Cronus, Diodorus

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The '''Tung-lin Movement''' (Dong-lin Movement) (c.1530 – c. 1630) was a political reform movement organized among the bureaucratic elite in the imperial government of the late [[Ming dynasty]] of [[China]]. At that time, corruption was rampant in the government, and members of the bureaucratic elite vied with eunuchs and court attendants to influence the policies of the emperors, who had withdrawn themselves from day-to-day political affairs. Members of the [[Confucianism|Confucian]] bureaucratic elite became concerned about this state of affairs and began to take matters into their own hands. They established private universities in their home states to train the Confucian scholars they believed were necessary for good government, and attempted to bring about a change in the structure of the government, so that all authority would not be vested in one despotic emperor, but shared with a council of elite Confucian officials.
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{{epname|Cronus, Diodorus}}
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'''Diodorus Cronus''' (fourth century, B.C.E.) was a Greek [[philosopher]] of the [[Megarian school]] who made important contributions to the development of [[modal logic]] and theories of [[conditional]]s. His teacher was [[Apollonius Cronus]], a student of Eubulides; he studied with Philo of Megara; and his most famous student was [[Zeno of Citium]], founder of the [[Stoicism|Stoa]]. His five daughters, Menexene, Argeia, Theognis, Artemisia, and Pantacleia, are all said to have been [[logic|logicians]].
  
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Early in the seventeenth century, the Tung-lin Acadmey joined with neighboring academies in Wu-chin and I-hsing to form the powerful Ch’ang-chou faction. Many of its members occupied high positions in the government bureaucracy, and from 1621 -1624 they were able to influence imperial policy in Peking. In the summer of  1625, Tung-lin leaders were purged, arrested, and tortured to death by the eunuch Wei Chung-hsien, and the private academies were destroyed. After Wei’s disgrace and death in 1627, there was a resurgence of the reform factions.  The movements disappeared after the fall of the Ming dynasty to the Manchu in 1644.  
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Diodorus examined the conditions under which conditional, “if…then” propositions might be true. Diodorus stated that a conditional proposition was true if there was never a time when the antecedent statement was true and the consequent statement was false. If there was any time when the consequent statement was false, the proposition was false.  
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== Politics of the Late Ming Dynasty==
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Diodrous devised the [[Maser Argument]], widely discussed during antiquity but now lost, to prove that, “Everything that is possible either is or will be true.” He also raised the paradox of future contingency with his question, “Will there be a sea battle tomorrow?” The logic of Diodorus influenced the logic of the Stoics, which was later taken up by twentieth century logicians.  Diodorus Cronus’ modal theory and his Master Argument served as a major philosophical inspiration for Arthur Prior, who founded tense logic.
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During the last century of the [[Ming dynasty]], between approximately 1530 and 1630, the bureaucratic elite and Chinese gentry rose up in an unprecedented reaction to “authoritarian [[Confucianism]].” Corruption was rampant among government officials, and the Ming emperors had withdrawn from day-to-day involvement in affairs of state, leaving a power vacuum that was filled by members of the imperial court, particularly eunuchs (by the end of the Ming dynasty, there were 70,000 eunuchs in the Forbidden City), and members of the bureaucratic elite and landed gentry, constantly vying for political control. Concerned about the condition of the government, many members of the bureaucratic elite began to take matters into their own hands.  
 
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The gentry, who wielded considerable power in their own states, began to establish private universities to train the Confucian scholars they believed were necessary for good government. At the same time they began attempting to bring about a change in the structure of the imperial government, in order to establish a system in which all authority would not be vested in one despotic emperor, but in a council of elite Confucian officials who would make decisions and oversee the daily affairs of government.
 
  
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==The Tung-lin Movement==
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==Life==
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The largest of these movements was the '''Tung-lin''', associated with the Tung-lin Academy. Early in the seventeenth century, the Tung-lin Academy joined with neighboring academies in Wu-chin and I-hsing to form the powerful Ch’ang-chou faction. Many of its members occupied high positions in the government bureaucracy, and they were able to influence imperial policy in Peking. They reached the height of their influence between 1621 and 1624.
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The most important philosopher of the [[Megarian school]] was Diodorus Cronus, who taught in Athens and Alexandria around 315-284 B.C.E. He left no writings, and his most famous pupil is [[Zeno of Citium]], founder of the [[Stoicism|Stoa]]. Little is known about the life of Diodorus Cronus.  [[Diogenes Laertius]] recounts two possible sources for the surname “Cronus.” One story is that Diodorus of Iasos, the son of Aminias, took the name of his teacher Apollonius Cronus, who was a student of Eubulides. Another story is that, while staying at the court of Ptolemy Soter, Diodorus was asked to solve a dialectical subtlety by Stilpo. When he was not able to answer on the spur of the moment, he was given the nickname “Cronus” by Ptolemy, referring to the God of time and mocking his slowness. He left the banquet, wrote an essay on Stilpo’s question, and died of despondency. Strabo, however, says that he took the name from Apollonius, his master. Laertius also credits him with being “the first person who invented the Concealed argument, and the Horned one” (Diogenes Laertius, ''Lives,'' "Life of Euclides," VII).
  
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In 1621, the young T'ien-ch'i Emperor came to the throne, and fell under the influence of the eunuch Wei Chung-hsien. Wei Chung-hsien had been a hoodlum and gambler, who had made himself a eunuch and changed his name to Li Chin-chung in order to escape from his debtors. Entering the imperial palace, he had managed to get into the service of Madam Ke (客氏) the wet-nurse of the future [[Ming Dynasty|Ming]] emperor. The couple began manipulating the young and illiterate Tianqi Emperor, who later made Wei his Grand Secretary of the State, giving him absolute power over the court. Wei gave  himself the name, ''Nine-Thousand Years' (九千歲), symbolizing that he was second only to the emperor, who was called the ''Ten-Thousand Years''(萬歲). Wei also built a number of shrines (生祠), placing god-like statues of himself in them. This was exactly the kind of situation that the Confucian officials abhorred, but they were powerless against it. Wei’s faction at court gradually undermined the power of the Tung-lin officials, and despite their high positions, they were dismissed from office. In the summer of  1625, Tung-lin leaders were purged, arrested, and tortured to death.  
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Like the rest of the Megarian school, he reveled in verbal arguments, proving that motion and existence are impossible. The impossible cannot result from the possible; a past event cannot become other than it is; but if an event, at a given moment, had been possible, from this possibility would result something impossible; therefore the original event was impossible. This problem was taken up by Chrysippus, who admitted that he could not solve it.
  
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The private academies were denounced as politically subversive organizations, and the emperor ordered them destroyed throughout the empire, especially those in Ch'ang-chou and Su-chou prefectures because these were assumed to be part of the Tung-lin organization. The halls of the Tung-lin Academy, partially destroyed in 1625, were completely torn down by imperial order in 1626.  
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Diodorus Cronus’ five daughters, Menexene, Argeia, Theognis, Artemisia, and Pantacleia are all said to have been logicians.  Philo of Megara studied with Diodorus; the logic of Philo and Diodorus influenced the logic of the Stoics, which was later taken up by twentieth century logicians.  Diodorus Cronus’ modal theory and his Master Argument served as a major philosophical inspiration for Arthur Prior.
  
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Wei Chung-hsien’s reign of terror ended abruptly with the death of the Tianqi Emperor, whose successor, the Chongzhen Emperor promptly dismissed him. He was killed and his corpse was disemboweled. The accession of the Chongzhen Emperor restored the fortunes of the Donglin faction. Later during Chongzhen's reign, Donglin partisans found themselves opposed to the Grand Secretary Wen Tiren, and eventually arranged his dismissal in 1637.
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==Thought==
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Diodorus Cronus made important contributions in [[logic]] to the development of theories of conditionals and [[modal logic]]. Diodorus devised a forerunner of strict implication, and developed a system of modal concepts that satisfies the basic logical requirements of modern modal theory. In antiquity, Diodorus Cronus was famous for his so-called Master Argument, which aimed to prove that only the actual is possible.
  
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==Fu She==
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===Conditional propositions===
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After Wei fell into disgrace in 1627, the private academies and associations re-emerged and engaged in the factionalism and political controversies which destabilized the last governments of the Ming dynasty. The '''Fu She''' (Return [to Antiquity] Society) movement, based in Su-chou during the 1620s and 1630s, represented the largest and most sophisticated political interest group ever organized within the imperial bureaucratic structure. It supported its members in the factional struggles that dominated late Ming politics.
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Historical evidence confirms that Diodorus conceived of logic as a logic of propositions. The [[Stoics]] later systematically developed propositional logic and created subtle classifications of predicates.  At the time of Diodorus and Philo, philosophers distinguished between “simple propositions” and “complex propositions.” Simple propositions were either positive or negative statements of a single fact. Complex propositions were thought to be composed of two or more simple propositions, and could be disjunctions, conjunctions or conditional statements. Diodorus probably examined the conditions under which all three types of complex propositions might be true, but most of his work was with conditional, “if…then” propositions.
  
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When the Ming dynasty fell in 1644, first to peasant rebels and then to Manchu conquerors, the activities of the Fu She ceased and the factionalism within the imperial government disappeared. The elite gentry, fearing peasant rebellion more than they feared Manchu occupation, recognized that their social and economic privileges depended on the political power of the state, and many of them quickly entered the administration of the Ch’ing dynasty. The new Ch’ing emperors actively participated in government affairs, keeping power struggles under control.
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Diodorus stated that a conditional proposition was true if there was never a time when the [[antecedent]] statement was true and the consequent statement was false.  If there was any time when the consequent statement was false, the proposition was false.  It was not a requirement that the antecedent and consequent statements be relevant to each other in any way.  The antecedent statement could be something impossible, even nonsensical, such as, “If the earth flies,”  but if the consequent statement was always true, or necessary, the whole proposition was true. This created a “paradox of strict implication;” one example found in Greek texts of Diodorean-true conditional, "If it is not the case that there are indivisible elements of things, then there are indivisible elements of things" (SE, ''Outlines of Pyrrhonism'' 2.111), suggests that there was some awareness of these paradoxes in antiquity.
  
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==Significance of the Tung-lin Movement==
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===Modalities===
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The appearance of a widespread, organized opposition movement among the officials within an imperial government was unprecedented in Chinese history. Confucian tradition dictated that the emperor exercised supreme power, and that the strength of the empire depended on the obedience and loyalty of officials to the imperial throne.  However, the actual political situation had become so distant from Confucian ideals of government that many officials feared that the Ming empire would lose its “mandate” and meet its downfall.  The Tung-lin movement aimed to remedy imperial abuses of power, and to protect the empire from incapable leaders by investing political authority in a group of professional Confucian officials who would assist the emperor in government.
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Diodorus considered the modalities “possible,” “impossible,” “necessary,” and “non-necessary” as properties of propositions or states of affairs, rather than as components of a proposition. One text reports all four definitions of Diodorus' modal notions:
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Possible is that which either is or will be true; impossible that which is false and will not be true; necessary that which is true and will not be false; non-necessary that which either is false already or will be false (Boethius, ''On Aristotle's On Interpretation'' 2.II.234-235).
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The modality of a particular proposition depended on its range of truth-values, in the present or in the future. A proposition that is always true, such as, ”If I walk, I move,” is both possible and necessary. If a proposition is sometimes, but not always, true, it is possible, but not necessary. The proposition, "It is day," is such a case, because it is true if spoken during the day, and false if spoken at night. In defining truth-values in terms of time, Diodorus and and other ancient Greek philosophers considered was true for their own time and place, but probably were not aware of time changes, or the fact that when it was night in Athens, it was day on the other side of the world. They did not include a specific date or time in their propositions. Since Diodorus based the modality of a proposition on what was true at a specific time, certain time-based propositions could change their modality from possible to impossible and from non-necessary to necessary as time passed. If the proposition, "Artemisia is five years old" was now true, then that proposition was now possible; but after she reached her sixth birthday, the proposition would become impossible, because it would never be true again.
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Diodorus also distinguished between propositions in the present tense like "Helen has three husbands" and "These men are marrying" and propositions in a tense of completion, "Helen had three husbands" and "These men married," and observed that it is possible for propositions like the latter two to be true, without there ever having been a time at which a corresponding one of the former type was true.<ref>Sextus Empiricus, ''Against the Physicists'' 2.97-8.</ref>
  
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[[Confucianism|Confucian]] scholars of the time attributed the fall of the [[Ming dynasty]] to the despotism of the emperors, but also to the factionalism within the government. Many cultivated Confucians feared that it was wrong to establish separate political organizations for the advancement of personal interests, and perceived Wei Chung-hsien’s brutal purge of the Tung-lin movement as a sign of heaven’s displeasure. Factionalism went against the emperor, who according to the Confucian ideal represented the public interest.
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===Master Argument===
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Diodorus used distinct claims to define what is “possible:” Everything that either is or will be true is possible, and, “Everything that is possible either is or will be true.” The first statement was not questioned by Hellenistic philosophers, but the second statement was considered counterintuitive required justification.  Diodorus attempted to support the second claim with his ''Master Argument''. (Epictetus, ''Dissertations'' 2.19).
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''The Master Argument'' was widely discussed in antiquity, but the complete thread of the argument has been lost.  One brief passage in the Dissertations of Epictetus makes reference to it:
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<blockquote>There is a general conflict between the following three statements: (I) Every past true proposition is necessary; and (II) the impossible does not follow from the possible; and (III) something is possible which neither is true nor will be true. Being aware of this conflict, Diodorus used the plausibility of the first two statements in order to show that (IV) nothing is possible that neither is nor will be true (Epictetus, ''Dissertations'' 2.19.1). </blockquote>
  
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Modern historians and scholars see the Tung-lin movement as the natural outcome of a situation in which an autocratic government attempts to exercise too much control over a large population with expanding urban centers. The Tung-lin movement and the political thought associated with it are also perceived as an advancement in Confucian political theory. Some Western scholars have speculated that Tung-lin efforts to reform the late Ming state "showed features strikingly similar to the trend against absolute monarchy and toward parliamentary rule in the West," <ref> Struve, Lynn A. 2005. Time, temporality, and imperial transition: East Asia from Ming to Qing., v. 9, pt 1 </ref>and that the continuation of the traditional imperial system after the Manchu conquest represents a point at which the political history of China diverged from that of Europe.
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Hellenistic philosophers generally regarded Diodorus' modal notions as jeopardizing freedom because they characterize as “impossible” anything that never happens or is never true. This amounted to a sort of logical determinism, since it limited the scope of contingency.
  
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==The '''Tung-lin (Donglin) Academy''' ==
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===[[Atomism]]===
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Diodorus Cronus is reported to have offered new arguments that there must be partless bodies or magnitudes, using logical arguments that depended on mutually exhaustive alternatives. Diodorus apparently used the idea that there is a smallest size at which an object at a given distance is visible, as the basis for an argument that there are indivisible magnitudes. His argument began with the idea that there is a difference in size between the smallest size at which a given object is visible, and the largest size at which it is invisible. Unless one concedes that there is a magnitude at which a body is both invisible and visible (or neither), there cannot be any other magnitude intermediate between these two magnitudes. Therefore, magnitudes must increase by discrete units.
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[[Sextus Empiricus]] (AM 10.48ff) also reported an argument of Diodorus' concluding that magnitudes have discrete intervals. The argument denied the existence of moving bodies, insisting that bodies move neither when they are in the place where they are, nor when they are in the place where they are not. These alternatives were presented as exhaustive, and the conclusion was that bodies are never moving. However, rather than assert that everything is static, Diodorus took the view that bodies must have moved without ever being in motion: They were simply at one place at one moment, and at another place at another moment.
  
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The '''Tung-lin (Donglin) Academy'''  (東林書院 ''Dōnglín Shūyuàn'' — literally meaning "Eastern Grove Academy"), also known as the '''Guishan Academy''' (龜山書院 ''Guīshān Shūyuàn''), was originally built in 1111 C.E. during the Northern Song (北宋) dynasty at present-day Wuxi in [[China]]. It was originally the school where the [[neo-Confucianism|neo-Confucian]] scholar Yang Shi taught, but later fell into disuse. In 1604, during the Wanli era, Gu Xiancheng (顧憲成 Gù Xiànchéng, (1550-1612), a Ming Grand Secretary, along with Gao Panlong (高攀龍 Gāo Pānlóng, 1562-1626), a scholar, restored the Tung-lin (Donglin) Academy on the same site with the financial backing of local gentry and officials.  
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===Contingency of a future event===
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The "problem of the future's contingents" is a logical paradox concerning the contingency of a future event, first posed by [[Diodorus Cronus]]  under the name of the "dominator," and then reactualized by [[Aristotle]] in Chapter Nine of ''De Interpretatione.'' It was later taken on by [[Leibniz]]. [[Deleuze]] used it to oppose a "logic of the event" to a "logic of signification."
  
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The motivation for founding the Tung-lin Academy was concern about the state of the bureaucracy and its inability to bring about improvement. The Academy represented a return to Confucian moral traditions as a means of arriving at fresh moral evaluations. In the late Ming and early Ch’ing periods, the Academy became a center of dissent for those involved in public affairs Many supporters of Tung-lin (Donglin) were members of the bureaucracy, and it become deeply involved in factional politics.
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Diodorus' problem concerned the question: "Will there be a sea battle tomorrow?" According to this question, two propositions are possible: "Yes, there will be a sea battle tomorrow" or "no, there will not be a sea battle tomorrow." This was a paradox in Diodorus' eyes, since either there would be a battle tomorrow or there wouldn't be one.  According to the basic principle of bivalence (''A'' is either true or false), one of the two propositions had to be correct and therefore excluded the other. This posed a problem, since the judgment on the proposition (whether it was right or wrong) could only be made after the event had happened. In Deleuze's words, "time is the crisis of truth."<ref>Gilles Deleuze, ''Cinema 2: The Time-Image'' (1989), chapter VI, section 1. </ref> The problem thus concerns the [[ontology|ontological]] status of the future, and therefore of human action: Is the future determined or not?
  
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During the reign of the Emperor Tianqi, Tung-lin (Donglin) opposition to the eunuch Wei Zhongxian resulted in the closure of the Academy in 1622 and the torture and execution of its head, Yang Lian, and five other members in 1624. The accession of the Chongzhen Emperor restored the fortunes of the Tung-lin (Donglin) faction. Later during Chongzhen's reign, Tung-lin ( Donglin) partisans found themselves opposed to the Grand Secretary Wen Tiren, and eventually arranged his dismissal in 1637.
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==== Aristotle's solution ====
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According to the principle of bivalence, something concerning reality is either true or false (''A'' is ''B,'' or ''A'' is not ''B''). Logic is thus based on disjunctive syllogism. This poses a problem when logic is applied to future possibilities instead of present reality. Diodorus' famous propositions are: "Will there be a sea battle tomorrow?" and/or "Will there not be a sea battle tomorrow?"  Are future events determined or not? Logical necessity seems to be defeated by real necessity.
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It can be said that the proposition is neither true nor false: Some possible futures make it true and others false; this may be called "indeterminacy intuition." It could also be said that the truth-value of the proposition will be only given in the future, that is, when the future unfolds. Thus, the truth value ''will always be given'' but never given in the present.
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Aristotle solved the problem by asserting that the principle of bivalence found its exception in this paradox of the sea battles: In this specific case, what is impossible is that both alternatives can be possible at the same time: Either there ''will'' be a battle, or there won't. Both options can't be simultaneously taken. Today, they are neither true nor false; but if one is true, then the other becomes false. According to Aristotle, it is impossible to say today if the proposition is correct: The observer must wait for the contingent realization (or not) of the battle, logic realizes itself afterwards:
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<blockquote>One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial, one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good (Aristotle, ''On Interpretation'' §9).<ref>E.M. Edghill, trans., [http://etext.library.adelaide.edu.au/a/aristotle/interpretation/ ''On Interpretation by Aristotle'' §9.] Retrieved May 21, 2007.</ref></blockquote>
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Diodorus concluded that the future battle was either impossible or necessary, meaning that the chain of causal events which would determine tomorrow’s action was already in place today. Aristotle added a third term, ''contingency,'' which preserves logic while at the same time leaving room for indetermination in reality. What is necessary is not that there will or that there won't be a battle tomorrow, but the alternative itself is necessary:
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<blockquote>A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow (Aristotle. ''De Interpretatione'''' 9, 19 a 30).<ref>Ibid.</ref></blockquote>
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Thus, an event always comes in the form of a future, undetermined event; logic always come afterwards. [[Hegel]] conveyed the same meaning by claiming that wisdom came at dusk. Aristotle also viewed this as a practical, [[ethics|ethic]]al question: Pretending that  the future is already determined would have unacceptable consequences for humanity.
  
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The Tung-lin (Donglin) Academy can be found at 867, Jiefang Donglu, Wuxi City.
 
 
==Notes==
 
==Notes==
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<references/>
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== References ==
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*Ammonius, David L. Blank, Norman Kretzmann, and Boethius. ''On Aristotle's On interpretation 9.'' Ithaca, N.Y.: Cornell University Press, 1998. ISBN 0801433355
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*Diogenes Laertius and Robert Drew Hicks. ''Lives of Eminent Philosophers.'' Harvard University Press, 1942.
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*Epictetus and T. W. Rolleston. ''The Teaching of Epictetus: Being the Encheiridion of Epictetus; with Selections from the 'Dissertations' and 'Fragments.''' London: W. Scott, 1888.
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*MacFarlane, John. "Sea Battles, Futures Contingents, and Relative Truth" and "Future Contingent and Relative Truth,"  ''The Philosophical Quarterly'' 53 (2003): 321-36.
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*Mates, Benson. ''Diodorean Implication.'' 1949.
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*Mikel, Anton F. ''The Master Argument of Diodorus Cronus''. Thesis (Ph. D.)—Florida State University, 1992.
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*Sextus and Robert Gregg Bury. ''Sextus Empiricus.'' The Loeb classical library, 311. Cambridge, Mass: Harvard University Press, 1987. ISBN 0674993446
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*Sextus. ''Outlines of Pyrrhonism, Book I.'' Great Books Foundation series. Chicago: Regnery, 1949.
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*Spranzi, Marta. ''Diodorus Cronus and Aristotle: Motion, Partless Quantities and the Possible''. Ferrara: Università degli Studi di Ferrara, 1992.
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== External links ==
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All links retrieved January 29, 2024.
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*[http://plato.stanford.edu/entries/dialectical-school/ Dialectical School], Stanford Encyclopedia of Philosophy.
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*[http://plato.stanford.edu/entries/atomism-ancient/ Ancient Atomism], Stanford Encyclopedia of Philosophy.
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===General philosophy sources===
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*[http://plato.stanford.edu/ Stanford Encyclopedia of Philosophy].
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*[http://www.iep.utm.edu/ The Internet Encyclopedia of Philosophy].
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*[http://www.bu.edu/wcp/PaidArch.html Paideia Project Online].
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*[http://www.gutenberg.org/ Project Gutenberg].
  
  
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==References==
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[[Category:philosophers]]
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*Conference on Seventeenth-Century Chinese Thought, and William Theodore De Bary. 1975. ''The unfolding of Neo-Confucianism. Studies in oriental culture'', no. 10. New York: Columbia University Press ISBN: 0231038283 9780231038287 0231038291 9780231038294 |
 
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*Lao, Siguang. 1970. ''The split within the Tung-Lin movement and its consequences.''
 
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*Hucker, Charles O. 1975. ''China's imperial past: an introduction to Chinese history and culture.'' Stanford, Calif: Stanford University Press. ISBN: 0804708878 : 780804708876
 
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*Spence, Jonathan D., and John E. Wills. 1979. ''From Ming to Ch’ing: conquest, region, and continuity in seventeenth-century China.'' New Haven: Yale University Press. ISBN: 0300022182 9780300022186
 
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*Struve, Lynn A. 2005. ''Time, temporality, and imperial transition: East Asia from Ming to Qing. Asian interactions and comparisons.'' Honolulu: Association for Asian Studies and University of Hawai'i Press. ISBN: 0824828275 9780824828271
 
  
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*This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.
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Latest revision as of 15:24, 29 January 2024

Diodorus Cronus (fourth century, B.C.E.) was a Greek philosopher of the Megarian school who made important contributions to the development of modal logic and theories of conditionals. His teacher was Apollonius Cronus, a student of Eubulides; he studied with Philo of Megara; and his most famous student was Zeno of Citium, founder of the Stoa. His five daughters, Menexene, Argeia, Theognis, Artemisia, and Pantacleia, are all said to have been logicians.

Diodorus examined the conditions under which conditional, “if…then” propositions might be true. Diodorus stated that a conditional proposition was true if there was never a time when the antecedent statement was true and the consequent statement was false. If there was any time when the consequent statement was false, the proposition was false.

Diodrous devised the Maser Argument, widely discussed during antiquity but now lost, to prove that, “Everything that is possible either is or will be true.” He also raised the paradox of future contingency with his question, “Will there be a sea battle tomorrow?” The logic of Diodorus influenced the logic of the Stoics, which was later taken up by twentieth century logicians. Diodorus Cronus’ modal theory and his Master Argument served as a major philosophical inspiration for Arthur Prior, who founded tense logic.

Life

The most important philosopher of the Megarian school was Diodorus Cronus, who taught in Athens and Alexandria around 315-284 B.C.E. He left no writings, and his most famous pupil is Zeno of Citium, founder of the Stoa. Little is known about the life of Diodorus Cronus. Diogenes Laertius recounts two possible sources for the surname “Cronus.” One story is that Diodorus of Iasos, the son of Aminias, took the name of his teacher Apollonius Cronus, who was a student of Eubulides. Another story is that, while staying at the court of Ptolemy Soter, Diodorus was asked to solve a dialectical subtlety by Stilpo. When he was not able to answer on the spur of the moment, he was given the nickname “Cronus” by Ptolemy, referring to the God of time and mocking his slowness. He left the banquet, wrote an essay on Stilpo’s question, and died of despondency. Strabo, however, says that he took the name from Apollonius, his master. Laertius also credits him with being “the first person who invented the Concealed argument, and the Horned one” (Diogenes Laertius, Lives, "Life of Euclides," VII).

Like the rest of the Megarian school, he reveled in verbal arguments, proving that motion and existence are impossible. The impossible cannot result from the possible; a past event cannot become other than it is; but if an event, at a given moment, had been possible, from this possibility would result something impossible; therefore the original event was impossible. This problem was taken up by Chrysippus, who admitted that he could not solve it.

Diodorus Cronus’ five daughters, Menexene, Argeia, Theognis, Artemisia, and Pantacleia are all said to have been logicians. Philo of Megara studied with Diodorus; the logic of Philo and Diodorus influenced the logic of the Stoics, which was later taken up by twentieth century logicians. Diodorus Cronus’ modal theory and his Master Argument served as a major philosophical inspiration for Arthur Prior.

Thought

Diodorus Cronus made important contributions in logic to the development of theories of conditionals and modal logic. Diodorus devised a forerunner of strict implication, and developed a system of modal concepts that satisfies the basic logical requirements of modern modal theory. In antiquity, Diodorus Cronus was famous for his so-called Master Argument, which aimed to prove that only the actual is possible.

Conditional propositions

Historical evidence confirms that Diodorus conceived of logic as a logic of propositions. The Stoics later systematically developed propositional logic and created subtle classifications of predicates. At the time of Diodorus and Philo, philosophers distinguished between “simple propositions” and “complex propositions.” Simple propositions were either positive or negative statements of a single fact. Complex propositions were thought to be composed of two or more simple propositions, and could be disjunctions, conjunctions or conditional statements. Diodorus probably examined the conditions under which all three types of complex propositions might be true, but most of his work was with conditional, “if…then” propositions.

Diodorus stated that a conditional proposition was true if there was never a time when the antecedent statement was true and the consequent statement was false. If there was any time when the consequent statement was false, the proposition was false. It was not a requirement that the antecedent and consequent statements be relevant to each other in any way. The antecedent statement could be something impossible, even nonsensical, such as, “If the earth flies,” but if the consequent statement was always true, or necessary, the whole proposition was true. This created a “paradox of strict implication;” one example found in Greek texts of Diodorean-true conditional, "If it is not the case that there are indivisible elements of things, then there are indivisible elements of things" (SE, Outlines of Pyrrhonism 2.111), suggests that there was some awareness of these paradoxes in antiquity.

Modalities

Diodorus considered the modalities “possible,” “impossible,” “necessary,” and “non-necessary” as properties of propositions or states of affairs, rather than as components of a proposition. One text reports all four definitions of Diodorus' modal notions: Possible is that which either is or will be true; impossible that which is false and will not be true; necessary that which is true and will not be false; non-necessary that which either is false already or will be false (Boethius, On Aristotle's On Interpretation 2.II.234-235). The modality of a particular proposition depended on its range of truth-values, in the present or in the future. A proposition that is always true, such as, ”If I walk, I move,” is both possible and necessary. If a proposition is sometimes, but not always, true, it is possible, but not necessary. The proposition, "It is day," is such a case, because it is true if spoken during the day, and false if spoken at night. In defining truth-values in terms of time, Diodorus and and other ancient Greek philosophers considered was true for their own time and place, but probably were not aware of time changes, or the fact that when it was night in Athens, it was day on the other side of the world. They did not include a specific date or time in their propositions. Since Diodorus based the modality of a proposition on what was true at a specific time, certain time-based propositions could change their modality from possible to impossible and from non-necessary to necessary as time passed. If the proposition, "Artemisia is five years old" was now true, then that proposition was now possible; but after she reached her sixth birthday, the proposition would become impossible, because it would never be true again. Diodorus also distinguished between propositions in the present tense like "Helen has three husbands" and "These men are marrying" and propositions in a tense of completion, "Helen had three husbands" and "These men married," and observed that it is possible for propositions like the latter two to be true, without there ever having been a time at which a corresponding one of the former type was true.[1]

Master Argument

Diodorus used distinct claims to define what is “possible:” Everything that either is or will be true is possible, and, “Everything that is possible either is or will be true.” The first statement was not questioned by Hellenistic philosophers, but the second statement was considered counterintuitive required justification. Diodorus attempted to support the second claim with his Master Argument. (Epictetus, Dissertations 2.19). The Master Argument was widely discussed in antiquity, but the complete thread of the argument has been lost. One brief passage in the Dissertations of Epictetus makes reference to it:

There is a general conflict between the following three statements: (I) Every past true proposition is necessary; and (II) the impossible does not follow from the possible; and (III) something is possible which neither is true nor will be true. Being aware of this conflict, Diodorus used the plausibility of the first two statements in order to show that (IV) nothing is possible that neither is nor will be true (Epictetus, Dissertations 2.19.1).

Hellenistic philosophers generally regarded Diodorus' modal notions as jeopardizing freedom because they characterize as “impossible” anything that never happens or is never true. This amounted to a sort of logical determinism, since it limited the scope of contingency.

Atomism

Diodorus Cronus is reported to have offered new arguments that there must be partless bodies or magnitudes, using logical arguments that depended on mutually exhaustive alternatives. Diodorus apparently used the idea that there is a smallest size at which an object at a given distance is visible, as the basis for an argument that there are indivisible magnitudes. His argument began with the idea that there is a difference in size between the smallest size at which a given object is visible, and the largest size at which it is invisible. Unless one concedes that there is a magnitude at which a body is both invisible and visible (or neither), there cannot be any other magnitude intermediate between these two magnitudes. Therefore, magnitudes must increase by discrete units. Sextus Empiricus (AM 10.48ff) also reported an argument of Diodorus' concluding that magnitudes have discrete intervals. The argument denied the existence of moving bodies, insisting that bodies move neither when they are in the place where they are, nor when they are in the place where they are not. These alternatives were presented as exhaustive, and the conclusion was that bodies are never moving. However, rather than assert that everything is static, Diodorus took the view that bodies must have moved without ever being in motion: They were simply at one place at one moment, and at another place at another moment.

Contingency of a future event

The "problem of the future's contingents" is a logical paradox concerning the contingency of a future event, first posed by Diodorus Cronus under the name of the "dominator," and then reactualized by Aristotle in Chapter Nine of De Interpretatione. It was later taken on by Leibniz. Deleuze used it to oppose a "logic of the event" to a "logic of signification."

Diodorus' problem concerned the question: "Will there be a sea battle tomorrow?" According to this question, two propositions are possible: "Yes, there will be a sea battle tomorrow" or "no, there will not be a sea battle tomorrow." This was a paradox in Diodorus' eyes, since either there would be a battle tomorrow or there wouldn't be one. According to the basic principle of bivalence (A is either true or false), one of the two propositions had to be correct and therefore excluded the other. This posed a problem, since the judgment on the proposition (whether it was right or wrong) could only be made after the event had happened. In Deleuze's words, "time is the crisis of truth."[2] The problem thus concerns the ontological status of the future, and therefore of human action: Is the future determined or not?

Aristotle's solution

According to the principle of bivalence, something concerning reality is either true or false (A is B, or A is not B). Logic is thus based on disjunctive syllogism. This poses a problem when logic is applied to future possibilities instead of present reality. Diodorus' famous propositions are: "Will there be a sea battle tomorrow?" and/or "Will there not be a sea battle tomorrow?" Are future events determined or not? Logical necessity seems to be defeated by real necessity.

It can be said that the proposition is neither true nor false: Some possible futures make it true and others false; this may be called "indeterminacy intuition." It could also be said that the truth-value of the proposition will be only given in the future, that is, when the future unfolds. Thus, the truth value will always be given but never given in the present.

Aristotle solved the problem by asserting that the principle of bivalence found its exception in this paradox of the sea battles: In this specific case, what is impossible is that both alternatives can be possible at the same time: Either there will be a battle, or there won't. Both options can't be simultaneously taken. Today, they are neither true nor false; but if one is true, then the other becomes false. According to Aristotle, it is impossible to say today if the proposition is correct: The observer must wait for the contingent realization (or not) of the battle, logic realizes itself afterwards:

One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial, one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good (Aristotle, On Interpretation §9).[3]

Diodorus concluded that the future battle was either impossible or necessary, meaning that the chain of causal events which would determine tomorrow’s action was already in place today. Aristotle added a third term, contingency, which preserves logic while at the same time leaving room for indetermination in reality. What is necessary is not that there will or that there won't be a battle tomorrow, but the alternative itself is necessary:

A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow (Aristotle. De Interpretatione'' 9, 19 a 30).[4]

Thus, an event always comes in the form of a future, undetermined event; logic always come afterwards. Hegel conveyed the same meaning by claiming that wisdom came at dusk. Aristotle also viewed this as a practical, ethical question: Pretending that the future is already determined would have unacceptable consequences for humanity.

Notes

  1. ↑ Sextus Empiricus, Against the Physicists 2.97-8.
  2. ↑ Gilles Deleuze, Cinema 2: The Time-Image (1989), chapter VI, section 1.
  3. ↑ E.M. Edghill, trans., On Interpretation by Aristotle §9. Retrieved May 21, 2007.
  4. ↑ Ibid.

References
ISBN links support NWE through referral fees

  • Ammonius, David L. Blank, Norman Kretzmann, and Boethius. On Aristotle's On interpretation 9. Ithaca, N.Y.: Cornell University Press, 1998. ISBN 0801433355
  • Diogenes Laertius and Robert Drew Hicks. Lives of Eminent Philosophers. Harvard University Press, 1942.
  • Epictetus and T. W. Rolleston. The Teaching of Epictetus: Being the Encheiridion of Epictetus; with Selections from the 'Dissertations' and 'Fragments.' London: W. Scott, 1888.
  • MacFarlane, John. "Sea Battles, Futures Contingents, and Relative Truth" and "Future Contingent and Relative Truth," The Philosophical Quarterly 53 (2003): 321-36.
  • Mates, Benson. Diodorean Implication. 1949.
  • Mikel, Anton F. The Master Argument of Diodorus Cronus. Thesis (Ph. D.)—Florida State University, 1992.
  • Sextus and Robert Gregg Bury. Sextus Empiricus. The Loeb classical library, 311. Cambridge, Mass: Harvard University Press, 1987. ISBN 0674993446
  • Sextus. Outlines of Pyrrhonism, Book I. Great Books Foundation series. Chicago: Regnery, 1949.
  • Spranzi, Marta. Diodorus Cronus and Aristotle: Motion, Partless Quantities and the Possible. Ferrara: Università degli Studi di Ferrara, 1992.

External links

All links retrieved January 29, 2024.

General philosophy sources

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