| Title | Digging up a Paradox: A Philological Note on Zeno's Stadium |
| Type | Article |
| Language | English |
| Date | 1982 |
| Journal | Rheinisches Museum für Philologie |
| Volume | 125 |
| Issue | 1 |
| Pages | 1-24 |
| Categories | no categories |
| Author(s) | Mansfeld, Jaap |
| Editor(s) | |
| Translator(s) |
| Of Zeno's four arguments against the reality of motion transmitted by Aristotle, the fourth, the so-called Stadium (Vors. 29 A 28), is perhaps the most difficult. The difficulties involved are of two sorts: philological problems on the one hand, questions of a philosophical nature on the other. In the present paper, I am concerned with the first sort, not the second, although I shall perhaps not be successful in keeping the latter out altogether. A study of the philosophical discussions to be found in the learned literature, however, has convinced me that the first problem to be solved is that of the interpretation of Aristotle's text. There is a general feeling that Aristotle, in reporting and arguing against Zeno's argument, somehow failed. I believe his report is sufficiently clear; although Aristotle's argument contra Zeno is not, perhaps, satisfactory in every respect, Zeno's original paradox can be found in his text. I shall attempt to show that, in order to find it, we must begin by taking both the topography of the stadium and the position of the bodies in it into account, which several recent reconstructions, however satisfactory they may appear to be in other respects, fail to do. I wish to start from a consideration concerned with a non-philosophical feature the four arguments against motion have in common: the fact that they are fun. They undoubtedly are very serious arguments, but they were also written in order to épater le bourgeois. The first argument proves that a runner will never get to the end of the stadium: once he has got halfway, he still has to get halfway the remaining half, halfway the remaining quarter, and so on, in infinitum. The second proves that swift-footed Achilles will never catch up with the slowest thing on earth, because the distance in between, although constantly diminishing, forever remains proportionally the same. The third proves that a flying arrow, which occupies a place equal to its own size, is at rest, because it does not move at the place where it is, and not at the place where it is not either. The first three arguments, then, are genuine and rather hilarious paradoxes. They reveal Zeno as a wit. To ask what is so funny about the fourth argument against motion, therefore, is a legitimate question. Yet I have hardly ever read an account of the fourth paradox which brought out the inevitable smile fetched by the others. Instead, one finds complicated discussions about infinite divisibility versus discrete or granular structure, and endless shufflings and reshufflings of the runners on the course. There are several reasons for this unfortunate situation, the most important of which, I believe, is that both ancient commentators (to judge from Simplicius' account) and modern scholars have failed to distinguish (or to distinguish sufficiently) between Zeno's paradox on the one hand and Aristotle's refutation on the other. Another reason is that Aristotle's text is plagued in parts with variae lectiones that seriously affect the meaning of the argument as a whole. Some of these readings enjoy the support of Simplicius, but this does not prove them right, for Simplicius points out one passage where Alexander of Aphrodisias followed a reading different from that accepted by himself and which, as he believes, Alexander "found in some manuscripts" (ἐν ταῖς ἀντιγράφοις εὗρον, In Phys. 1017, 19). Furthermore, as Simplicius likewise tells us (In Phys. 1019, 27–31), Alexander proposed to interpolate Phys. Z 9, 240a15-16 λαὸν-φρήσιν immediately after 240a11 διελῆλυθεν. Alexander, then, found it difficult to understand the argument of the text as transmitted (which, at at least one other point, differed from Simplicius’). Simplicius' lengthy reconstruction of the fourth argument against motion and of Aristotle's critique thereof (In Phys. 1016, 7–1020, 6, printed—as far as 1019, 9—by Lee as T 36) appears to have no other authority than his own, for he differs from Alexander, and the only other person cited (Eudemus, Fr. 106 Wehrli) is only adduced for points which do not affect the interpretation of the more difficult parts of Phys. Z 9, 239b33–240a17. Although scholars have dealt rather freely with Simplicius' commentary, using only those sections which fit their own views, it should be acknowledged that his reconstruction of the paradox, and especially his diagram of the stadium featuring three rows of runners, have been of crucial importance to the modern history of interpretation of Zeno's argument. I believe, however, that Simplicius (and perhaps Alexander as well) already made the fundamental mistake of failing to distinguish in the proper way between Zeno's paradox and Aristotle's refutation, although in Simplicius' case this is somewhat mitigated by the fact that he apparently noticed the joke of Zeno's argument (one doesn’t know if Alexander did). We are not bound, then, to follow Simplicius all, or even half the way, and need not even accept his guidance as to the choice to be made among the variae lectiones. These different readings themselves, so it seems, reflect different ancient interpretations of Aristotle's exposition. In some manuscripts, interpretamenta may have got into the text (as at 240a6), or even have ousted other, more difficult readings (as at 240a11). [introduction p. 1-3] |
| Online Resources | https://uni-koeln.sciebo.de/s/y2jILmoDyxD389y |
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The difficulties involved are of two sorts: philological problems on the one hand, questions of a philosophical nature on the other. In the present paper, I am concerned with the first sort, not the second, although I shall perhaps not be successful in keeping the latter out altogether. A study of the philosophical discussions to be found in the learned literature, however, has convinced me that the first problem to be solved is that of the interpretation of Aristotle's text. There is a general feeling that Aristotle, in reporting and arguing against Zeno's argument, somehow failed. I believe his report is sufficiently clear; although Aristotle's argument contra Zeno is not, perhaps, satisfactory in every respect, Zeno's original paradox can be found in his text. I shall attempt to show that, in order to find it, we must begin by taking both the topography of the stadium and the position of the bodies in it into account, which several recent reconstructions, however satisfactory they may appear to be in other respects, fail to do.\r\n\r\nI wish to start from a consideration concerned with a non-philosophical feature the four arguments against motion have in common: the fact that they are fun. They undoubtedly are very serious arguments, but they were also written in order to \u00e9pater le bourgeois. The first argument proves that a runner will never get to the end of the stadium: once he has got halfway, he still has to get halfway the remaining half, halfway the remaining quarter, and so on, in infinitum. The second proves that swift-footed Achilles will never catch up with the slowest thing on earth, because the distance in between, although constantly diminishing, forever remains proportionally the same. The third proves that a flying arrow, which occupies a place equal to its own size, is at rest, because it does not move at the place where it is, and not at the place where it is not either.\r\n\r\nThe first three arguments, then, are genuine and rather hilarious paradoxes. They reveal Zeno as a wit. To ask what is so funny about the fourth argument against motion, therefore, is a legitimate question. Yet I have hardly ever read an account of the fourth paradox which brought out the inevitable smile fetched by the others. Instead, one finds complicated discussions about infinite divisibility versus discrete or granular structure, and endless shufflings and reshufflings of the runners on the course. There are several reasons for this unfortunate situation, the most important of which, I believe, is that both ancient commentators (to judge from Simplicius' account) and modern scholars have failed to distinguish (or to distinguish sufficiently) between Zeno's paradox on the one hand and Aristotle's refutation on the other. Another reason is that Aristotle's text is plagued in parts with variae lectiones that seriously affect the meaning of the argument as a whole. Some of these readings enjoy the support of Simplicius, but this does not prove them right, for Simplicius points out one passage where Alexander of Aphrodisias followed a reading different from that accepted by himself and which, as he believes, Alexander \"found in some manuscripts\" (\u1f10\u03bd \u03c4\u03b1\u1fd6\u03c2 \u1f00\u03bd\u03c4\u03b9\u03b3\u03c1\u03ac\u03c6\u03bf\u03b9\u03c2 \u03b5\u1f57\u03c1\u03bf\u03bd, In Phys. 1017, 19). Furthermore, as Simplicius likewise tells us (In Phys. 1019, 27\u201331), Alexander proposed to interpolate Phys. Z 9, 240a15-16 \u03bb\u03b1\u1f78\u03bd-\u03c6\u03c1\u03ae\u03c3\u03b9\u03bd immediately after 240a11 \u03b4\u03b9\u03b5\u03bb\u1fc6\u03bb\u03c5\u03b8\u03b5\u03bd. Alexander, then, found it difficult to understand the argument of the text as transmitted (which, at at least one other point, differed from Simplicius\u2019). Simplicius' lengthy reconstruction of the fourth argument against motion and of Aristotle's critique thereof (In Phys. 1016, 7\u20131020, 6, printed\u2014as far as 1019, 9\u2014by Lee as T 36) appears to have no other authority than his own, for he differs from Alexander, and the only other person cited (Eudemus, Fr. 106 Wehrli) is only adduced for points which do not affect the interpretation of the more difficult parts of Phys. Z 9, 239b33\u2013240a17.\r\n\r\nAlthough scholars have dealt rather freely with Simplicius' commentary, using only those sections which fit their own views, it should be acknowledged that his reconstruction of the paradox, and especially his diagram of the stadium featuring three rows of runners, have been of crucial importance to the modern history of interpretation of Zeno's argument. I believe, however, that Simplicius (and perhaps Alexander as well) already made the fundamental mistake of failing to distinguish in the proper way between Zeno's paradox and Aristotle's refutation, although in Simplicius' case this is somewhat mitigated by the fact that he apparently noticed the joke of Zeno's argument (one doesn\u2019t know if Alexander did). We are not bound, then, to follow Simplicius all, or even half the way, and need not even accept his guidance as to the choice to be made among the variae lectiones. These different readings themselves, so it seems, reflect different ancient interpretations of Aristotle's exposition. In some manuscripts, interpretamenta may have got into the text (as at 240a6), or even have ousted other, more difficult readings (as at 240a11). [introduction p. 1-3]","btype":3,"date":"1982","language":"English","online_url":"","online_resources":"https:\/\/uni-koeln.sciebo.de\/s\/y2jILmoDyxD389y","doi_url":null,"categories":[],"authors":[{"id":29,"full_name":"Mansfeld, Jaap","role":{"id":1,"role_name":"author"}}],"book":null,"booksection":null,"article":{"id":1108,"journal_id":null,"journal_name":"Rheinisches Museum f\u00fcr Philologie","volume":"125","issue":"1","pages":"1-24"}},"sort":[1982]}
| Title | Digging up a Paradox: A Philological Note on Zeno's Stadium |
| Type | Article |
| Language | English |
| Date | 1982 |
| Journal | Rheinisches Museum für Philologie |
| Volume | 125 |
| Issue | 1 |
| Pages | 1-24 |
| Categories | no categories |
| Author(s) | Mansfeld, Jaap |
| Editor(s) | |
| Translator(s) |
Of Zeno's four arguments against the reality of motion transmitted by Aristotle, the fourth, the so-called Stadium (Vors. 29 A 28), is perhaps the most difficult. The difficulties involved are of two sorts: philological problems on the one hand, questions of a philosophical nature on the other. In the present paper, I am concerned with the first sort, not the second, although I shall perhaps not be successful in keeping the latter out altogether. A study of the philosophical discussions to be found in the learned literature, however, has convinced me that the first problem to be solved is that of the interpretation of Aristotle's text. There is a general feeling that Aristotle, in reporting and arguing against Zeno's argument, somehow failed. I believe his report is sufficiently clear; although Aristotle's argument contra Zeno is not, perhaps, satisfactory in every respect, Zeno's original paradox can be found in his text. I shall attempt to show that, in order to find it, we must begin by taking both the topography of the stadium and the position of the bodies in it into account, which several recent reconstructions, however satisfactory they may appear to be in other respects, fail to do. I wish to start from a consideration concerned with a non-philosophical feature the four arguments against motion have in common: the fact that they are fun. They undoubtedly are very serious arguments, but they were also written in order to épater le bourgeois. The first argument proves that a runner will never get to the end of the stadium: once he has got halfway, he still has to get halfway the remaining half, halfway the remaining quarter, and so on, in infinitum. The second proves that swift-footed Achilles will never catch up with the slowest thing on earth, because the distance in between, although constantly diminishing, forever remains proportionally the same. The third proves that a flying arrow, which occupies a place equal to its own size, is at rest, because it does not move at the place where it is, and not at the place where it is not either. The first three arguments, then, are genuine and rather hilarious paradoxes. They reveal Zeno as a wit. To ask what is so funny about the fourth argument against motion, therefore, is a legitimate question. Yet I have hardly ever read an account of the fourth paradox which brought out the inevitable smile fetched by the others. Instead, one finds complicated discussions about infinite divisibility versus discrete or granular structure, and endless shufflings and reshufflings of the runners on the course. There are several reasons for this unfortunate situation, the most important of which, I believe, is that both ancient commentators (to judge from Simplicius' account) and modern scholars have failed to distinguish (or to distinguish sufficiently) between Zeno's paradox on the one hand and Aristotle's refutation on the other. Another reason is that Aristotle's text is plagued in parts with variae lectiones that seriously affect the meaning of the argument as a whole. Some of these readings enjoy the support of Simplicius, but this does not prove them right, for Simplicius points out one passage where Alexander of Aphrodisias followed a reading different from that accepted by himself and which, as he believes, Alexander "found in some manuscripts" (ἐν ταῖς ἀντιγράφοις εὗρον, In Phys. 1017, 19). Furthermore, as Simplicius likewise tells us (In Phys. 1019, 27–31), Alexander proposed to interpolate Phys. Z 9, 240a15-16 λαὸν-φρήσιν immediately after 240a11 διελῆλυθεν. Alexander, then, found it difficult to understand the argument of the text as transmitted (which, at at least one other point, differed from Simplicius’). Simplicius' lengthy reconstruction of the fourth argument against motion and of Aristotle's critique thereof (In Phys. 1016, 7–1020, 6, printed—as far as 1019, 9—by Lee as T 36) appears to have no other authority than his own, for he differs from Alexander, and the only other person cited (Eudemus, Fr. 106 Wehrli) is only adduced for points which do not affect the interpretation of the more difficult parts of Phys. Z 9, 239b33–240a17. Although scholars have dealt rather freely with Simplicius' commentary, using only those sections which fit their own views, it should be acknowledged that his reconstruction of the paradox, and especially his diagram of the stadium featuring three rows of runners, have been of crucial importance to the modern history of interpretation of Zeno's argument. I believe, however, that Simplicius (and perhaps Alexander as well) already made the fundamental mistake of failing to distinguish in the proper way between Zeno's paradox and Aristotle's refutation, although in Simplicius' case this is somewhat mitigated by the fact that he apparently noticed the joke of Zeno's argument (one doesn’t know if Alexander did). We are not bound, then, to follow Simplicius all, or even half the way, and need not even accept his guidance as to the choice to be made among the variae lectiones. These different readings themselves, so it seems, reflect different ancient interpretations of Aristotle's exposition. In some manuscripts, interpretamenta may have got into the text (as at 240a6), or even have ousted other, more difficult readings (as at 240a11). [introduction p. 1-3] |
| Online Resources | https://uni-koeln.sciebo.de/s/y2jILmoDyxD389y |
{"_index":"sire","_id":"1108","_score":null,"_source":{"id":1108,"authors_free":[{"id":2070,"entry_id":1108,"agent_type":"person","is_normalised":1,"person_id":29,"institution_id":null,"role":{"id":1,"role_name":"author"},"free_name":"Mansfeld, Jaap","free_first_name":"Jaap","free_last_name":"Mansfeld","norm_person":{"id":29,"first_name":"Jaap","last_name":"Mansfeld","full_name":"Mansfeld, Jaap","short_ident":"","is_classical_name":null,"dnb_url":"http:\/\/d-nb.info\/gnd\/119383217","viaf_url":"","db_url":"","from_claudius":null}}],"entry_title":"Digging up a Paradox: A Philological Note on Zeno's Stadium","main_title":{"title":"Digging up a Paradox: A Philological Note on Zeno's Stadium"},"abstract":"Of Zeno's four arguments against the reality of motion transmitted by Aristotle, the fourth, the so-called Stadium (Vors. 29 A 28), is perhaps the most difficult. The difficulties involved are of two sorts: philological problems on the one hand, questions of a philosophical nature on the other. In the present paper, I am concerned with the first sort, not the second, although I shall perhaps not be successful in keeping the latter out altogether. A study of the philosophical discussions to be found in the learned literature, however, has convinced me that the first problem to be solved is that of the interpretation of Aristotle's text. There is a general feeling that Aristotle, in reporting and arguing against Zeno's argument, somehow failed. I believe his report is sufficiently clear; although Aristotle's argument contra Zeno is not, perhaps, satisfactory in every respect, Zeno's original paradox can be found in his text. I shall attempt to show that, in order to find it, we must begin by taking both the topography of the stadium and the position of the bodies in it into account, which several recent reconstructions, however satisfactory they may appear to be in other respects, fail to do.\r\n\r\nI wish to start from a consideration concerned with a non-philosophical feature the four arguments against motion have in common: the fact that they are fun. They undoubtedly are very serious arguments, but they were also written in order to \u00e9pater le bourgeois. The first argument proves that a runner will never get to the end of the stadium: once he has got halfway, he still has to get halfway the remaining half, halfway the remaining quarter, and so on, in infinitum. The second proves that swift-footed Achilles will never catch up with the slowest thing on earth, because the distance in between, although constantly diminishing, forever remains proportionally the same. The third proves that a flying arrow, which occupies a place equal to its own size, is at rest, because it does not move at the place where it is, and not at the place where it is not either.\r\n\r\nThe first three arguments, then, are genuine and rather hilarious paradoxes. They reveal Zeno as a wit. To ask what is so funny about the fourth argument against motion, therefore, is a legitimate question. Yet I have hardly ever read an account of the fourth paradox which brought out the inevitable smile fetched by the others. Instead, one finds complicated discussions about infinite divisibility versus discrete or granular structure, and endless shufflings and reshufflings of the runners on the course. There are several reasons for this unfortunate situation, the most important of which, I believe, is that both ancient commentators (to judge from Simplicius' account) and modern scholars have failed to distinguish (or to distinguish sufficiently) between Zeno's paradox on the one hand and Aristotle's refutation on the other. Another reason is that Aristotle's text is plagued in parts with variae lectiones that seriously affect the meaning of the argument as a whole. Some of these readings enjoy the support of Simplicius, but this does not prove them right, for Simplicius points out one passage where Alexander of Aphrodisias followed a reading different from that accepted by himself and which, as he believes, Alexander \"found in some manuscripts\" (\u1f10\u03bd \u03c4\u03b1\u1fd6\u03c2 \u1f00\u03bd\u03c4\u03b9\u03b3\u03c1\u03ac\u03c6\u03bf\u03b9\u03c2 \u03b5\u1f57\u03c1\u03bf\u03bd, In Phys. 1017, 19). Furthermore, as Simplicius likewise tells us (In Phys. 1019, 27\u201331), Alexander proposed to interpolate Phys. Z 9, 240a15-16 \u03bb\u03b1\u1f78\u03bd-\u03c6\u03c1\u03ae\u03c3\u03b9\u03bd immediately after 240a11 \u03b4\u03b9\u03b5\u03bb\u1fc6\u03bb\u03c5\u03b8\u03b5\u03bd. Alexander, then, found it difficult to understand the argument of the text as transmitted (which, at at least one other point, differed from Simplicius\u2019). Simplicius' lengthy reconstruction of the fourth argument against motion and of Aristotle's critique thereof (In Phys. 1016, 7\u20131020, 6, printed\u2014as far as 1019, 9\u2014by Lee as T 36) appears to have no other authority than his own, for he differs from Alexander, and the only other person cited (Eudemus, Fr. 106 Wehrli) is only adduced for points which do not affect the interpretation of the more difficult parts of Phys. Z 9, 239b33\u2013240a17.\r\n\r\nAlthough scholars have dealt rather freely with Simplicius' commentary, using only those sections which fit their own views, it should be acknowledged that his reconstruction of the paradox, and especially his diagram of the stadium featuring three rows of runners, have been of crucial importance to the modern history of interpretation of Zeno's argument. I believe, however, that Simplicius (and perhaps Alexander as well) already made the fundamental mistake of failing to distinguish in the proper way between Zeno's paradox and Aristotle's refutation, although in Simplicius' case this is somewhat mitigated by the fact that he apparently noticed the joke of Zeno's argument (one doesn\u2019t know if Alexander did). We are not bound, then, to follow Simplicius all, or even half the way, and need not even accept his guidance as to the choice to be made among the variae lectiones. These different readings themselves, so it seems, reflect different ancient interpretations of Aristotle's exposition. In some manuscripts, interpretamenta may have got into the text (as at 240a6), or even have ousted other, more difficult readings (as at 240a11). [introduction p. 1-3]","btype":3,"date":"1982","language":"English","online_url":"","online_resources":"https:\/\/uni-koeln.sciebo.de\/s\/y2jILmoDyxD389y","doi_url":null,"categories":[],"authors":[{"id":29,"full_name":"Mansfeld, Jaap","role":{"id":1,"role_name":"author"}}],"book":null,"booksection":null,"article":{"id":1108,"journal_id":null,"journal_name":"Rheinisches Museum f\u00fcr Philologie","volume":"125","issue":"1","pages":"1-24"}},"sort":["Digging up a Paradox: A Philological Note on Zeno's Stadium"]}