A "solution" to Zeno's paradox.
Consider, for example, the variability which is nearest to homogeneity, that of movement in space. Along the whole of this movement we can imagine possible stoppages; these are what we call the positions of the moving body, or the points by which it passes. But with these positions, even with an infinite number of them, we shall never make movement. They are not parts of the movement, that are so many snapshots of it; they are, one might say, only supposed stopping-places. The moving body is never really in any of the points; the most we can say is that it passes through them. But passage, which is movement, has nothing in common with stoppage, which is immobility. A movement cannot be superposed on an immobility, or it would then coincide with it, which would be a contradiction. The points are not in the movement, as parts, nor even beneath it, as positions occupied by the moving body. They are simply projected by us under the movement, as so many places where a moving body, which by hypothesis does not stop, would be if it were to stop. They are not, therefore, properly speaking, positions, but "suppositions," aspects, or points of view of the mind. But how could be construct a thing with points of view? - Henri Bergson, An Introduction to Metaphysics
I think I'm beginning to see how Deleuze was able to appropriate Bergson's philosophy of intuition and duration, and brilliantly synthesize it with Spinoza's neutral monism. At first, I was tempted, albeit tentatively, to compare it with Zizek's Lacanian analysis of Zeno's paradox in its overwhelming abstraction. However, upon closer inspection, I'm starting to believe that this study is steeped neither purely in the physical nor psychical realm, as a distinction as such is arbitrary at best, and, for all intents and purposes, doesn't even exist, fitting splendidly with Spinoza's ontology.
The "solution" to Zeno's Paradox, then, consists in the fact that a paradox as such does not exist and/or exists purely in man's limited psyche, the mutual inclusion of mind/matter the two halves of "God" (The term "God" being used in a purely regulative and not theological manner). The arrow hits the target and appears to stop, but, for all practical purposes, paradoxically never even starts or stops moving in the first place. Motion never had a beginning, nor does Motion ever have an end. What are time and space, then, but two sides of the same coin, an eternal, dialectically mediated flux whose two components can only be arbitrarily distinguished?
EDIT: I've noted that Bergson pointed out that "movement serves as a means of representation [of time]." It would thus follow that Zeno's Paradox is a fallacy, since movement is studied in the absence of time.
I think I'm beginning to see how Deleuze was able to appropriate Bergson's philosophy of intuition and duration, and brilliantly synthesize it with Spinoza's neutral monism. At first, I was tempted, albeit tentatively, to compare it with Zizek's Lacanian analysis of Zeno's paradox in its overwhelming abstraction. However, upon closer inspection, I'm starting to believe that this study is steeped neither purely in the physical nor psychical realm, as a distinction as such is arbitrary at best, and, for all intents and purposes, doesn't even exist, fitting splendidly with Spinoza's ontology.
The "solution" to Zeno's Paradox, then, consists in the fact that a paradox as such does not exist and/or exists purely in man's limited psyche, the mutual inclusion of mind/matter the two halves of "God" (The term "God" being used in a purely regulative and not theological manner). The arrow hits the target and appears to stop, but, for all practical purposes, paradoxically never even starts or stops moving in the first place. Motion never had a beginning, nor does Motion ever have an end. What are time and space, then, but two sides of the same coin, an eternal, dialectically mediated flux whose two components can only be arbitrarily distinguished?
EDIT: I've noted that Bergson pointed out that "movement serves as a means of representation [of time]." It would thus follow that Zeno's Paradox is a fallacy, since movement is studied in the absence of time.