Eubulides was a pupil of Euclid of Megara, the founder of the Megarian school. He was a contemporary of Aristotle, against whom he wrote with great bitterness. He taught logic to Demosthenes, and he is also said to have taught Apollonius Cronus, the teacher of Diodorus Cronus, and the historian Euphantus. He may have been the author of a book about Diogenes of Sinope.
Paradoxes of Eubulides
- The Liar (pseudomenos) paradox:
A man says: "What I am saying now is a lie." If the statement is true, then he is lying, even though the statement is true. If the statement is a lie, then he is not actually lying, even though the statement is a lie. Thus, if the speaker is lying, he tells the truth, and vice versa.
- The Masked Man (egkekalummenos) paradox:
"Do you know this masked man?" "No." "But he is your father. So - do you not know your own father?"
- The Electra (Elektra) paradox:
Electra doesn't know that the man approaching her is her brother, Orestes. Electra knows her brother. Does Electra know the man who is approaching?
- The Overlooked Man (dialanthanôn) paradox:
Alpha ignored the man approaching him and treated him as a stranger. The man was his father. Did Alpha ignore his own father and treat him as a stranger?
- The Heap (sôritês) paradox:
A single grain of sand is certainly not a heap. Nor is the addition of a single grain of sand enough to transform a non-heap into a heap: when we have a collection of grains of sand that is not a heap, then adding but one single grain will not create a heap. And yet we know that at some point we will have a heap.
- The Bald Man (phalakros) paradox:
A man with a full head of hair is obviously not bald. Now the removal of a single hair will not turn a non-bald man into a bald one. And yet it is obvious that a continuation of that process must eventually result in baldness.
- The Horns (keratinês) paradox:
What you have not lost, you have. But you have not lost horns. Therefore you have horns.
The first paradox (the Liar) is probably the most famous, and is similar to the famous paradox of Epimenides the Cretan. The second, third and fourth paradoxes are variants of a single paradox and relate to the problem of what it means to "know" something and the identity of objects involved in an affirmation. The fifth and sixth paradoxes are also a single paradox and is usually thought to relate to the vagueness of language. The final paradox attacks presumptions involved in a proposition, and is related to the syllogistic fallacy.
These paradoxes were very well known in ancient times, some are alluded to by Eubulides' contemporary Aristotle and even partially by Plato. Aulus Gellius mentions how the discussion of such paradoxes was considered (for him) after-dinner entertainment at the Saturnalia, but Seneca, on the other hand, considered them a waste of time: "Not to know them does no harm, and mastering them does no good."
A plausible interpretation of the motivation for proposing these paradoxes is that these paradoxes were, like those of Zeno of Elea, intended to argue to the truth of the Parmenidean views that reality consists of one unextended entity and that nothing coherent can be expressed by "what is not." How do the paradoxes bear on Parmenides' views? Understanding a lie as "saying what is not" the Liar shows that "what is not" is incoherent, according to Eubulides. The Masked Man, the Electra, and the Overlooked Man are three version of the same problem. They each require that if an entity is known under any description, it must be known under every true description. This means that to know anything about an entity a person would have to know everything about it. Only a completely simple object such as the One Being of Parmenides, would thus be knowable. An ordinary (alleged) material object would have an infinite number of true descriptions, e.g. its distance from any other object at any time. The Heap and the Bald Man are intended to show that concepts of physical objects and physical properties, respectively, are incoherent. If there were physical objects, the question whether a given object existed or not would be determinate. The Heap shows that that is not the case. For any material object there is a part which can always be removed apparently leaving the object in existence. But if this is continued,the object will cease to exist. But there is no point at which it ceases to exist. If material objects were a logically coherent notion, there would have to be a first point at which the object ceasaed to exist. Likewise ordinary material properties would, if logically coherent, have to be either present in an object or not. The Bald Man is an example of why that is not the case. Any property, such as redness, tallness, obesity, and so on, seems to run into analogous difficulty. Eubulides' conclusion is that, since reality must be logically coherent, physical objects and properties cannot be part of it. The Horns is an ancient use of what is now termed "failed presupposition." "Have you stopped beating your father" presupposes that you have been beating your father. "Have you lost your horns" presupposes that you had horns. Eubulides understands the intuitive oddity of uttering these sentences when the presupposition is false as due to the attempt to speak of what is not. Your previous beating of your father, and your previous horns, are things which are not. According to Parmenides, what is not cannot be coherently spoken of. One could ask why Eubulides did not come out and say, "These paradoxes show that one cannot speak of what is not and that reality cannot consist of physical objects and properties." An obvious difficulty in saying this is that the very sentence uses "not", speaks of what is not, and consists of multiple physical words. So an overt statement of what Eubulides and Parmenides believe would itself be self-contradictory. The paradoxes are designed to show what the truth is, since the truth cannot be said. Something similar applies to the arguments of Zeno of Elea, another Parmenidean. In that case, we have the opening of Plato's dialogue Parmenides as evidence that a Parmenidean argument was the intent of the paradoxes.
- Diogenes Laërtius, ii. 108
- Diogenes Laërtius, ii. 109; Athenaeus, vii. 354; Aristocles, in Eusebius Praeparatio Evangelica xv. 2
- Plutarch, Vit. X Orat.; Apuleius, Orat. de Mag.; Photius, Bibliotheca, 265
- Diogenes Laërtius, vi. 20. However, there may be confusion with an unknown "Eubulus" who is mentioned as an author of work about Diogenes at vi. 30
- Andrea Borghini. "Paradoxes of Eubulides". About.com (New York Times). Retrieved 2012-09-04.
- Diogenes Laërtius, ii. 111
- "This phenomenon at the heart of the [sorites] paradox is now recognised as the phenomenon of vagueness." Sorites Paradox entry by Dominic Hyde in the Stanford Encyclopedia of Philosophy
- Aristotle, Sophistici Elenchi, 24, 25, 22
- Plato, Euthydemus
- Aulus Gellius, xviii. 2. 9
- Seneca, Epistles, 45. 8
- Rescher, N. (2001) Paradoxes: Their Roots, Range, and Resolution. Open Court Publishing.
- Seuren, P. A. M. (2005) Eubulides as a 20th-century semanticist. Language Sciences, 27(1), 75-95.
- Wheeler, S. C. (1983) Megarian Paradoxes as Eleatic Arguments, American Philosophical Quarterly, 20 (3), 287-295.