into material being and into the nature of being itself. It is also of interest to psychologists, for the perception of motion—examined in scholastic and modern psychology alike—has given rise to several theories on this subject. Accordingly, the present article treats motion under two aspects, the first part dealing with it from the standpoint of philosophy, the second from that of psychology.

Motion In Philosophy

Originating among the early Greeks, the philosophical analysis of motion reached its fullest development in the thought of Aristotle and the scholastics. This analysis forms the conceptual background against which the characteristic approach of modern science, as well as further contributions by modern philosophers, are most easily discussed.

Early Greeks. Since the early Greek philosophers lacked precise concepts of the different kinds of being, they reduced all changes to the simplest type of motion, local motion or change of place. From the beginning they spoke of the process of becoming in this terminology: things came into being by being "separated" from an original mass, by condensation and rarefaction, or by a downward and upward path. The only philosophers to deny the possibility of change were parmenides and his Eleatic school. The famous paradoxes of zeno of elea, for example, purported to disprove the intelligibility of local motion. Because his concept of being was absolute, Parmenides himself denied that anything could come to be. The subsequent atomists were one in denying the possibility of absolute coming into being. They reduced all change to local motion, that is, to the redistribution of atoms in space (see atomism; greek philosophy).

plato distinguished motion from becoming (γένεσις; Theaetetus 152D–153E), although he usually understood motion as local motion (Laws 893B–894A). In Theaetetus (181C–182A), however, he introduced the concept of qualitative change or alteration (ἀλλοίωσιν) as one of the two types of motion. He also defined soul as "the motion which can move itself" (Laws 896A), and he listed psychic operations as examples of motion (Laws 897A). Yet he was constrained to think even of the movement of reason as similar to the local motion of a sphere and its relatively immobile central point (Laws 898A; cf. Tim. 33B–34A).

Aristotelian concept. It remained for aristotle to give the first reasonably complete analysis (Physics 200b 12–231a 20; 250b 11–267b 26). In this he was followed by St. thomas aquinas, whose commentary on Aristotle's Physics is the fullest account of a philosophy of motion. Beause of his historical milieu, Aristotle had first to justify the possibility of motion by assigning principles that would account for motion in the face of the Eleatic denial. The possibility of change he saved by distinguishing being into ten categories and into actual and potential being. For Aristotle motion was the proper formality from which to study nature and natural phenomena. No other formality, such as being or extension, can in his view reveal the nature and explain the sensible properties of matter. He maintained it necessary, however, to distinguish motions that are natural from motions that result from art, chance, or compulsion. The first kind is of fundamental relevance to his scientific study of the world.

In Book 3 of the Physics the famous definition of motion is given. Aristotle begins by stating the concepts to be used in its definition. Since motion spans several categories of being, the elements of the definition must also transcend the categories; the only available prior concepts for defining motion are potency and act. Motion must be situated midway between potentiality and full actuality. When a body is only in potency, it is not yet in motion; when it has been fully actualized, the motion has ceased. Therefore, motion consists of imperfect act. But since imperfect act can be the termination of a motion or the starting point of a new motion, it is necessary to indicate motion as the act of a being in potency precisely as still in potency to more of the same act. Hence, motion is defined as "the fulfilment [act] of what exists in potency in so far as it is in potency" (201a, 10).

Types of motion. Plato had adumbrated various types of motion, but Aristotle put the classification on a scientific basis. Motions are distinguished by the goal or terminus ad quem (Physics 224b 7). Motion does not of itself belong in the categories of being, since it is not being, but becoming; however, it is reduced to the category of the being in which it terminates.

Local Motion. The first, most obvious, and easiest motion to observe is change of place, or local motion. It is divided into circular, straight, and mixed, as well as into uniform and accelerated. The nature of motion is most easily seen in local motion, and even the terms one uses to describe other types are terms applied primarily to local motion. Local motion clearly goes from term to term, from a point of departure to one of arrival. These two terms are opposed and incompatible, but admit intermediary states: thus, they are called contraries. The motion between them is continuous, or unbroken and successive, that is, traversing the intervening positions. It is divisible by reason of the extension crossed. Since an instant is not divisible, motion cannot be instantaneous, but takes time. Likewise, motion properly speaking belongs only to bodies, since only they have the divisibility essential to motion. Local motion of some sort is involved in all other motions, and other motions are called such by analogy with local motion.

Alteration. Qualitative motion is called alteration. It is realized only in the third species of quality, namely, sensible qualities. Only these fit the definition of motion as continuing and successive actualization of potency. Changes occurring in the vital or psychic orders are not motions in the same sense as local change and change of sensible qualities. One speaks of the mind as "proceeding" from known to unknown, of discursive reasoning; this, however, is only by analogy with local motion. Vital and psychic operations are not acts of beings in potency, but of beings already proximately determined to act; these operations are not the fulfillment of potentialities, but the products of potentialities already actualized (cf. St. Thomas, Summa theologiae 1a, 18.3 ad1). Further, in psychic acts there is not the successiveness characteristic of motion, nor the contrariety between the terms of the process. In sensation the preliminary stimulation of the sensory organs is a qualitative change, but the determination of the faculty itself is not a gradual reception of act and thus is not motion. In the sensitive appetite there is motion, insofar as there is a physical accompaniment to the psychic act; the motion may be qualitative or local. Changes of moral disposition, although gradual, are not truly motions, but rather one or a series of instantaneous changes. Substantial changes are preceeded by alterations that dispose matter toward becoming a new being, but the actual generation of a new substance and destruction of the old are instantaneous, and are thereby not classified as motions in the strict sense. (see substantial change.)

Augmentation and Diminution. Motion in the category of quantity is called augmentation or growth and diminution or decrease. Augmentation does not consist of mere addition of distinct quantities to form an aggregation; such would reduce to local motion and would be augmentative, but not the motion of augmentation. The motion of augmentation must take place within the unity of a single substance. This happens only in living beings. By nutrition these assimilate their food into their own substance and consequently achieve growth. This is a true motion. It involves some local motion, as a growing body extends spatially. It is gradual, ordinarily so slow as to escape observation. It passes through successive stages, from the smallest one-cell stage to the full measure of growth determined by the specific nature. It also goes from contrary to contrary, from one positive state to another in the order of quantity. Such a motion is obviously immanent operation on the part of the living subject as agent, but it is true motion on the part of the subject as receptive of a new perfection. The opposite of augmentation is diminution or decrease.

Other Categories. The two categories of action and passion do not constitute separate types of motion, for they are really identified with motion. Action is motion considered as being from the agent. Passion is the same motion considered in the patient. There is no motion in the category of "when" (quando ), since time itself is the measure of motion. Nor is there motion in the category of relation. A new relation arises as a result of a change in some other category; for instance, by reason of a change of place, a relation of proximity arises, and from change of quality in one being, a relation of similarity or dissimilarity results in another being. A mutual relation can come into being and cease to be without any change in one of the related members. Hence, change is merely incidental to relation. The categories of situation (situs ) and condition or vestition (habitus ) are constituted by relations, and so do not found separate types of motion.

Reality of motion. The objective reality of motion is known through a recognition of the various stages of actualization from the beginning to the ultimate termination of motion, even though these stages are not identified with motion. Fundamentally, each one has immediate experience of his own motions, particularly local (see below, Motion in Psychology). The paradoxes of Zeno, while purporting to disprove the reality of local motion, can be solved by an analysis of the continuum and of the infinite (cf. Physics 239b 5–240a 18). Though directed against the intelligibility of motion, they do not overturn the immediate evidence of the fact of motion.

The reality of motion is further confirmed by the need of an efficient cause or mover. Motion is an emergence from a state of potentiality to one of actuality. This is possible only under the influence of some being in act. Even vital movement requires that one part of a living being function as agent and another part as patient; otherwise the same being would be in potency and act together. The mover must be distinct from the moved and must be proportioned to the motion produced. There must be contact, at least mediate; there is no action at a distance. In a series of movers that are themselves moved, there is no ultimate explanation for the motion unless there be a first unmoved mover, a first cause of motion (see motion, first cause of).

Motion in modern science. The Aristotelian requirement of a mover in act as necessary to account for motion was not easily satisfied; this was particularly the case in assigning the cause of projectile motion, such as of a stone thrown upward. Aristotle had explained the motion of the projectile after it left contact with the mover by supposing that the agent moves not only the stone, but also the surrounding air, giving the air motive power to continue projecting the stone. In the 6th century, john philoponus of Alexandria criticized the Aristotelian theory and proposed the theory of impetus in its stead: the mover imparts a "motive power" or energy to the projectile itself. In the 14th century john buridan spoke of the impetus as a qualitative power given to the body by the mover. He suggested that impetus theory could explain the motion of the heavenly bodies, once God had put them in motion. His doctrine has been assimilated into Aristotelianism and scholasticism, where impetus is explained as a quality or an instrumental power communicated by the mover. It is usually not thought to be an efficient cause of motion, but rather it is seen as analogous to the internal principle of natural motion.

Ockhamist Critique. william of ockham reduced all physical being to the two categories of substance and quality, the only two that denoted distinct realities. The reality of local motion and position in place were thus denied, and there was no longer need to find a cause for the continuance of projectile motion. Accordingly, Ockham could deny both the original Aristotelian and the impetus theory.

Galileo's Contribution. Galileo galilei initiated a radical departure from such theory and study of motion. Confining himself to local motion, he stated that he had discovered by experiment certain properties of motion not hitherto observed or demonstrated. He set himself to study these properties through the method of measurement and correlation. Motion, for him, gave way to momentum, the product of the quantity of matter and velocity. Galileo identified momentum with impetus, and this became no longer an instrument or principle of motion, but a property of motion. He was not interested in an efficient cause for the continuance of motion, but in a measurable external cause of the acceleration or retardation of motion. Therefore, observing that a velocity once imparted to a body is accelerated or retarded according to the slope of the plane along which the motion takes place, he inferred that frictionless motion along a horizontal plane is uniform and perpetual. However, since in the real world this horizontal plane is circular—the surface of the sea, the path of the heavenly bodies—then the motion of bodies continues in a circular path, rather than in a straight line. Thus did Galileo give partial formulation to the principle of inertia.

Newton and Mechanism. Sir Isaac Newton correctly stated the principle of inertia as the first of his axioms, or laws of motion: "Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed on it." From this and other axioms, Newton developed the science of mechanics, discovering in the process a formula of gravitation that is applicable to celestial as well as terrestrial phenomena. He also studied the properties of light according to principles of motion, and in his Optics he proposed a science of nature guided and inspired by mechanics. Newton's successors thereupon extended mechanics into every region of science, into acoustics, hydrodynamics, magnetism, electricity, heat, even into biology, psychology, economics, and sociology, at the expense of denying all that is not reducible to matter and motion (see mechanism).

Recent Physics. The use of mechanical principles as ultimate explanations of physical reality ran into difficulties in the 20th century with the advent of relativity and quantum theory. The Heisenberg principle of uncertainty, according to which it is impossible in principle to measure both the position and velocity of a particle, makes it impossible to construct a mechanical model of the world. Moreover, the concept of quantum jumps is interpreted by some to involve a denial of the continuity of motion.

Motion in modern philosophy. René descartes recalled the common doctrine that nature is the principle of motion and rest, but he could conceive of motion only as local motion. Therefore, he attempted an explanation of all material reality from a mechanical point of view, i.e., in terms of matter and local motion. He held that all that man can know of external objects are their figure, magnitudes, and motions—all modes of extension. Color, odor, taste, and other sensible qualities, in this view, are not objective. Descartes also taught that in the beginning God created a definite quantity of motion, which remains constant. Not interested in the Aristotelian or qualitative definition of motion, which he never understood, he concentrated instead on the quantity of motion, or momentum. Motion became, for him, an actual and measurable state of a body, without consideration of a potential state that is being further actualized (cf. Principles of Philosophy 2.24–36).

Leibniz and Kant. leibniz objected to Descartes's idea that the quantity of motion in the universe remains constant; this, for Leibniz, is true rather of force (Discourse on Metaphysics 17–18). Likewise, he denied that extension is a clear and distinct idea. Extension, together with size, figure, and motion, are subjective phenomena, no less than the other sensible qualities the mechanists had rejected. Accordingly, he formulated his monadology, a doctrine in which bodies are composed of simple forces, psychic in character (see monad). The dynamism of the system did not prevent Leibniz from interpreting bodily actions mechanically, even though they do not act upon one another. Bodies are divine machines or natural automatons (The Monadology 64). The motions of bodies, however, are regulated by their preestablished harmony with one another and with souls, which act according to final causality and the divine plan of the best possible world.

Immanuel kant, in his precritical days, developed the monadology of Leibniz. In his definitive philosophy he defined motion as "actuation in space" (Critique of Pure Reason B291). Motion is an empirical concept, since experience apprises one of something moving in space and time. But there is also a subjective element to it: the two forms of sensibility, space and time, organize the successive determinations of a movable object.

Bergson's Critique. The most searching criticism of such views was that of Henri bergson, who held that the scientific mind cannot grasp the reality of motion. The intellect makes static, snapshot views of various stages of a transition, thereby solidifying into discontinuous images the fluid continuity of the real. Just as a movie projector, by reason of the movement of the apparatus, reconstitutes the motion that had been immobilized in a series of still pictures, so does the mind string snapshots of reality upon an abstract "becoming" contributed by the mind itself. The mechanism of ordinary knowledge is "cinematographical." In order to grasp reality, which is duration or change itself, one must escape from the cinematographical mechanism and employ a metaphysical intuition. Since change is the essence of reality, there is no underlying subject of change; movement does not imply a mobile [see Creative Evolution (New York 1911); The Creative Mind (New York 1946)]. The mobile continuity of the real, or concrete duration, is for Bergson the subject of metaphysics. If Bergson's critique accomplishes nothing else, it at least intimates that modern thinkers, by reducing motion to a state, have allowed reality in flux to escape them.

See Also: philosophy of nature; matter and form; science (in the middle ages).

Bibliography: aristotle, Physics, tr. r. p. hardie and p. k. gaye, v. 2 of The Works of Aristotle, ed. w. d. ross, 12 v. (Oxford 1908–52). thomas aquinas, Commentary on Aristotle's "Physics," tr. r. j. blackwell et al. (New Haven, Conn. 1963). m. j. adler, ed. The Great Ideas: A Syntopicon of Great Books of the Western World (Chicago, Ill. 1952) 1:193–217; 2:80–112. j. a. weisheipl, Nature and Gravitation (River Forest, Ill. 1955). j. tonquÉdec, La Philosophie de la nature (Paris 1956) 1.3. c. mazzantini, Enciclopedia filosofica (Venice-Rome 1957) 1:1676–87. s. caramella, Enciclopedia filosofica (Venice-Rome 1957) 3:750–758.

[m. a. glutz]

Motion in Psychology

The study of motion in psychology has a long and interesting history. Once it was realized that motion could be experienced when there was no physical movement and that actual physical motion might not be experienced as such, the investigation of just how man perceives movement captured the interest of psychologists. To explain these illusions, most psychologists relied upon some type of logical analysis in terms of space and time, until the significant research of Max Wertheimer on apparent movement showed that a new phenomenological approach was needed.

Perception of Movement. Current investigation of the perception of movement may be classified under the following headings: induced movement; autokinetic movement; direction, speed, and causality of movement; and apparent movement.

Induced Movement. In induced movement one object is displaced in relation to another, but the subject is not able to perceive which has moved. He may, for example, see the object move when in reality it is the frame that has moved. The tendency is to interpret the figure as moving rather than the background. Also the meaning of the stimulus for the particular subject can determine which of two stimuli the subject perceives as moving.

Autokinetic Movement. Another interesting illusion of movement is the autokinetic effect, in which a stationary point of light is perceived as moving in a completely dark room. This phenomenon is explained largely in terms of nystagmus eye movements, but it is influenced also by the posture of the body, and kinesthetic sensations from the muscles. Moreover the autokinetic phenomenon is greatly influenced by social suggestibility of the subject. In both induced and autokinetic movement, the experienced movement cannot be differentiated from real movement.

Direction, Speed, and Causality. More recently it has been discovered that both direction and speed of movement depend upon the organizational factors present. It appears that the speed of movement is apprehended independently of distance or time. One peculiarity of directional movement is the trapezoidal illusion, in which a rotating trapezoid is perceived as oscillating because of the conflict in cues. Another interesting piece of research by A. E. Michotte (1881–1965) indicates that movement can have more complex attributes such as causality. The simulated appearance of one ball striking another is perceived as the first ball causing the second to move, even though there is no actual contact.

Apparent Movement. Of great importance is the study of the perception of movement. To illustrate this phenomenon two lights are mounted side by side. First one, then the other, is turned on and off. By varying the time between the turning on of the two lights, one induces three different perceptual experiences. If the time interval is long, the first light is perceived simultaneously. If the time interval is just right, one light is perceived as moving from position A to position B. A light is seen as moving when in fact there is no movement at all, and across a space where there is no stimulus present. The same phenomenon of apparent movement has also been reported for skin sensitivity of two successive stimuli, and for the hearing of two successive clicks.

The conditions governing the occurrence of the phi-phenomenon were investigated by Korte (1915). He found that the threshold was determined by distance between stimuli, the time interval of the succession, and the intensity of the stimuli. Moreover, the direction of the apparent movement was determined by the grouping laws of proximity and similarity. Finally the spatial arrangement of the successive stimuli may direct the apparent movement.

Theories of Perception. On the basis of the phi-phenomenon, field theorists maintain that movement is a primary sensory phenomenon not reducible to sensory attributes or to space or time. On the other hand the sensory-tonic theory of H. Werner and S. Wapner stresses the role of muscle activity in enhancing the autokinetic effect of apparent movement. The transactional functionalism theory of Ames's group and the probabilist theory of Brunswick attempt to explain the illusion of movement in terms of the cues of position, size, distance, and past experience, maintaining that these operate immediately and unconsciously. The explanation offered by Thomistic psychologists is that movement is a per accidens sensible known through the operation of the internal senses, operating simultaneously in conjunction with the external senses and through physiological and psychological cues. The imagination is the faculty that supplies the sense of movement in conjunction with the work of the senses; thus the phenomenon of apparent movement results from the work of the imagination. This faculty fuses together the successive sense impressions, e.g., moving pictures, and at the same time relates this information to the past experience of actual moving things to give an experience of movement. Such a Thomistic view can give a rational explanation of all the phenomena of movement reported in experimental psychology; yet it should be noted that what it subjects to complex analysis is in reality a spontaneous and frequently an unconscious process.

See Also: sensation; sense knowledge; senses.

Bibliography: f. h. allport, Theories of Perception and the Concept of Structure (New York 1955). a. ames, Visual Perception and the Rotating Trapezoidal Window (Psychological Monographs: General and Applied 65.7; Washington 1951). s. h. bartley, Principles of Perception (New York 1958). e. g. boring, Sensational and Perception in the History of Experimental Psychology (New York 1942). d. krech and r. s. crutchfield, Elements of Psychology (New York 1958).

[j. h. voor]

MOTION

The nature of motion and the philosophical problems surrounding it have been perennial issues in Western philosophy. Motion is a special case of change, and much discussion relevant to motion extends naturally to change in general (see Mortensen 2002).

Notable among the problems of motion are those provided by Zeno's paradoxes. Perhaps the hardest of these is the Arrow paradox. Consider an object in motion. At any instant of that motion, since it is an instant, the object makes no advance on its journey. But if it makes no advance in any instant of its journey, how can it make advance in all of them? The sum of a collection of nothings—even an infinite collection—is nothing. It would seem that it cannot move at all.

Motion and the Calculus

Substantial progress concerning the topic of motion was made with the development of the calculus by Isaac Newton and Gottfried Wilhelm Leibniz in the seventeenth century. The velocity of an object at time t, v (t ) (with respect to a frame of reference), is given by the derivative of its spatial location, x (t ), with respect to time. That is, v (t ₀) is dx (t )/dt, evaluated at t ₀. An object is in motion at an instant if its velocity at that instant is nonzero; it is at rest if its velocity is zero.

The understanding of motion thus provided is, of course, parasitic on an understanding of the calculus itself and specifically on the notion of a derivative. In the eighteenth and early nineteenth centuries this depended on the notion of an infinitesimal; and infinitesimals behaved in a notoriously inconsistent fashion. Specifically, they were assumed to be nonzero (sometimes) and zero (sometimes).

Hegel on Motion

Georg Wilhelm Friedrich Hegel, writing at the start of the nineteenth century, put the contradictory properties of the infinitesimal to the service of his dialectic. The continuous and the discrete are contradictory notions. There is, therefore, something that is their synthesis. This is a variable point: the infinitesimal. It has the property of being a point, so having zero extension, and being extended, so having nonzero extension.

This understanding allows him a particular view of the account of motion provided by the calculus. To be in motion at an instant is precisely to move an infinitesimal amount. Thus,

[when a body is moving] there are three different places: the present place, the place about to be occupied and the place which has just been vacated; the vanishing of the dimension of time is paralyzed. But at the same time there is only one place, a universal of these places, which remains unchanged throughout all the changes [i.e., the variable point]; it is duration existing immediately in accordance with its notion, and as such it is motion. (Hegel 1970, p. 43)

That is, "Something moves not because at one moment of time it is here and at another there, but because at one and the same moment it is here and not here, because in this 'here' it at once is and is not" (Hegel 1969, p. 440). This provides Hegel with a simple solution to the Arrow paradox. The object advances on its journey because it does advance at each instant: It moves a tiny amount at each instant.

Russell on Motion

Within fifty years Hegel's analysis of motion was rendered obsolete by new mathematical developments. Toward the end of the nineteenth century the notion of an infinitesimal disappeared from standard mathematics. This was because, through the work of Baron Augustin-Louis Cauchy, and particularly Karl Weierstrass, a different understanding of the derivative was developed. A derivative came to be understood simply as the limit of a certain ratio as some variable approaches a value. In particular, the velocity v (t ₀), that is, dx (t )/dt as evaluated at t ₀, came to be understood as the limit of (x (t ₀+ε)-x (t ₀))/ε as ε approaches 0.

Therefore, the new interpretation of the calculus provided a different understanding of motion. This was spelled out by Bertrand Russell in The Principles of Mathematics as follows:

[I]n consequence of the denial of the infinitesimal, and in consequence of the allied purely technical view of the derivative of a function, we must entirely reject the notion of a state of motion. Motion consists merely in the occupation of different places at different times.… There is no transition from place to place … no such thing as velocity except in the sense of a real number which is the limit of a certain set of quotients. (1938, p. 473)

The paradox of the Arrow can then be dismissed:

In the case of motion, [Zeno's Arrow paradox] denies that there is such a thing as the state of motion. In the general case of a continuous variable, it may be taken as denying actual infinitesimals. For infinitesimals are an attempt to extend to the values of a variable the variability which belongs to it alone.… [The modern account of the variable has clarified this confusion, but] its absence in Zeno's day led him to suppose that continuous change was impossible without a state of change, which involves infinitesimals and the contradiction of a body's being where it is not. (Russell 1938, pp. 350–351)

Problems with the Orthodox Account

The view concerning motion expressed by Russell became the orthodox view of motion in the twentieth century. It is not without its problems, however. As Russell makes clear, according to this account there is no such thing as an intrinsic state of motion. That is, the instantaneous states of two objects, one in motion and one at rest at that instant, but at the same place, would be identical. Whether the object is in motion or at rest at that instant depends entirely on its states at neighboring instants. This is highly counterintuitive: Motion turns out to be a sequence (albeit a continuous one) of states that are indistinguishable from rest-states. There is no genuine flux. Motion occurs in much the same way as it appears to when successive stills in a cinema film are shown so fast that something seems to move. Indeed, one might call this the cinematic view of change. One way to bring home its oddity is as follows. Suppose that there is a particle that behaves as follows: At any time it exists simply at some place, but at any time it may disappear and reappear at some other place. Suppose that, by an accidental string of occurrences, the positions of the particle over a short period just happen to be a continuous function of time with a nonzero derivative. One would not, on this account, be inclined to say that the particle is in motion at each instant.

The cinematic account of change is not just counterintuitive. It has a number of other untoward consequences, as Russell himself notes (1938, p. 482). It is natural to take laws of nature to state causal relations between various quantities, such as velocity and its derivative, acceleration. Indeed, one normally takes it that the states of these quantities at a time are causal determinants of later states. If, in nature, there are no such things as these quantities, all this must be foregone—including the possibility of Laplacean determinism: the view that the intrinsic state of a system at any time determines its future states.

Further problems arise when one considers discontinuities of various kinds. Thus, suppose that an object is at rest before time t, and then starts to move with velocity 1. That is, x (t ) = 0 if t <0 and x (t ) = t if t ≥0. The object has no velocity at t = 0 (since x (t ) has no derivative there), and a fortiori no acceleration. Still, it would seem that it ought to, if the motion is the result of an impulse applied to the object at t = 0. Worse: suppose that the object moves instantaneously at t = 0 to some other position where it is at rest; so x (t ) = 0 if t <0 and x (t ) = 1 if t ≥ 0. If t ≠ 0, the velocity of the particle is 0; and if t = 0, the velocity is undefined. Hence, the particle has changed places at t = 0, yet it has never been in motion!

Finally, and Russell's protestations to the contrary notwithstanding, it would appear that he has not so much solved the Arrow paradox as ignored it. He accepts that no progress is made on the journey in an instant, but simply insists that, nonetheless, progress is made in the whole journey. This is not a solution, it is what must be explained.

Tooley's Account

These and other objections were leveled against the Russellean account by Graham Priest (1985, 1987) and Michael Tooley (1988), each of whom offers an account of motion according to which velocity (relative to a frame of reference) is an instantaneous property of an object.

According to Tooley velocity is a theoretical (i.e., unobservable) property of an object that is causally efficacious in determining its behavior. Specifically, it is a quantity, v (t ), satisfying the equations:
x (t ₁) = x (t ₀) + ₀ ∫¹v (t )dt
m (t ₁). v (t ₁) = m (t ₀). v (t ₀) + ₀ ∫¹F (t )dt
where m (t ) is the inertial mass of the object at t and F (t ) is the force acting on it at that time. These, note, are the two key laws in (relativistic) kinematics involving velocity. The first relates velocity to position; the second to the forces acting. The crucial point is that, on Tooley's view, these equations should be interpreted as stating relations between (instantaneous) physical quantities.

Priest's Account

Priest's account draws on Hegel. It does not resurrect Hegel's account of the categories; nor does it rehabilitate the notion of the infinitesimal. What it does do is take seriously the possibility that, at an instant, the position of a moving object may be spread out over a short (but noninfinitesimal) region. Because the object is in motion it may be impossible to localize it to any one position. This is called the spread hypothesis.

More specifically, let x (t ) be the locus of motion of an object, as it occurs in the laws of motion cited in the previous section. One can write r_t for the value of this function at t. For Russell, the state of the object at time t is characterized by the set of statements S_t = {'The object is at r_t '}∪ {'The object is not at r '; where r ≠ r_t }. Given the spread hypothesis, one must suppose that there is an interval of times containing t, θ_t , such that the object is equally at x (t ′) for all t ′εθ_t . The state of the object at t is therefore characterized by the set of all those statements in S_t′ for t′εθ_t. (What, exactly, θ_t is, is a matter to be determined by other consideration; possibly by nature itself. But it is not unnatural to suppose that the width of θ_t is proportional to dx (t )/dt if this is defined.)

If x (t′ ) is constant for t′ εθ_t (and, in particular, if θ_t contains just t ), the state-description is identical to the Russellean state-description; in particular, it is consistent. But if x (t′ ) takes different values, r ₁ and r ₂, for t′ εθ_t , then it will be inconsistent: it will contain the statements that the object both is and is not at r ₁ (and r ₂).

To be in motion at an instant, then, according to this account, is to have an inconsistent state description at that instant. Objects in motion are at one place at one time, and another at another. But this is not sufficient. This would be equally true of an object at rest at each of these places. To be in motion at a time, an object must both be and not be at a place at that time.

The Arrow Again

If one is to have a theory according to which motion is an intrinsic property of an object, then the accounts of Tooley and Priest may not be the only ones; but they are the only two presently on offer. Therefore, it is natural to compare their relative merits.

One feature of Tooley's account, unlike Priest's, is that it is consistent. Priest's account (and Hegel's) presupposes that one can make sense of the possibility that the truth about a situation can be contradictory (dialetheism). It requires the use of a logic that is such that contradictions do not imply everything. One may take this to be a strong mark in Tooley's favor. Other objections against Priest can be found by consulting Tooley (1988). It appears that there are perfectly natural replies to these objections, but this is not the place to go into the matter.

On the other side, it is clear that Priest's account solves the Arrow paradox essentially as does Hegel's. The object, by occupying more than one point at an instant, does make progress during each instant, and so in the whole comprising them. Tooley's account would not appear to solve the paradox. It still leaves one with the fact that the object makes no progress during an instant of its journey. Russell, whether rightly or wrongly, took the problem to be solved by rejecting instantaneous states of motion. Even this step is not open to Tooley.

Doubtless, there is more to be said on these matters. Regardless, one thing is clear: Even after the development of the calculus, the theory of the limit, the understanding that it is possible to postulate unobservables in science, and even of paraconsistency, Zeno's paradox of the Arrow still haunts us.

See also Hegel, Georg Wilhelm Friedrich; Motion, A Historical Survey; Russell, Bertrand Arthur William; Zeno of Elea.

Bibliography

Boyer, Charles B. The History of the Calculus and Its Conceptual Development. New York: Dover, 1959.

Cajori, Florian. A History of Mathematics. 5th ed. New York: Chelsea, 1991.

Hegel, Georg W. F. Hegel's Philosophy of Nature: Being Part Two of the Encyclopaedia of the Philosophical Sciences. Translated by A. V. Miller. Oxford, U.K.: Clarendon Press, 1970. Originally published as Encyclopädie der Philosophischen Wissenschaften im Grundrisse (Heidelberg, Germany: Druk und Verlag von August Owald, 1827).

Hegel, Georg W. F. Hegel's Science of Logic. Translated by A. V. Miller. London: Allen and Unwin, 1969. Originally published as Wissenschaft der Logic (Nuremberg: Johann Leonhard Schrag, 1812–1816).

Mortensen, Chris. "Change." In Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. Stanford, CA: Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University, 2002. Available at http://plato.stanford.edu/entries/change/.

Priest, Graham. In Contradiction: A Study of the Transconsistent. Dordrecht, Netherlands: Nijhoff, 1987.

Priest, Graham. "Inconsistencies in Motion." American Philosophical Quarterly 22 (1985): 339–346.

Russell, Bertrand. The Principles of Mathematics. New York: Norton, 1938.

Salmon, Wesley C., ed. Zeno's Paradoxes. Indianapolis, IN: Bobbs-Merrill, 1970.

Tooley, Michael. "In Defence of the Existence of States of Motion." Philosophical Topics 16 (1988): 225–250.

Graham Priest (2005)

MOTION

A written or oral application made to a court or judge to obtain a ruling or order directing that some act be done in favor of the applicant. The applicant is known as the moving party, or themovant.

In the U.S. judicial system, procedural rules require most motions to be made in writing and can require that written notice be given in advance of a motion being made. Written motions specify what action the movant is requesting and the reasons, or grounds, for the request. A written motion may contain citations to case law or statutes that support the motion. A motion almost always contains a recitation of the facts of the case or the situation prompting the movant to make the request.

For example, suppose that a plaintiff in a lawsuit has refused to submit to a deposition—questioning under oath—by the defendant. The defendant therefore files a motion with the court to compel in an effort to compel the plaintiff to attend the deposition. The written motion briefly explains the nature of the lawsuit, describes the efforts made by the defendant to get the plaintiff to submit to a deposition, addresses any known reasons for the plaintiff's failure to cooperate, and recites the statute that permits the taking of depositions in civil litigation. The motion may also request that the issue be addressed at a hearing before the judge with all parties present.

Once the judge receives the motion, he or she may grant or deny the motion based solely on its contents. In the alternative, the judge may schedule a hearing. At a motion hearing, each party has an opportunity to argue its position orally, and the judge can ask specific questions about the facts or the law. The judge's decision on the motion is called an order.

Under some circumstances motions can be made orally. Oral motions frequently occur during trials, when it is impractical to draft a written motion. A common oral motion occurs during witness testimony. Witnesses sometimes give inadmissible testimony before an attorney can object. When that happens, the attorney must object and move the court to strike the inadmissible testimony from the record. Motions for mistrial—made when courtroom proceedings are fraught with errors, inadmissible evidence, or disruptions so prejudicial to a party's case that justice cannot be served—often are made orally. Sometimes judges themselves take action on

behalf of a party, such as changing or adding necessary language to a pleading without a motion from a party. This is known as making an amendment on the court's own motion.

A motion to dismiss asks the court to dismiss an action because the initial pleading, or complaint, fails to state a cause of action or claim for which the law provides a remedy. For example, a complaint alleges that an employer unfairly fired an employee but does not allege illegal discrimination or labor practices. Merely firing an employee for unfair reasons is not illegal; thus a court may dismiss this complaint.

A motion to strike asks the court to remove from the record inadmissible evidence or language in pleadings that is redundant, immaterial, impertinent, or scandalous. A party can file a motion for a more definite statement when the language in a pleading is so vague or ambiguous that the party cannot reasonably be expected to draft a responsive pleading.

A motion for summary judgment, also known as a motion for judgment on the pleadings, asks the court to make a judgment solely on the facts set forth in the pleadings, without the necessity of trial. A court will grant a summary judgment motion when the material facts of the case are not in dispute and all that remains to be determined are questions of law. For example, in Stieber v. Journal Publishing Co., 120 N. M. 270, 901 P.2d 201 (App. 1995), the court found that the issue of whether a newspaper company's treatment of a reporter was extreme and outrageous was a legal question, not a factual question. In that case the reporter, Tamar Stieber, sued her employer for, among other things, intentional infliction of emotional distress. Stieber charged that the newspaper asked her to write so many daily stories that she could not perform her duties as a special projects reporter. To recover for the tort of intentional infliction of emotional distress, the court noted, Stieber had to prove that the newspaper's conduct was so extreme and outrageous as to go "beyond all possible boundaries of decency, and to be regarded as atrocious, and utterly intolerable in civilized community." The court ruled that as a matter of law, Stieber failed to prove this allegation, and the lower court's summary judgment was affirmed.

A motion in limine, also made before trial, asks the court to prohibit an opposing party from offering evidence or referring to matters that would be highly prejudicial to the movant during a trial. A motion to suppress is similar to a motion in limine but asks the court to keep out of a criminal trial evidence that was obtained illegally, usually in violation of the Fourth, Fifth, or Sixth Amendments to the U.S. Constitution. For example, a defendant in a murder trial may move the court to suppress her confession because she was questioned without being told of her right to have an attorney present.

Following a trial but before a jury verdict, a party may move for a directed verdict, asking the judge to make a judgment without letting the jury reach a verdict. Following a jury verdict, a party may move for judgment notwithstanding the verdict, or JNOV. This motion requests that the court enter a judgment contrary to the jury verdict, and is granted when no reasonable jury could have reached that verdict. A motion for a new trial asks the judge to order a new trial, setting aside the judgment or verdict, because the trial was improper or unfair. This motion is sometimes brought as the result of newly discovered evidence.

further readings

Dessem, R. Lawrence. 2001. Pretrial Litigation in a Nutshell. 3d ed. St. Paul, Minn.: West Group.

cross-references

Civil Procedure; Criminal Procedure.

282. Motion

See also 399. TRAVEL .

apheliotropism

the tendency of some plants to grow in a direction away from the sun.

apogeotropism

the tendency of some plants to grow away from the earth and the pull of gravity. —apogeotropic , adj.

bradykinesia, bradykinesis

slowness of movement. —bradykinetic , adj.

chemotaxis

the property of some plants and animals of moving toward or away from certain chemicals.

chemotropism

growth or motion in response to a chemical stimulus. —chemotropic , adj.

diatropism

the capacity or tendency of some plants to adopt a position transverse to the line of force of an external stimulus. — diatropic , adj.

dromophobia

kinetophobia.

galvanotropism

growth or movement of an organism in response to an electric current. —galvanotropic , adj.

geotaxis

the movement of an organism in response to the force of gravity.

kinematics

the study of the motion of bodies considered independently of external forces. Also called phoronomy . —kinematic , adj.

kinesomania

a mania for movement.

kinetics

the branch of physics that studies the motion of masses in relation to the forces acting on them.

kinetophobia

an abnormal fear or dislike of motion. Also called dromophobia .

phoronomy

kinematics.

photokinesis

movement of bodies, organisms, etc., in response to the stimulus of light. —photokinetic , adj.

phototaxis, phototaxy

the movement of an organism away from or toward a source of light. —phototactic , adj.

phototropism

motion in a particular direction under the stimulus of light, as exhibited by certain plants, organisms, etc. —phototropic , adj.

rheotaxis

the tendency of certain living things to move in response to the mechanical stimulus of a current of water.

stereotaxis

orientation or movement of an organism in response to the stimulus of a solid object. Cf. stereotropism. —stereotactic , adj.

stereotropism

growth or movement determined by contact with a solid. Also called thigmotropism . Cf. stereotaxis. —stereotropic , adj.

tachophobia

an abnormal fear of speed.

thigmotropism

stereotropism. —thigmotropic , adj.

trochilics

Rare. the science of rotary motion. —trochilic , adj.

trophotropism

the movement of cells in relation to food or nutritive matter. —trophotropic, adj.

tropism

the tendency of a plant, animal, or part to move or turn in response to an external stimulus, as sunlight or temperature. —tropistic , adj.

mo·tion / ˈmōshən/ • n. 1. the action or process of moving or being moved: the laws of planetary motion a cushioned shoe that doesn't restrict motion. ∎  a gesture: she made a motion with her free hand. ∎  a piece of moving mechanism.2. a formal proposal put to a legislature or committee: the head of our commission made a motion that we rewrite the constitution. ∎  Law an application for a rule or order of court.3. Mus. the movement of a melodic line between successive pitches: they rely heavily on repeated chord tones and much less often on conjunct melodic motion.• v. [tr.] direct or command (someone) with a movement of the hand or head: he motioned Dennis to a plush chair | [tr.] he motioned the young officer to sit down | [intr.] he motioned for a time out. PHRASES: go through the motions do something perfunctorily, without any enthusiasm or commitment. ∎  simulate an action: a child goes through the motions of washing up.in motion moving: flowing blonde hair that was constantly in motion.set something in motion start something moving or working. ∎  start or trigger a process or series of events: plunging oil prices set in motion an economic collapse.DERIVATIVES: mo·tion·al / -shənl/ adj.mo·tion·less adj.mo·tion·less·ly adv.