ON MOTION AND PLURALITY
Nagarjuna and Zeno of Elea on Time, Motion, Oneness and Plurality
Jan C. Westerhoff
|A. INTRODUCTORY REMARKS|
|In this paper I attempt a
comparison of two sets of arguments by authors from two radically different cultural and
philosophical traditions, namely of the second century Indian Buddhist master Nagarjuna
and of Zeno of Elea, the Greek eleatic philosopher living around the fifth century B.C. I
would like to show in which points their respective arguments are similar and - and this
is one of the main aims of this essay - inhowfar the reactions towards them, i.e. the
place, significance and value ascribed to them depended to a large amount on the tacit
epistemological as well as ontological assumptions of the respective cultural tradition
In doing this I will firstly discuss a set of arguments concerning time and movement and secondly one dealing with plurality and the question of determining the basis of designation connected therewith. I am well aware of the difficulties of such a discussion of arguments from two different cultures and am convinced that an enterprise as this can only bear fruit if its limits are clearly seen and respected.These limits are to be seen as relating to three points :
Each philosophical inquiry has an aim, a position it wants to establish, as well as a line of argumentation and is in some cases directed against another doctrine to which it is related as a criticism. Of these three points the main aims to be established by the respective philosopher are obviously not the same; the philosophy of the Middle Way of Nagarjuna and the Parmenidian doctrines of Zeno of Elea do actually show not much resemblance at first sight, (though, as we will see later, some secondary aspects do indeed prove to be similar) (1). What does show similarities are on the one hand some means of argumentation Nagarjuna and Zeno employed, and on the other hand in all examples discussed here the doctrines against which their arguments were directed as a criticism. If these points and their mutual differences are correctly understood, the reader will be saved of misunderstandings and will be able to acknowledge the fruits of this inquiry bringing together two different traditions.
I would like first to give the reader some short information regarding both philosophers, second to expound their respective arguments conerning time and motion as well as oneness and plurality in order to subsequently show which reactions towards them occured in the respective tradition receiving them, also discussing on what epistemological and ontological foundations these were grounded.
Nagarjuna is considered to be one of the most eminent masters of Indian Mahayana Buddhism and especially in the Tibetan tradition his authority outshines all of the other various Buddhist teachers of ancient India.He is revered as the founder of the Madhyamika school of Buddhist thought, the school of the Middle Way. Its main theory is the doctrine of Emptiness, i.e. the view that all phenomena, both mental and physical, lack a permanent,unchanging, independent self-existence.Phenomena are thus received as wholly depending upon causes and conditions, even their "substantial" identity being dependent on our labelling.Nevertheless, phenomena are not seen as only existing as mere phantasies, they are known to posses a conventional existence, in which they appear to have a self-nature, although in reality they do not.This philosophical point of view is therefore known as the Middle Way, avoiding both the extremes of eternalism as well as of nihilism.
This teaching has also to be seen in the context of the whole Buddhist world- picture as explained by the Buddha in the Four Noble Truths. All sentient beings live in an infinite cycle of suffering. This suffering is at its very root caused by their ignorance concerning the true nature of phenomena, i.e. their lack of self-existence.Not realizing the Emptiness both of things as well as of mental phenomena, sentient beings adopt attitudes of like and dislike which in their further cause keep the process of suffering in motion.This suffering can be stopped if the deceptive appearance of phenomena is realized and their true nature is known. The way which has to be followed in order to achieve this aim is laid down in the teachings of the Buddha.
In the following dicussion of Nagarjunas arguments concerning time, motion and oneness, I will concentrate on some passages from one of Nagarjunas main works, the Mulamadhyamikakakarika, on passages from his "Seventy stanzas", as well as on some arguments that arose as a commentary on his works in the Tibetan tradition.(2)
Regarding Zeno of Elea, today most widely known for his paradoxes, it has to be remarked that he was a follower of Parmenides, obviously devising his paradoxes in order to defend his teacher by finding flaws in his opponents asumptions.Of what we know today, Parmenides held a teaching that does not seem to be very appealing to mans everyday conception of things, neither in his times nor today.He conceived reality as a steady, unchanging whole, like a well-rounded ball, static and unmoving.Reality, as ordinarily seen, namely as containing change and motion, was therefore regarded by him as being illusory.This teaching being criticized by Parmenides opponents because of its distance from experience was defended by Zenos attempt to show the absurdity and contradictoriness of their everyday conceptions of reality. Besides this critical position, there is little known about any "positive" philosophical views Zeno might have held independent of, or opposing to his teacher Parmenides. (3)
Of primary interest regarding this discussion will be Zenos arguments concerning motion, especially the "dichotomy" as well as the "arrow", and one concerning oneness and plurality, namely the "heap" .
|B. The Arguments Concerning Time and Motion|
|In introducing this section
it might be helpful to shortly introduce the argument of the "dichotomy". It
consists of the following line of argumentation: If a runner wanted to cross a given
distance A, he would first have to transgress 1/2 A, then 1/4 A, 1/8 A etc. This would
constitute an infinite series which per definitionem would be impossible to transgress,
for before reaching any point, another point lying between this point and the starting
point would have to be reached between which still another point lied and so on ad
infinitum.It would not matter how long the distance to transgress were, the important
point is that not only its end would never be reached but that the runner could never
start moving for before he could transgress any distance he would have to transgress an
infinite number of smaller ones.As the conception of movement therefore leads to a
contradiction, Zeno concludes all movement to be impossible and hence our perception of it
to be illusory.(4)
B1. The common conception of the infinite divisibility of time
Regarding Zenos arguments, we can attempt to understand them in two different ways, as proving the actual impossibility of motion as well as refuting a particular conception of motion by showing it as leading to impossible results.This distinction will be of importance later on in our discussion. If we, however, regard Zenos arguments for the time being as concept-critical, we can observe the "dichotomy" as being intrinsically linked with the conception of the infinite divisibility of space as well as of time.Time here is assumed as consisting of infinitively small, "atomic" moments, during each of which movement cannot take place, as infinitively many instances of space would have to be transgressed.As what is true for one "time-instant" is also true for each preceeding and each succeding one, motion could never have started if the conditions of time and space were as they had been assumed.If both were hold to be continua, the impossible conclusions of Zenos arguments would not follow.
B2. The common conception of a thing remaining the same throughout the course of motion
Another commonly held opinion regarding time and motion is the view that the moved object does not change during the course of motion.This argument possesses an interesting relationship to the argument of the "arrow" invented by Zeno.Its line of argumentation is briefly this : A moving arrow can neither move in the place where it is not - for it is not there -, nor in the place where it is, for this is a place equal to itself.As every thing is at rest when it is at a place equal to itself, and the arrow is always at a place equal to itself, the arrow is always at rest and can therefore never move.(5)
This argument derives it conclusion from a particular view we hold about a moving object.Is a moving thing really the same during the different instants of time when it occupies different places? If it is not, then how can we assert the identity of the different things occupying separate positions of space, of what we denote as "an arrow moving"? Are those not rather different things at different places, which we arbitrarily - and unjustifiedly - connect?If we however decide for the opposite position in asserting that the moving arrow remains really the same during the movement, we have difficulties to explain how it might ever move at all.Obviously Zeno takes this second position, thereby showing the absurdity it leads to : If the arrow remained really the same during the motion, the same with all its attributes, with the part of space which it occupied - for if an attribute changed, how could we ever speak of the "same" thing - then it could never move.
Zenos arguments of the "dichotomy" and the "arrow" respectively can be regarded as critizising two common notions associated with time and motion, namely the infinite divisibility of moments of time,the "atomic" conception of time, as well as the assumption that the moved object remaines really the same during the motion (the opposite assumption here being also problematic).
B1. The relations of Nagarjunas arguments to B1
The arguments of Nagarjuna I want to discuss relate as a criticism towards the same "common conceptions".The arguments found in the second chapter of Nagarjunas Mulamadhyamikakakarika,entitled"Examination of the Moved and the Not-Moved" referring to these conceptions have actually been directed against the view of time and motion held by the Sautrantikas, a Hinayana school of thinking, which believed time to consist of succeding, discrete moments of origin and destruction, a view obviously difficult to harmonize with Nagarjunas theory of selflessness.In order to identify a changed or moved object as the "same" after a sequence of discrete, atomic moments, the Sautrantikas had to assume the existence of a continuity of a subtle, underlying substance in an object, a notion which Nagarjuna wanted to refute.Nagarjuna therefore critizises in the first verse of the second chapter the concept that " what has moved is being moved" (6) as relating to an unchanging, underlying substance.In the twelfth verse Nagarjuna argues " Movement is not begun in the moved, nor is it begun in the not moved.Neither is it initiated in the present moving.Wherein is the movement initiated ? " (7) This shows the problems connected with the assumption of time as atomic in the same way as does Zenos argument of the "dichotomy".Neither can the moved object begin a motion for it is already moving, nor can the non-moving object get started if an atomic conception of time is assumed.How can the runner ever get started if he cannot get started in the present moment - either because he had to transgress an infinite series of space-segments or because the atomic moment in which the movement should have started could not be atomic for it had to consist of two moments, one in which the object rested and one in which it moved - and also not in any following "present" moment ? (8)
This problem is also discussed in the following two verses: " Prior to the commencement of moving there is neither the present moving nor the moved from which the movement is initiated.How could be movement in the not moved?"(9)
Before an object can start to move in an atomic time-instant "commencement of moving" it has to be in some state concerning motion and non-motion in the preceding moment.This cannot be the "present moving" - for this moment precedes it - nor can it be another "moved" for the preceding moment had to be a state of non-motion, for the object starts to move.(Nor can it, as we have already seen, be a moment of rest, so what kind of moment is actually preceding ?)
The moment in which the movement should begin is also not perceivable as an atomic entity for in this case it ought to be in two opposite states, namely moving and not-moving.Nagarjuna nevertheless does not want to refute the possibility of perceiving motion as such but only in relation to a certain conception held, which here is the infinite divisibility of moments of time.
The aims Nagarjunas arguments in the quotations given up to now were directed against, have been shown as being similar to those against which Zenos arguments, especially the argument of the arrow, can be understood as a criticism.That this assumption of Zenos arguments as "concept-critical" might be justified becomes probable when taking modern treatments of them into account.Ushenkos paper (11), as an example, does this and sees some of Zenos arguments as being directed against the atomic conception of time. He shows that Zenos argument of the arrow "derives its force from the assumption that there is a gap, i.e. there is no time between the consecutive instants" and also sees Zenos arguments to rest on false assumptions in stressing that " the series of instants, like the series of points on a line, is a mathematical continuum : no two instants are consecutive, and between any two instants there is time because there is a third instant. "
B2. The relation of the arguments of Nagarjuna to B2
The criticism of the second "common notion" regarding time and change to be discussed here, namely the concept that the moved object remains the same during the course of motion, proves to constitute yet another link between the arguments of Nagarjuna and Zeno of Elea. The thought of an unchanging, permanent substance in phenomena being one of the basic conceptions Nagarjuna wanted to refute, he argued that a moved object cannot posses a substance remaining really the same throughout the course of motion.In verse eighteen of the second chapter Nagarjuna writes: " The view that movement is identical with the mover is not proper.The view that the mover is different from motion is also not proper. " (12) This presents in a more comprehensive manner the problems that are also implicit in the argument of the arrow.If we have the conception of an inherent identity of the object and its attributes - or the arrow and its position - the object cannot really change its attributes and, as Zeno shows the arrow can never move.If we conceive the two as inherently different, we cannot explain the continuity of the one moving object.Nagarjuna explains this in the two following verses: " If movement were to be identical with the mover, it would follow that there is identity of agent and action. "
Nagarjuna covers the matter here in a more sophisticated way than Zeno in discussing also the problems connected with the conception of an inherent difference of substance and predicate which for the above-mentioned reason is also impossible.In the concluding verses he states: " An existent mover does not carry out the movement in any of the three ways.Neither does a non-existent mover carry out the movement in any of the three ways.Nor does a person carry out the movement, both existent and non-existent, in any of the three ways.Therefore neither motion, nor the mover, nor the space moved is evident. " (14)
It is important to note that not the mover and the motion as such or in their possibility to be empirically perceived are rejected here by Nagarjuna but rather " the really or substantially or independently existent (...) mover and movement" (15) i.e. motion seen under special conceptual conditions (as explained above).
That it is this certain conception of motion that Zenos arguments - and especially the argument of the arrow - want to critizise is made clear right at the beginning of Ushenkos paper.He writes that Zeno " has refuted the ordinary idea of motion" which he conceives as partly consisting of the idea " that the moving thing remains the same through the change of position" (16). The argument of the arrow showing the impossibility of this particular assumption is further explained in his discussion of the "Physical Refutations": " Since a physical body (...) turns out to be a real world-line, there is no transition from one event to another (...) and no need for an agent (...) to perform such a transition. " (17). Later he shows how the impossible conclusions of Zenos arguments can be avoided if this common conception is abolished.What is stated by him under the heading "Philosophical Refutations" points into a similar direction as Nagarjunas closing verses of the second chapter cited above: " The unifying factor in the state of motion is not an actual body but a power.Accordingly, there is no actual thing which occupies a definite position at a definite moment, or proceeds from one position to another, and remains the same actual thing through the process of motion. " (18)
Summing up our discussion of this subject we can say that some of the arguments of Nagarjuna and Zeno were similar refering to their respective line of argumentation - such as the argument of the arrow - and, although the teachings Nagarjuna and Zeno of Elea wanted to establish were different, their aims - supposing Zenos arguments as being concept critical - in critizising common notions regarding time, space and motion were indeed similar.
|C. The Arguments Concerning Oneness and Plurality|
|The problem of how one thing
could be simultaneously one (thing) and many (parts) was a question much discussed in
antiquity. Zeno of Elea invented an argument that also belonged to the scope of this
discussion, namely the argument of the millet seed (19). It
consisted in the problem of how a large quantitiy of millet seeds could make a noise when
falling, but a single millet seed falling made no noise.Zeno argued with this against the
reliability of sense perception, as he was able to produce an argument that a single
falling millet seed must make a sound (since it is the part of a noise-producing whole)
and yet it was impossible to hear it, which Zeno took as a proof that our senses must be
deceiving us.Nevertheless his argument of the millet seed can also be seen as a more
particular form of a very famous problem of antiquity - though not explicitly known to be
authored by Zeno - the argument of the heap. It poses the problem of a heap of grains from
which one grain is regularly substracted.If we substract one grain it is clear that we
still have a heap before us, but after continuing this process long enough we are at the
end left with one grain, which is obviously not a heap anymore, without being able to name
any sharp line of division.The similarity of both arguments is clear: the first one states
"The whole makes a noise, but the part being part of the whole makes no
noise"and the second argument states "The whole is a heap, but the part being
part of the whole is no heap".
The same underlying problem is the question of the basis of designation, the problem of whether we designate an object primarily as a whole, neglecting its parts, or primarily as an array of its parts constituting the whole.With the question of designation, however, there also arises the question regarding the existence of a particular object: is it just its parts, or is it more in some way ? Zenos argument of the millet seed suggests that what we can attribute to the whole - namely the noise-making - we cannot attribute to the parts, thereby showing the whole to possess different attributes than its parts.The parts being so different from the whole however, how can they ever constitute it ? Beside questioning the reliability of sense-perception, Zeno also puts into doubt the conception regarding one and many, namely that the whole has the same attributes as its parts and is thus really its parts.
This criticism is further elaborated in the argument of the heap. On the one hand, we cannot see the heap to be really one with its parts - for then even the substraction of one part should destroy the whole, which, however, it does not as the heap remains a heap even after the substraction of one grain, - on the other hand we cannot see it to be really different from its parts - for the heap has no existence independent of its parts, after substracting a certain number of grains the heap no longer remains a heap , thus being neither inherently the same as, nor inherently different from its parts. The problem of the heap thus not only shows that the whole is not really the same as its parts, but also that it is not inherently different.
These two common notions regarding the relationship between one and many are also criticized by the philosophy of Nagarjuna in order to refute self-existence, as each of these notions is incompatible with the teaching of Emptiness. Jang-Gya, a Tibetan Gelugpa scholar belonging to the Prasangika Madhyamika school which has emerged out of differences in commentating Nagarjunas works writes: " A chariot does not inherently exist because of not being its parts, not being other than its parts, not being in its parts, not being that in which its parts exist, not possessing its parts, not being the composite of its parts, and not being the shape of the composites of its parts. " (20) The first two possibilities - inherently being its parts or inherently being different of its parts - are shown by Jang-Gya in the further course of the discussion as being impossible because otherwise the object, the chariot would be many, as its parts are, or if it were inherently other would be apprehendable apart from the chariot.
The next three posibilities are then shown to entail these impossible states of existence, thereby also being impossible and the last two possibilities are explained to be incompatible with inherent existence. The first two conceptions here are to be seen as very similar to those against which the argument of the millet seed and the argument of the heap are directed. This can also be seen by comparing some arguments concerning this matter from writings of Nagarjuna himself. In verse thirty-two of his "Seventy Stanzas" he writes: " If we examine composite and non-composite phenomena then we cannot find them as one, because then we cannot differentiate between these two types of phenomena and we cannot find them as many, because then these two would be completely unrelated(...), taking up the same theme in verse forty-six : " A form cannot have the fourfold nature of reality because if the form has four elements then it will be fourfold ,or else they will become one like form (...)." (21).
The means of argumentation employed by Nagarjuna and Zeno and the inventor of the argument of the heap are obviously not wholly the same, the one arguing with the empirical unfindability of an inherent "oneness" of the whole besides its parts and the doubled unity and difference of them if both were one, the other showing in what degrees the parts of the object can be changed, thus allowing neither a real unity nor a real difference between the parts and the whole, but their aims in criticizing certain common notions regarding oneness and plurality are indeed the same.
The comparison of the arguments concerning time, motion, oneness and plurality has made clear that a partial similarity exists in the means of argumentations employed by Nagarjuna and by Zeno of Elea and that an interesting coincidence regarding both thinkers can be observed insofar as both criticise the same "common", everyday conceptions existing in the field of thought they reason about.
|D. The Reactions and their Foundations|
|In the final section of this
paper I would like to discuss what kind of reactions occured towards the arguments of Zeno
and of Nagarjuna and would like to show inhowfar these were connected to the different
ontological and epistemological assumptions of the respective cultures receiving
them.Concerning the arguments of Zeno of Elea two reactions are of main interest.The first
is the attempt to show his arguments to be fallacies, resting on ambigously expressed or
ill-formulated premisses, resolving the problem by showing the falsity of the particular
premiss or premisses.
The second attempt tries to show inhowfar Zenos arguments were directed not against the actual reality of motion or plurality, but against a certain conception of it, the impossible consequences of which they wanted to make explicit.This latter view requires a careful distinction between what Zeno himself presuposes, what we do presupose, and which concept might be the more adequate account of reality.
These two views do not make any difference concerning the inherent validity of Zenos arguments; to say an argument of his rested on the false premiss (and not on an invalid scheme of deduction) (22) of, for example, assuming the infinite divisibility of time and space or to hold that it exposes the erroneousness of such a conception by showing it to lead to contradictory conclusions implies the same view of the relation between the premisses and the conclusion, namely the argument being valid but not sound.What is indeed a difference between these two conceptions is that in the first case the problem of the counterfactual conclusion is resolved by showing the particular premiss or premisses to be false, whereas in the second case, the argument still remains of interest, presenting itself to be a useful tool leading to an inquiry concerning the common conceptions employed (both by oneself as well as by the proposer of the argument) in dealing with that particular notion.
Up to most recent treatments of Zenos arguments, the first way of dealing with them has been the most common. It can be observed from the times of Aristotle onwards, who dealt with Zenos arguments amongst other works in his "Physica" (23) and is still present in most of the discussions on them up to rather modern works (one using them to show inhowfar " common sense is always endangered" by the arguments of Zeno and those of similar types.) (24)
Somewhat of a middle position between this and the second type of reaction is presented by the view of the French historian Paul Tannery who did not hold Zenos arguments to be directed against common notions but rather against the specific positions held by the Pythagoreans.He received Zenos arguments not as fallacies but as " clear, forceful, irrefutable" reactions against the Pythagorean arguments. (25)
Although it has been shown to be improbable that his arguments were directed specifically against this school of thinking, the view of Zenos arguments as concept-critical extends even to modern treatments of them, here nevertheless not seen as critizising any particular doctrine but rather the common notion ," that most uncritical people would accept as an adequate account" (26/27) . The views of Ushenko already cited above are of particular interest here. He held that Zeno " refuted the ordinary idea of motion" (26) and showed that Zenos arguments can lead to a reexamination of commom-sense conceptions concerning time, space and motion, thereby harmonizing them with their scientific notions. A statement of A.R. White might also be interesting in this context. It says that " Zeno did not prove that one cannot hit a moving target, he only proved that one cannot hit it if one aims at the point where one sees it when shooting. "(28)
How is the fact that the dominating amount of treatments of Zenos arguments corresponds to what has been described as the first reaction to be explained ? The main reason for this is a basic asumption of western philosophy also present up to our times, namely the concept of thinking a unity of the laws of being and the laws of thinking. Laws of logic - such as the principium contradictionis et identitatis - were founded upon and deduced from metaphysical and ontological principles (29). The problematic issue regarding Zenos paradoxes now consisted in bringing empirical reality and results reached by logical deduction into conflict, a conflict that could not occur in a logic founded upon the most general laws of being, not drawing any distinction between the common-sense idea of motion and other different conceptions that could also be seen as corresponding to empirical reality. Zenos arguments were regarded as fallacious due to their resting on false premisses and not as a reductio ad impossibile of a common-sense notion. This view made the evaluation of Zenos arguments as fallacies rather than as tools more likely. As can be seen from some of the above quotations this latter account of his arguments is a very modern one and does by large not represent the usual evaluation.
After having shown Nagarjunas and Zenos arguments to concern the same conceptions it might be interesting to compare what reactions to the former occured.Nagarjunas arguments have never widely been criticized for resting on fallacious assumptions but were rather seen as a very effective way to discern the nature of reality.In order to understand how two sets of arguments of interesting similarity in some respects can be faced with such opposite assignments of significance and value, a few remarks concerning Buddhist epistemology and the view of logic linked with this have to be made.As has already been hinted at, human mind is generally seen in Buddhist philosophy as deluded insofar as it misrepresents the nature of reality in perceiving a self-nature in phenomena where none is present.In order to gain freedom from this erroneous view of reality, the basic contradictoriness of such a view of self-nature has to be shown in order that the truth of Emptiness can be realized. In Buddhist epistemology knowledge is conceived to be of two kinds, direct knowledge gained through direct perception and indirect knowledge attained by inference.The former, being considered as the most rich and true one, has to be attained by meditating over a mental image, until a direct realization can be attained. In order to realize Emptiness, firstly the view of the contradictoriness of the common conception of self-nature has to be attained by means of reasoning in order that consecutively by meditating over this absence, a direct cognition of Emptiness, and at the end liberation can be attained. It seems therefore understandable inhowfar the criticism of common notions was seen as necessary in a Buddhist context which is why arguments similar to those of Zeno were not regarded as fallacies but rather as a tool for approaching the true nature of reality. Logic was in a Buddhist context not seen as mirroring the structure of reality, but rather as a means by help of which its true nature cold be approached. Inhowfar this view and its difference from the western one can result in the different appreciations of similar arguments I hope to have made clear in this paper.
|1. As e.g.
to undermine the trust in uncritical common-sense conceptions of certain notions.
2. In the first two cases all references
are made to the commentated and translated editions: Kalupahana, D.J.
:Mulamadhyamikakakarika of Nagarjuna, The Philosophy of the Middle Way, Dehli 1991;
3. Maansfeld, J. :Die Vorsokratiker II, Stuttgart 1996, p.10
4. For a concise discussion of this and Zenos other arguments, as well as reconstructions of how the original form of them might have been, see Vlastos, G. :Zeno of Elea, in Edwards, P.(ed.) :The Encyclopedia of Philosophy, New York 1967, pp.369-379
5. Following the reconstruction of Vlastos, op.cit. pp.374f.
6. Kalupahana, op.cit. pp.118f
7. Kalupahana, op.cit. pp.124f
8.The similarity between the argumentations of Nagarjuna and Zeno in critizising certain common notions is also mentioned in Kalupahanas commentary : " Metaphysical speculations regarding time leading to a theory of existence analyzed in terms of discrete momentary events (...) provided Nagarjuna with the opportunity to utilize a method comparable to Zenos paradoxes in order to expose the meaninglessness of such metaphysics." p. 125.
9. Kalupahana, op.cit., II.13, p.125
10. Kalupahana op.cit. II.14 pp. 125f
11.Ushenko, A. :Zenos Paradoxes, Mind 55, 1946, pp.151-161the following two quotations are to be found on page 158
12.Kalupahana, op.cit., II.18, p.128
13. Kalupahana, op.cit., II.19/20, pp.128f.
14. The "three ways" are the assertions "what has moved is being moved", "what has not moved is being moved"and "what has both moved and not moved is being moved", the first implying a stable, substantial entity, the second a completely different, unconnected entity, the third both of these, all three of these are impossible.
15. Kalupahana, op.cit.,p.131
16. Ushenko, op.cit.,p.152
17. Ushenko, op.cit.,p.161
18. Ushenko, op.cit.,p.164
19. Zeno also authored arguments against plurality in order to establish the eleatic doctrine of metaphysical oneness. Cf. Vlastos, op.cit.,pp.369-372 Maansfeld argues the first argument against plurality to be also interpretable against this conception of metaphysical oneness, which would show a large amount of independence of thought of Zeno from his teacher Parmenides.Cf. Maansfeld, op.cit. p.10 and p.19
20. Hopkins, op.cit.,p.179 and pp.677-697
21. Komito,op.cit., Verse 32 p.86 and Verse 46 p.90
22. This is not very often seen as a point of criticism regarding Zenos arguments, most of them resting on very basic and unproblematic methods of reasoning such as the modus ponens. Cf. Sainsbury, R.M. :Paradoxes, Cambridge UK 1988, sections 1.3 and 2.3
23. See e.g. for the paradoxes of motion "Physica", Z9,239b, 5ff., 30ff., and for the paradox of the heap "Physica", H5,250b
24. Rüdiger, H. :Sokrates ist nicht Sokrates. Der Kampf mit dem gesunden Menschenverstand. Klassische Trug- und Fangschlüsse, Third Edition, Zürich, 1983
25. cf. Vlastos.op.cit.,pp.376f.
26. Ushenko, op.cit.,p.152
27. Vlastos also aggrees with this. Cf. op.cit.,p.376
28. White, A.R, cited in Hughes, P., Brecht, G.: Vicious circles and infinity. A Panoply of Paradoxes, London 1975
29. cf. e.g. Stöckl, Dr.A. :Lehrbuch der Philosophie, seventh edition, Mainz 1892, 1. I, 1, §2, 6, p.5 (translation by the author) "The fundamental laws of all being are the three principles of contradiction, of the excluded middle, and of sufficient reason.As these three are fundamental laws of thinking, they also represent the highest ontological principles."
Author: Jan C. Westerhoff is studying philosophy at the University of Cambridge, UK. His fields of interest lie in the domains of comparative philosophy and the philosophy of Baroque.
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