People - Ancient Greece: Eubulides of Miletus Ancient Greek philosopher of the Megarian school who
flourished during 4th century BCE.
Eubulĭdes in Harpers Dictionary of Classical Antiquities
（Εὐβουλίδης). A native of Miletus and successor of Euclid in the Megaric school. He was a strong opponent of Aristotle, and seized every opportunity of censuring his writings and calumniating his character. He introduced new subtleties into the art of disputation, several of which, though often mentioned as proof of great ingenuity, deserve only to be remembered as examples of egregious trifling. Of these sophistical modes of reasoning, called by Aristotle “Eristic syllogisms,” a few examples may suffice.
Eubulides in Wikipedia
Eubulides (Greek: Εὑβουλίδης; fl. 4th century BCE) of Miletus was a philosopher of the Megarian school, and a pupil of Euclid of Megara. He is famous for his paradoxes.
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
Eubulides is most famous for inventing the forms of seven famous paradoxes, some of which, however, are also ascribed to Diodorus Cronus:
1. 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.
2. 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?"
3. The Electra (Elektra) paradox:
Electra doesn't know that the man approaching her is her brother, Orestes. Electra knows her brother. Does Electra know that the man is her brother?
4. 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?
5. The Heap (sôritęs) 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.
6. 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.
7. The Horns (keratinęs) 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 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 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." What value Eubulides and the other Megarian philosophers placed on these paradoxes is unclear, but the Megarians were very interested in the logic of whole propositions, in contrast to Aristotle's logic of predicates.