Diodorus Cronus
Encyclopedia
Diodorus Cronus was a Greek
philosopher and dialectician
connected to the Megarian school. He was most notable for logic innovations, including his master argument fomulated in response to Aristotle
's discussion of future contingents.
, and he lived at the court of Alexandria
in the reign of Ptolemy I Soter
, who is said to have given him the surname of Cronus ("old fogey") on account of his inability to solve at once some dialectic
problem proposed by Stilpo
, when the two philosophers were dining with the king. Diodorus is said to have taken that disgrace so much to heart, that after his return from the meal, and writing a treatise on the problem, he died in despair. However, according to Strabo
, Diodorus himself adopted the surname of Cronus from his teacher, Apollonius Cronus
. Diodorus died around 284 BCE, his date of birth is unknown. It was once thought that he was old enough to have influenced Aristotle
(384–322 BCE), but there is no strong evidence for this.
Diodorus was particularly celebrated for his great dialectic skill, for which he was called The Dialectician. This effectively became his surname, and descended even to his five daughters, Menexene, Argia, Theognis, Artemesia, and Pantaclea, who were likewise distinguished as dialecticians. His pupils included Philo the Dialectician
, and Zeno of Citium
- the founder of the Stoic
school. Although influenced by the Megarian school it is not clear how closely Diodorus and his fellow dialecticians were connected to that particular philosophical school.
art of the Megarians. He was much occupied with the theory of proof and of hypothetical propositions. In the same manner as he rejected in logic the divisibility of the fundamental notion, he also maintained, in his physical doctrines, that space was indivisible, and consequently that motion was impossible. He further denied the coming into existence and all multiplicity both in time and in space; but he considered the things that fill up space as one whole composed of an infinite number of indivisible particles.
Diodorus made use of the Sorites paradox
, and is said to have invented two others of the same kind, viz. The Masked Man and The Horns, which are, however, also ascribed to Eubulides. He also rejected the view that words are ambiguous, any uncertainty in understanding was always due to speakers expressing themselves obscurely.
, in his work On Interpretation, had wrestled with the problem of future contingents. In particular whether one can meaningfully regard future contingents
as true or false now, if the future is open, and if so, how?
In response, Diodorus maintained that possible was identical with necessary; so that the future is as certain and defined as the past. Alexander of Aphrodisias
tells us that Diodorus believed that that alone is possible which either is happening now, or will happen at some future time. When speaking about facts of an unrecorded past, we know well that a given fact either occurred or did not occur, yet without knowing which of the two is true - and therefore we affirm only that the fact may have occurred: so also about the future, either the assertion that a given fact will at some time occur, is positively true, or the assertion that it will never occur, is positively true: the assertion that it may or may not occur some time or other, represents only our ignorance, which of the two is true. That which will never at any time occur, is impossible.
Diodorus went on to formulate an argument that became known as the Master Argument (or Ruling Argument: ho kurieuôn logos). The most succinct description of it is provided by Epictetus
:
Epictetus' description of the Master Argument is not in the form as it would have been presented by Diodorus, which makes it difficult to know the precise nature of his argument. To modern logicians, it is not obvious why these three premisses are inconsistent, or why the first two should lead to the rejection of the third. Modern interpretations therefore assume that there must have been extra premisses in the argument tacitly assumed by Diodorus and his contemporaries.
One possible reconstruction is as follows: For Diodorus, if a future event is not going to happen, then it was true in the past that it would not happen. Since every past truth is necessary (proposition 1), it was necessary that in the past it would not happen. Since the impossible cannot follow from the possible (proposition 2), it must have always been impossible for the event to occur. Therefore if something will not be true, it will never be possible for it to be true, and thus proposition 3 is shown to be false.
Epictetus goes on to point out that Panthoides
, Cleanthes
, and Antipater of Tarsus
made use of the second and third proposition to demonstrate that the first proposition was false. Chrysippus
, on the other hand, agreed with Diodorus that everything true as an event in the past is necessary, but attacked Diodorus' view that the possible must be either what is true or what will be true. He thus made use of the first and third proposition to demonstrate that the second proposition was false.
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...
philosopher and dialectician
Dialectician
A dialectician is a philosopher who views the world in terms of complementary opposites and the interactions thereof. In popular usage, the central feature of dialectic is the concept of "thesis, antithesis, synthesis" - when an idea or phenomenon arises, it carries within itself the seed of its...
connected to the Megarian school. He was most notable for logic innovations, including his master argument fomulated in response to Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
's discussion of future contingents.
Life
Diodorus was a son of Ameinias of Iasus in CariaCaria
Caria was a region of western Anatolia extending along the coast from mid-Ionia south to Lycia and east to Phrygia. The Ionian and Dorian Greeks colonized the west of it and joined the Carian population in forming Greek-dominated states there...
, and he lived at the court of Alexandria
Alexandria
Alexandria is the second-largest city of Egypt, with a population of 4.1 million, extending about along the coast of the Mediterranean Sea in the north central part of the country; it is also the largest city lying directly on the Mediterranean coast. It is Egypt's largest seaport, serving...
in the reign of Ptolemy I Soter
Ptolemy I Soter
Ptolemy I Soter I , also known as Ptolemy Lagides, c. 367 BC – c. 283 BC, was a Macedonian general under Alexander the Great, who became ruler of Egypt and founder of both the Ptolemaic Kingdom and the Ptolemaic Dynasty...
, who is said to have given him the surname of Cronus ("old fogey") on account of his inability to solve at once some dialectic
Dialectic
Dialectic is a method of argument for resolving disagreement that has been central to Indic and European philosophy since antiquity. The word dialectic originated in Ancient Greece, and was made popular by Plato in the Socratic dialogues...
problem proposed by Stilpo
Stilpo
Stilpo was a Greek philosopher of the Megarian school. He was a contemporary of Theophrastus, Diodorus Cronus, and Crates of Thebes. None of his writings survive, he was interested in logic and dialectic, and he argued that the universal is fundamentally separated from the individual and concrete...
, when the two philosophers were dining with the king. Diodorus is said to have taken that disgrace so much to heart, that after his return from the meal, and writing a treatise on the problem, he died in despair. However, according to Strabo
Strabo
Strabo, also written Strabon was a Greek historian, geographer and philosopher.-Life:Strabo was born to an affluent family from Amaseia in Pontus , a city which he said was situated the approximate equivalent of 75 km from the Black Sea...
, Diodorus himself adopted the surname of Cronus from his teacher, Apollonius Cronus
Apollonius Cronus
Apollonius Cronus from Cyrene was a philosopher of the Megarian school.Very little is known about him. He was the pupil of Eubulides, and was the teacher of Diodorus Cronus, as Strabo relates:Apollonius Cronus, was from Cyrene, .....
. Diodorus died around 284 BCE, his date of birth is unknown. It was once thought that he was old enough to have influenced Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
(384–322 BCE), but there is no strong evidence for this.
Diodorus was particularly celebrated for his great dialectic skill, for which he was called The Dialectician. This effectively became his surname, and descended even to his five daughters, Menexene, Argia, Theognis, Artemesia, and Pantaclea, who were likewise distinguished as dialecticians. His pupils included Philo the Dialectician
Philo the Dialectician
Philo the Dialectician was a dialectic philosopher of the Megarian school. He is often called Philo of Megara although the city of his birth is unknown...
, and Zeno of Citium
Zeno of Citium
Zeno of Citium was a Greek philosopher from Citium . Zeno was the founder of the Stoic school of philosophy, which he taught in Athens from about 300 BC. Based on the moral ideas of the Cynics, Stoicism laid great emphasis on goodness and peace of mind gained from living a life of virtue in...
- the founder of the Stoic
STOIC
STOIC was a variant of Forth.It started out at the MIT and Harvard Biomedical Engineering Centre in Boston, and was written in the mid 1970s by Jonathan Sachs...
school. Although influenced by the Megarian school it is not clear how closely Diodorus and his fellow dialecticians were connected to that particular philosophical school.
Philosophy
On the doctrines of Diodorus we possess only fragmentary information, and not even the titles of his works are known. He seems to have fully developed the dialecticDialectic
Dialectic is a method of argument for resolving disagreement that has been central to Indic and European philosophy since antiquity. The word dialectic originated in Ancient Greece, and was made popular by Plato in the Socratic dialogues...
art of the Megarians. He was much occupied with the theory of proof and of hypothetical propositions. In the same manner as he rejected in logic the divisibility of the fundamental notion, he also maintained, in his physical doctrines, that space was indivisible, and consequently that motion was impossible. He further denied the coming into existence and all multiplicity both in time and in space; but he considered the things that fill up space as one whole composed of an infinite number of indivisible particles.
Diodorus made use of the Sorites paradox
Sorites paradox
The sorites paradox is a paradox that arises from vague predicates. The paradox of the heap is an example of this paradox which arises when one considers a heap of sand, from which grains are individually removed...
, and is said to have invented two others of the same kind, viz. The Masked Man and The Horns, which are, however, also ascribed to Eubulides. He also rejected the view that words are ambiguous, any uncertainty in understanding was always due to speakers expressing themselves obscurely.
Master Argument
AristotleAristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
, in his work On Interpretation, had wrestled with the problem of future contingents. In particular whether one can meaningfully regard future contingents
Contingency (philosophy)
In philosophy and logic, contingency is the status of propositions that are neither true under every possible valuation nor false under every possible valuation . A contingent proposition is neither necessarily true nor necessarily false...
as true or false now, if the future is open, and if so, how?
In response, Diodorus maintained that possible was identical with necessary; so that the future is as certain and defined as the past. Alexander of Aphrodisias
Alexander of Aphrodisias
Alexander of Aphrodisias was a Peripatetic philosopher and the most celebrated of the Ancient Greek commentators on the writings of Aristotle. He was a native of Aphrodisias in Caria, and lived and taught in Athens at the beginning of the 3rd century, where he held a position as head of the...
tells us that Diodorus believed that that alone is possible which either is happening now, or will happen at some future time. When speaking about facts of an unrecorded past, we know well that a given fact either occurred or did not occur, yet without knowing which of the two is true - and therefore we affirm only that the fact may have occurred: so also about the future, either the assertion that a given fact will at some time occur, is positively true, or the assertion that it will never occur, is positively true: the assertion that it may or may not occur some time or other, represents only our ignorance, which of the two is true. That which will never at any time occur, is impossible.
Diodorus went on to formulate an argument that became known as the Master Argument (or Ruling Argument: ho kurieuôn logos). The most succinct description of it is provided by Epictetus
Epictetus
Epictetus was a Greek sage and Stoic philosopher. He was born a slave at Hierapolis, Phrygia , and lived in Rome until banishment when he went to Nicopolis in northwestern Greece where he lived the rest of his life. His teachings were noted down and published by his pupil Arrian in his Discourses...
:
The argument called the Master Argument appears to have been proposed from such principles as these: there is in fact a common contradiction between one another in these three propositions, each two being in contradiction to the third. The propositions are: (1) every past truth must be necessary; (2) that an impossibility does not follow a possibility; (3) something is possible which neither is nor will be true. Diodorus observing this contradiction employed the probative force of the first two for the demonstration of this proposition: That nothing is possible which is not true and never will be.
Epictetus' description of the Master Argument is not in the form as it would have been presented by Diodorus, which makes it difficult to know the precise nature of his argument. To modern logicians, it is not obvious why these three premisses are inconsistent, or why the first two should lead to the rejection of the third. Modern interpretations therefore assume that there must have been extra premisses in the argument tacitly assumed by Diodorus and his contemporaries.
One possible reconstruction is as follows: For Diodorus, if a future event is not going to happen, then it was true in the past that it would not happen. Since every past truth is necessary (proposition 1), it was necessary that in the past it would not happen. Since the impossible cannot follow from the possible (proposition 2), it must have always been impossible for the event to occur. Therefore if something will not be true, it will never be possible for it to be true, and thus proposition 3 is shown to be false.
Epictetus goes on to point out that Panthoides
Panthoides
Panthoides was a dialectician and philosopher of the Megarian school. He concerned himself with "the logical part of philosophy," and at some point taught the Peripatetic philosopher Lyco of Troas...
, Cleanthes
Cleanthes
Cleanthes , of Assos, was a Greek Stoic philosopher and the successor to Zeno as the second head of the Stoic school in Athens. Originally a boxer, he came to Athens where he took up philosophy, listening to Zeno's lectures. He supported himself by working as water-carrier at night. After the...
, and Antipater of Tarsus
Antipater of Tarsus
Antipater of Tarsus was a Stoic philosopher. He was the pupil and successor of Diogenes of Babylon as leader of the Stoic school, and was the teacher of Panaetius...
made use of the second and third proposition to demonstrate that the first proposition was false. Chrysippus
Chrysippus
Chrysippus of Soli was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of Cleanthes in the Stoic school. When Cleanthes died, around 230 BC, Chrysippus became the third head of the school...
, on the other hand, agreed with Diodorus that everything true as an event in the past is necessary, but attacked Diodorus' view that the possible must be either what is true or what will be true. He thus made use of the first and third proposition to demonstrate that the second proposition was false.
Further reading
- David Sedley. Diodorus Cronus and Hellenistic Philosophy. Proceedings of the Cambridge Philological Society 203, N.S. 23 (1977), P. 74-120.
- Jules Vuillemin: Nécessité ou contingence. L'aporie de Diodore et les systèmes philosophiques. Paris 1984. (Englische Übersetzung: Necessity or contingency. The Master Argument. Stanford 1996. ISBN 1-881526-86-0, Taschenbuchausgabe ISBN 1-881526-85-2)
- Jarmuzek J. Reconstructions of Diodor Cronos' reasoning in point ontology of time. Analiza i Egzystencja. Czasopismo Filozoficzne (Analysis and Existence. Philosophical Journal) year: 2006, vol: , number: 3, pages: 197-215
External links
- Selected Bibliography on the "Master Argument", Diodorus Cronus, Philo the Dialectician with a bibliography on the problem of future contingents