by Corry Shores
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[The following is summary. Bracketed commentary and boldface are my own. Text quotations are copied from wikisource. Proofreading is incomplete, so I apologize for my distracting typos.]
Summary of
Bertrand Russell
“The Philosophy of Bergson”
sections 2.10-2.14
[critique of Bergson’s theory of motion in its Zeno’s paradox elaboration]
Brief summary:
Bergson criticized the mathematical account of movement and proposed instead that motion is indecomposable into such parts as spatial or temporal determinations. One way Bergson elaborated this insight was by showing how the notion of decomposable motion results in the absurd conclusions of Zeno’s paradoxes. Russell, however, defends the mathematical account against Bergson’s critiques by exploiting certain vague concepts in Bergson’s account and interpreting them uncharitably. According to Bergson, the motion of a moving object is something that while it happens does not admit of partitions in its location and duration. All moments of its motion, while it is happening, are intertwined. It is only afterward upon an abstract and conceptual analysis that we can discern the places it was and coordinate them with times in the past. But were we to make such a secondary analysis and were we furthermore to want to do as much justice as possible to the way the motion had happened, we would say that it was passing through the spatial positions (in a sort of indeterminate occupation) but was never determinately occupying them like objects at rest do. This notion of passing through points is vague (and I think it could be made less vague using paraconsistent reasoning), and Russell exploits this vagueness by claiming that for Bergson, the object never is in any place while it is moving. (This is true, but a more accurate claim would be that for Bergson, it is never determinately in any place, although upon retrospective analyses, we would say it still moved through all places along its course without determinately occupying any.) So Bergson’s assessment is that Zeno’s paradoxes lead to absurdity when we mistakenly view motion as decomposable. Russell, however, claims that the absurdity does not result so long as we believe that the motion is infinitely decomposable but just not into parts which are themselves motions. (The basic parts for Russell are space-time positions, like being at position p at time t, or what we might call ‘at-at’ determinations.) Russell believes that motion is nothing more than an object’s occupying every possible spatial determination at every instant along its course. Russell thus does not think that an account of motion requires explaining how the object moves from one place to another. (As he puts it, being at different positions at different times, with those positions differing no matter how near the times are.) In other words, for Russell, the density of the spatial continuum of the motion’s path is enough to account for the motion itself. (Russell’s “at-at” theory of motion thus fails to account for how motion transpires. It only describes the properties of the space traversed, which Bergson has already shown to be an inadequate tactic.)
Summary
2.10
[Bergson argued against the mathematical, “cinematographic” representation of motion and change, which sees it as being composed of discrete, determinate states or positions and which comes naturally to the intellect. Instead, Bergson thinks, we should recognize the real duration where moments interpenetrate and thus there are no determinate states or positions.]
Russell will concern himself now with Bergson’s treatment of Zeno and rejection of what Bergson “calls the ‘cinematographic’ representation of the world” (337). Russell says this is “the chief point at which Bergson touches mathematics” (337). [While it is true that mathematicians may conceptualize change this way, I think for Bergson the cinematographic representation is not simply something mathematicians would think but is rather something we all are given to think when for practical reasons we fabricate that mathematicized space onto real motion. (See for example Matter and Memory section 4.2.6; Creative Evolution sections 4.5.3 to 4.5.4.) Bergson thinks in fact that the cinematographic representation is the product of our misguided common sense.] Russell explains that “Mathematics conceives change, even continuous change, as constituted by a series of states” [and thus it is cinematographic, like the series of still frames in a film that move rapidly enough to give the illusion of real motion.] Bergson, however, “contends that no series of states can represent what is continuous, and that in change a thing is never in any state at all” (337). [A theme I will keep returning to is Russell’s confusion between continuity taken simply and continuous motion. The important difference here is that in order to give an account of continuous motion, it is not enough to only provide a mathematical description of the spatial continuity of the motion, although that might be shown to be necessary to do as one part of the account. It is insufficient to merely do that, however, because one also needs to account for the motion itself which happens to be continuous. We will see Russell using language that allows him to slip among these senses, which might confuse us into thinking that his mathematical accounts of continuity thereby are sufficient to account for continuous motion. But let us instead be clear and precise, and let us closely track his concepts and language. He says, “Bergson [...] contends that no series of states can represent what is continuous”. But for Bergson, the continuity in question is a durational continuity, not a spatial one. Thus it involves motion, change, becoming. Russell should have written something like, “Bergson [...] contends that no series of states can represent what is continuously moving or changing.” He continues to say that Bergson also contends that “in change a thing is never in any state at all”. This should be written, “in change a thing is never in any fixed, determinate state at all”. But perhaps these qualifications are built into the sense Russell intends them to have anyway.] Russell then notes how for Bergson, the cinematographic view comes naturally to the intellect, “but is radically vicious”. Bergson thinks that instead we need to take a dynamic rather than a static view of the world, where past and present interpenetrate somehow [rather than lie discretely juxtaposed beside one another].
Apart from the question of number, which we have already considered, the chief point at which Bergson touches mathematics is his rejection of what he calls the “cinematographic” representation of the world. Mathematics conceives change, even continuous change, as constituted by a series of states; Bergson, on the contrary, contends that no series of states can represent what is continuous, and that in change a thing is never in any state at all. This view that change is constituted by a series of changing states he calls cinematographic; this view, he says, is natural to the intellect, but is radically vicious. True change can only be explained by true duration; it involves an interpenetration of past and present, not a mathematical succession of static states. This is what is called a “dynamic” | instead of a “static” view of the world. The question is important, and in spite of its difficulty we cannot pass it by.
(338-339. Text copied from Wikisource)
2.11
[Bergson’s argument against the cinematographic representation of motion and change is illustrated in his discussions of Zeno’s paradoxes. (Bergson says there is no absurdity when we recognize that the motion itself does not have all the mathematical properties of the space travelled, including infinite divisibility). Russell however thinks that the infinite divisibility of the space is enough to account for the continuity of the motion (although Russell does not seem thereby to account for the motion itself which takes the object out of one position and into another). Russell defines continuous motion simply as the object being at all the infinitely many intervening locations each at a different time.]
Russell now looks at how Bergson elaborates his insights using the absurdities of Zeno’s paradoxes, with one being the argument of the arrow. Russell reminds us that “since the arrow at each moment simply is where it is, therefore the arrow in its flight is always at rest” (339). Russell then says it would seem that there is not an obvious problem here, and then he uses what has come to be called the “at-at” account of motion to show that such a view of static states can still account for physical movement: “Of course, it will be said, the arrow is where it is at one moment, but at another moment it is somewhere else, and this is just what constitutes motion” (339). [Returning to our theme, this in fact does not constitute motion, because it does not explain the main defining property of motion, namely, changing location. Russell seems blind to Bergson’s fundamental claim that we must be careful not to think that a simple description of the mathematical or geometrical properties of the space travelled is enough to tell us about the motion that travelled that space. But this is all that Russell seems capable or willing to do. Its inadequacy is evinced by the fact that this description of being at one place at one time and at another place at another time (even though those places can be brought arbitrarily near), does not give us any intuition of the movement which takes the object from one such place to the other. He is doing no more than describing the mathematical properties of the space traversed and giving no account for the motion of travel. And even the most superficial reading of Bergson should have alerted him to this inadequacy in his account.] Russell then writes: “Certain difficulties, it is true, arise out of the continuity of motion, if we insist upon assuming that motion is also discontinuous”. [Russell is trying to be clever here, and it makes his point a bit buried in the language. When he writes, “assuming that motion is also discontinuous,” I think what he really means to say is “assuming that being determinately in every position implies not changing between positions and thus being composed of discrete steps with no transition between them.” And moreover, the paradoxes are not necessarily about the problems of the continuity of motion. The assumption of the paradox is not “assume motion is continuous”. Rather, it assumes simply that there is motion and that the motion is metrically divisible with limit. So Russell again is trying to confuse us into seeing these issues as boiling down to spatial or temporal continuity rather than with the problem of understanding how things can change place. Russell wants us to believe that simply being at every spatial point is the same as moving to every spatial point. And he often tells us that if we understood mathematics more, we would get this intuition. But where is the mathematical insight which turns an intuition of an object at a position into an intuition of an object moving away from a position? Probably it is just too technical for a mathematically inept person like myself to understand. But can he not at least point us to a text that provides the technical account for how this is to be undersood? The fact that he does not do this suggests the possibility that he just wants us to go along with his inferior account simply on our trust of his excellent understanding of math. But his philosophical claim is that mathematical findings should also serve as philosophical findings. Where in mathematics is it proven that mathematical continuity accounts for physical motion, or at least where is there the mathematical intuition of spatial continuity that also provides the intuition of continuous physical motion? It seems to me that the best mathematics can do is to show the mathematical continuity of the space travelled and not of the motion itself travelling through that space. In other words, what Russell is doing is redundant and useless for his stated purpose. He wants to account for continuous motion. But he is only able to say that a dense continuum of space has dense continuity.] Bergson claims that this mathematical notion of dense continuum is sufficient to account for motion, and he does so by building upon the cinematograph metaphor: “A cinematograph in which there are an infinite number of films, and in which there is never a next film because an infinite number come between any two, will perfectly represent a continuous motion.” [It is odd that Russell has read the relevant sections of Creative Evolution so closely and yet seems blind to the most important and obvious insights Bergson makes there. Bergson uses the metaphor of the cinematograph, because it involves mechanisms that turn the frames one to the next, adding the motion artificially from the outside rather than the motion being inherent to the images. And Bergson wants us to see that mechanical motion metaphorically as being like the abstract notion of Becoming or general motion that we erroneously think transpires between positions or states, as if it were not inherently a part of the motion and change itself. (See Creative Evolution section 4.5.2.) So Russell, in building upon this metaphor, should recognize at least that the motion of the cinematographic device’s mechanisms is portrayed as being what turns the frames. But he wants us to think instead that by having an infinity of intervening frames that the mechanism (or the movement of duration, more literally) would be unnecessary for the motion, because the frames (or moments, states, positions, etc.) would turn all on their own simply by means of their dense continuity. So still even with this modified metaphor, he is explaining the continuity but not the motion.] [Russell thinks he thus has an easy solution to Zeno’s paradoxes, and so] he ends by asking: “Wherein, then, lies the force of Zeno’s argument?”
Bergson’s position is illustrated—and what is to be said in criticism may also be aptly illustrated—by Zeno’s argument of the arrow. Zeno argues that, since the arrow at each moment simply is where it is, therefore the arrow in its flight is always at rest. At first sight, this argument may not appear a very powerful one. Of course, it will be said, the arrow is where it is at one moment, but at another moment it is somewhere else, and this is just what constitutes motion. Certain difficulties, it is true, arise out of the continuity of motion, if we insist upon assuming that motion is also discontinuous. These difficulties, thus obtained, have long been part of the stock-in-trade of philosophers. But if, with the mathematicians, we avoid the assumption that motion is also discontinuous, we shall not fall into the philosopher’s difficulties. A cinematograph in which there are an infinite number of films, and in which there is never a next film because an infinite number come between any two, will perfectly represent a continuous motion. Wherein, then, lies the force of Zeno’s argument?
(338-339. Text copied from Wikisource)
2.12
[We have the natural insight that there are things that change. But philosophers have broken off into camps which take extreme positions on the matter and thereby generate their own absurdities. Heraclitus and Bergson think there are changes but no things. The Eleatics (including Zeno) thought there are things but no changes.]
Russell then gives more background for Zeno’s paradoxes and situates Bergson’s philosophy into this context. He explains how Zeno, as an Eleatic philosopher, believed that “there could be no such thing as change” (339). Russell then writes, “The natural view to take of the world is that there are things which change; for example, there is an arrow which is now here, now there” (339). [I am not sure, but I am assuming that the natural view is not the Eleatic one. He simply wants us to think of the common sense distinction between things and their changes, but I am not sure.] Russell then says that this natural intuition then spins off into two opposing positions which lead to their own paradoxes: {1} “The Eleatics said that there were things but no changes”, and {2} “Heraclitus and Bergson said that there were changes but no things” (339). [I am not sure that Bergson’s philosophy commits him to the claim that there are changes but not things. There are certainly changes for him. But I would like to know more why for him there are no things, but only changes. Is it because a thing is defined as having determinate limits, like spatial and developmental ones, but the nature of duration prevents there from being such determinate limits while real duration is transpiring? Or is it something like the idea of there being no closed systems with everything composing one All, Whole, or Duration? in other words, that the distinctions we make between things are artificial carvings out of one unified whole? It would not surprise me if Bergson claims there are not things but only changes, but I also think it is possible Russell is confusing Bergson’s more nuanced philosophy with a simple Heraclitean conception.] So in the case of the arrow paradox: “The Eleatics said there was an arrow, but no flight; Heraclitus and Bergson said there was a flight but no arrow.” [What could be interesting here is if for Bergson the arrow continually changes identity throughout its flight, perhaps because it is never self-same on account of small differences that somehow make a substantial difference, or perhaps on account of the incommensurability of each moment to others at other times. But I again am not exactly sure yet where Russell is getting the idea that there is no arrow for Bergson, because I do not recall him saying anything like that when discussing the arrow.] Russell then portrays the situation as philosophers taking two absurd sides and conducting their arguments by focusing only on the other’s absurdity: “Each party conducted its argument by refutation of the other party. How ridiculous to say there is no arrow! say the ‘static’ party. How ridiculous to say there is no flight! say the ‘dynamic’ party.” Russell then says there is a [better] position in the middle which says there is both the arrow and its flight. [Again, is Bergson in his Zeno commentaries really saying there is no arrow but instead there is just its flight?] Russell ends by suggesting that there is still an insight to be gained from Zeno’s paradoxes of motion.
Zeno belonged to the Eleatic school, whose object was to prove that there could be no such thing as change. The natural view to take of the world is that there are things which change; for example, there is an arrow which is now here, now there. By bisection of this view, philosophers have developed two paradoxes. The Eleatics said that there were things but no changes; Heraclitus and Bergson said that there were changes but no things. The Eleatics said there was an arrow, but no flight; Heraclitus and Bergson said there was a flight but no arrow. Each party conducted its argument by refutation of the other party. How ridiculous to say there is no arrow! say the “static” party. How ridiculous to say there is no flight! say the | “dynamic” party. The unfortunate man who stands in the middle and maintains that there is both the arrow and its flight is assumed by the disputants to deny both; he is therefore pierced, like St. Sebastian, by the arrow from one side and by its flight from the other. But we have still not discovered wherein lies the force of Zeno’s argument.
(339-340. Text copied from Wikisource)
2.13
[The absurdity of Zeno’s paradoxes results from defining motion to always involve the moving thing being in a state of motion. In order for the arrow to change positions, it needs to be in a state of motion. But if it does change positions, it determinately occupies all the intervening positions. And to determinately occupy a position means to have no intrinsic property to distinguish it from being at rest. In other words, it must also never be in a state of motion, even though we also inferred that it always is. We must reject our original assumption that motion is real and conclude there is no such thing as motion or change.]
[I may not get the next ideas right, but my sense is that they are the following. The way Zeno presents the absurdity in the following way. He on the one hand notes that the moving object occupies particular positions. He also notes that if we look at the intrinsic properties of the object, it would be no different were it at rest. In other words, when an object occupies a determinate position along is course of motion, there is nothing about that object that would determine whether it is in motion or at rest. At the same time, however, Zeno wants us to hold on to the intuition that since the object is in motion, it should have some intrinsic property that would indicate it is in motion, namely, it would have “some internal state of change”. So we begin by assuming the arrow is in motion, which means we must infer that the arrow always has an internal state of (positional) change. At the same time, we analyze that motion into its component parts and find that at no moment does it have such a internal state of change. On the basis of that observation, we infer that it is not in motion. So it is both in motion and is not. (But, if I am not mistaken, this is a reductio argument on the original claim that motion is real, thus we must somehow conclude there is no motion. Maybe the argument works like the following, but I am guessing: {1} Assume motion is real. {2} That means the motion of an arrow is real. {3} This means it is in a state of motion whenever it is moving. {4} But throughout its motion it can only be said to be occupying determinate positions where it is not in a state of motion. This contradicts 3 above. {5} Thus our original assumption 1 is false, and therefore motion is not real.)]
Zeno assumes, tacitly, the essence of the Bergsonian theory of change. That is to say, he assumes that when a thing is in a process of continuous change, even if it is only change of position, there must be in the thing some internal state of change. The thing must, at each instant, be intrinsically different from what it would be if it were not changing. He then points out that at each instant the arrow simply is where it is, just as it would be if it were at rest. Hence he concludes that there can be no such thing as a state of motion, and therefore, adhering to the view that a state of motion is essential to motion, he infers that there can be no motion and that the arrow is always at rest.
(340. Text copied from Wikisource)
2.14
[Bergson responds to Zeno’s paradox by claiming that the arrow is never anywhere. His claim that mathematical view of change implies the absurd notion that motion is composed of immobilities makes the following error: not everything is composed of parts homogenous with the whole, and motion is composed not of motions but rather of spatio-temporal determinations. Motion is nothing more than the moving object being in different places at different times, with those places remaining different no matter how near we make the times (the so called “at-at” theory of motion).]
[This final paragraph on Bergson’s treatment of Zeno is in fact quite interesting and promising, but very tricky to follow. Let us go part by part. “Zeno’s argument, therefore, though it does not touch the mathematical account of change, does, prima facie, refute a view of change which is not unlike M. Bergson’s.” (The first point I think is that Zeno’s argument is not the same as Russell’s at-at “mathematical” theory. Zeno is not saying that motion is composed of a dense infinity of rests like Russell is. Zeno is rather saying this is absurd. The second point seems to be that Russell also thinks that Zeno’s argument still holds up to Bergson’s critique.) “How, then, does M. Bergson meet Zeno’s argument? He meets it by denying that the arrow is ever anywhere. After stating Zeno’s argument, he replies: ‘Yes, if we suppose that the arrow can ever be in a point of its course. Yes again, if the arrow, which is moving, ever coincides with a position, which is motionless. But the arrow never is in any point of its course’ (C. E., p. 325). This reply to Zeno, or a closely similar one concerning Achilles and the Tortoise, occurs in all his three books.” (Note: See Time and Free Will ch.2, §70; Matter and Memory section 4.2; and Creative Evolution section 4.5. Russell’s quotation comes from CE 4.5.8. What we see here is something that does seem conceptually vague in Bergson’s texts. I considered a number of ways to interpret Bergson’s meaning. The one I settled with is the following. There are two ways we can understand motion: either correctly, by intuitively grasping it as it is happening, or erroneously, but analyzing it abstractly and spatially after its completion by means of our intellect, common sense, and language. Were we to follow the motion as it is happening, we would not say it is constituted by a series of instants. We would always be following it in its present moment of change, which is structurally intertwined with past moments in such a way that we cannot say the present moment is like a cut in time. It is rather maybe like a “zone of indetermination” or something vague like that. Whatever is in motion or change is not following some predeterminable path and is rather alive with vital mutation and unpredictability. Also, the intertwinement of all the moments is so thorough that a motion like that of our hand going from A to B is one solid indivisible motion with no further internal temporal sequentialization being possible. In a block of measurable time it goes a block of measurable space. But the motion itself does not consist of a series of discrete space-time coordinates. If we fail to recognize this fact, it is because we are using our intellects in such a way that we are no longer thinking about the movement itself but rather abstractly about the spatializable or mathematicizable extents of time and space we measure it to have occupied throughout the course of its motion. Were we instead to think solely of the movement, we would be aware directly of that movement itself, which means we would be aware of it while it is happening, and thus we would be aware that it is indivisible as it is happening. Now having established that, Bergson also seems to entertain a way of revising the erroneous abstract conception so to make it less erroneous, although still not adequate for the task of understanding motion intuitively. If we are going to make the mistake of designating points of traversed space to be coordinated with instants of time, would say say that instead of the object ever being in one location ((at some time)) we should say that it is passing at some location. ((See Matter and Memory section 4.2.3.)) This is vague and perhaps he does not clarity it, perhaps because the framework it is set within is erroneous to begin with ((that is to say, it assumes distinct moments or short intervals that divide the motion, during which the object can be said to be around some point.)) But I argue it could be clarified further by using paraconsistent reasoning. To be “passing at” some point rather than “being at” some point means to both occupy it and not to occupy it. Let me extend this claim to say that although using such a paraconsistent reasoning will not give us a direct intuition of motion as it is happening, it would still however give us a more suitable translation of that intuition were we compelled to render it in these abstract terms. And so by grasping it paraconsistently, we might better direct our minds to its more proper mental realization. In other words, what I am going for more generally is to use notions of determination, plus paraconsistent reasoning, to move our minds in the direction of the indeterminacies found in the notions we want to intuit or conceive.) “Bergson’s view, plainly, is paradoxical;” (Recall the view from above, which Russell says is paradoxical: “Yes, if we suppose that the arrow can ever be in a point of its course. Yes again, if the arrow, which is moving, ever coincides with a position, which is motionless. But the arrow never is in any point of its course”. I am not exactly sure where the paradox is here. Bergson never says that the object both is and is not in every position, exactly. He says that passes through them but never occupies any. Bergson thinks there is something about motion that prevents the moving object from being determinately at any position. So in this ((erroneous)) spatialized understanding of the completed path of the object, we would say that at some supposed time it was not at some place determinately but was there indeterminately, with how to understand that indeterminate occupation left vague ((perhaps because it is part of what Bergson thinks is a faulty framework to begin with and thus does not require further clarification; rather, what is required is a different framework, one that is not a spatialization of the motion. If Russell thinks the paradox is something other than the object is both occupying and not occupying positions, then I am not sure what it would be. It is not clear to me yet how the indeterminate occupation interpretation is paradoxical;) “whether it is possible, is a question which demands a discussion of his view of duration.” (I am not sure of the point here. Russell might be saying that although Bergson’s account is paradoxical, it still might be possible in the context of his concept of duration ((if for example the duration of the motion is such that it allows for paradoxes of position)).) “His only argument in its favor is the statement that the mathematical view of change ‘implies the absurd proposition that movement is made of immobilities’ (C. E., p. 325).” ( ((See Creative Evolution section 4.5.5.)) I agree here that Bergson could do more to make his case more convincing. He does appeal to experience in a phenomenological sort of way, which could be convincing to others. But maybe Russell is making the following point. The evidence here in this context of Zeno ((let us allow Russell to exclude the phenomenological evidence)) is taken as proof for Bergson’s claim, in Russell’s reading. So because Zeno’s arguments are absurd, the assumption that we are to reject is that the object occupies positions while it is moving. ((If I had to guess again, perhaps Russell thinks Bergson is setting up the argument in the following way. ({0} Take for granted that motion is real.) {1} Assume that motion involves occupation at points or positions along the course of the movement. {2} Note that at any such occupation, the object has no intrinsic properties that would indicate it is in motion rather than in rest. {3} But also note that since it is in motion at each point, it must have some such intrinsic property or state of change. This contradicts 2 above. Thus we must reject assumption 1 and conclude that the moving object does not occupy any positions along its motion. Supposing that is how Russell reads Bergson’s argument, I am not sure he followed the main thrust of it. I would think Bergson’s argument is more like the following. {1} Suppose motion is infinitely divisible like the space it travels. That means {2} the motion is made of nothing more than immobile positions, in other words, that it is both in always in motion but never in motion. This is absurd, so we reject supposition 2 and conclude on the one hand that motion cannot be infinitely divisible. Now to be sure we check the following. {4} Suppose motion is not divisible, finitely or infinitely. That means it cannot be said to occupy immobile positions. Thus it is simply in motion. So the assumption that motion is decomposable leads to absurd conclusions, but assuming it is indecomposable does not. This may not conclusively prove that motion is indecomposable. Perhaps it at least demonstrates one way that this notion is consistent with our other intuitions regarding motion (that for example it involves a state of motion in any of its parts, contra Russell’s claim). So again, I agree with Russell that the discussion of Zeno is not proof of Bergson’s thesis, but it is rather a way of elaborating it. I have two questions then: {a} does Bergson have any other arguments that do suffice as proof? As far as I know, he seems only to have phenomenological evidence along with many more such interesting elaborations and illustrations. I would need to check the arguments again to see if there are no “proofs”, especially in Duration and Simultaneity, which could have candidates. My second question, {b}: does Russell have any “proof” of his own at-at account? He certainly does not have phenomenological proof, since we do not perceive motion as a series of still positions. The phenomenological evidence goes completely against his thesis. We also have conceptual intuitions of motion that go against his thesis; that is to say, we have intuitions that motion is the opposite of rests, no matter how many, but is rather the change of position, which cannot be a matter of rest whatsoever. And recall Russell’s charge that Bergson’s theory is paradoxical, and let us look at his own theory to see how it holds up to that critique. Russell wants us to believe that the moving object is never at any moment transiting from one position to another, but rather it simply occupies every possible position in dense continuum. It would seem then that the real danger of absurdity is in Russell’s account, because he both claims that the object changes place while also claiming that during no moment does it change place. (Simply having been in all places is enough to say that it moved, for Russell.) So Bergson’s conception is consistent (when we do not misinterpret him as saying the object never even passes through positions), and it corresponds with our intuitions, and it also corresponds with phenomenological evidence. Russell’s conception, however, is counter-intuitive, seemingly paradoxical, and goes against all phenomenological evidence. But let us look more at how he wants us to conceive the matter, which should make it seem less paradoxical)).) “But the apparent absurdity of this view is merely due to the verbal form in which he has stated it, and vanishes as soon as we realize that motion implies relations.” (I am not sure, but maybe the ‘verbal form’ here is that “movement is made of immobilities” which suggests that something’s composition must be consistent with it as a whole.) “A friendship, for example, is made out of people who are friends, but not out of friendships; a genealogy is made out of men, but not out of genealogies. So a motion is made out of what is moving, but not out of motions. It expresses the fact that a thing may be in different places at different times, and that the places may still be different however near together the times may be.” (His basic claim here is that were we to decompose motion, it would be decomposable either into parts that are homogeneous with the whole or parts that are not homogenous. And furthermore, he claims that they are not homogeneous. He does not supply any proof that the parts of motion are not themselves motions. So this part is unclear: “a motion is made out of what is moving, but not out of motions” like how a friendship is made out of people but not friendships. But if motion is not made out motions, then what is it made out of? As far as I can tell, what the thing’s motion is made out of are all its space-time determinations. Note here the slipperiness of the language. He is defining not the spatial continuity of motion nor “continuous motion” but just simply “motion”. The motion is made out of what is moving. What is moving are its space-time determinations. The problem here is that on the one hand we are to infer that the space-time determinations are moving ((because “a motion is made out of what is moving”)) while at the same time, those positions are determinately in their place. Suppose the object in the middle of its motion at t3 is in position p3. That is one part of its motion. But that part itself does not move to position p4 at t4. Rather, that is another determinate space-time location altogether. So it is not the same space-time location that has moved, as Russell’s wording seems to want us to conceive. Russell has not given us the motion yet. He has only given us a description of the static spatial and temporal determinations of the motion. The best I can think for seeing how this has something to do with motion is if we always keep in mind that to each spatial location corresponds a temporal one, and that we must think about that coordination itself in order to uncover the motion. But I am not seeing it there yet. Perhaps the best way to interpret Russell is on the basis of what might be an intrinsic/extrinsic distinction with regard to motion. He said above that there is no intrinsic state of change. But maybe he is saying that motion is an extrinsic relation between time-space determinations. But I am not sure how to understand the relation between points as necessarily constituting the motion between them. Cannot the relations simply be ones of spatial and temporal succession? And if he is saying that the motion is found in the extrinsic relations between time-space determinations, that would suggest that motion still “slips through the cracks”, that we always miss it, because we can never for Russell capture it in any moment.) “Bergson’s argument against the mathematical view of motion, therefore, reduces itself, in the last analysis, to a mere play upon words.” (I do not see how it is nothing more than a play on words, unless we want to fault him for not making certain distinctions we placed into our interpretation, like determinate occupation at a point and indeterminate passage through a point. To me it seems instead that Bergson hit upon a very philosophically profound insight, but given how deeply rooted it is, he found it very difficult to “prove” and to make clearly conceptualizable. If this were really so, than I would think that a more fruitful approach would be to read Bergson’s texts more charitably and cooperatively (think Deleuze’s Bergsonism), rather than to nitpick through all the ways Bergson fell short in conceptualizing and communicating this insight. Russell’s stance seems to be that because it was not laid completely bare and proven logically, that there may as well be no philosophical insight in it at all. And yet his counter explanation of motion is even less promising and less philosophically interesting than Bergson’s is.)]
Zeno’s argument, therefore, though it does not touch the mathematical account of change, does, prima facie, refute a view of change which is not unlike M. Bergson’s. How, then, does M. Bergson meet Zeno’s argument? He meets it by denying that the arrow is ever anywhere. After stating Zeno’s argument, he replies: “Yes, if we suppose that the arrow can ever be in a point of its course. Yes again, if the arrow, which is moving, ever coincides with a position, which is motionless. But the arrow never is in any point of its course” (C. E., p. 325). This reply to Zeno, or a closely similar one concerning Achilles and the Tortoise, occurs in all his three books. Bergson’s view, plainly, is paradoxical; whether it is possible, is a question which demands a discussion of his view of duration. His only argument in its favor is the statement that the mathematical view of change “implies the absurd proposition that movement is made of immobilities” (C. E., p. | 325). But the apparent absurdity of this view is merely due to the verbal form in which he has stated it, and vanishes as soon as we realize that motion implies relations. A friendship, for example, is made out of people who are friends, but not out of friendships; a genealogy is made out of men, but not out of genealogies. So a motion is made out of what is moving, but not out of motions. It expresses the fact that a thing may be in different places at different times, and that the places may still be different however near together the times may be. Bergson’s argument against the mathematical view of motion, therefore, reduces itself, in the last analysis, to a mere play upon words. And with this conclusion we may pass on to a criticism of his theory of duration.
(340-341)
Russell, Bertrand. 1912. “The Philosophy of Bergson.” Monist vol. 22, no. 3: pp.321-347.
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