Eubulides of

Miletus Miletus (; gr, Μῑ́λητος, Mī́lētos; Hittite transcription ''Millawanda'' or ''Milawata'' (exonyms); la, Mīlētus; tr, Milet) was an ancient Greek city on the western coast of Anatolia, near the mouth of the Maeander River in a ...

( grc, Εὐβουλίδης; fl. 4th century BCE) was a

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

philosopher A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...

of the

Megarian school The Megarian school of philosophy, which flourished in the 4th century BC, was founded by Euclides of Megara, one of the pupils of Socrates. Its ethical teachings were derived from Socrates, recognizing a single good, which was apparently combined ...

, a pupil of

Euclid of Megara Euclid of Megara (; grc-gre, Εὐκλείδης ; c. 435 – c. 365 BC) was a Greek Socratic philosopher who founded the Megarian school of philosophy. He was a pupil of Socrates in the late 5th century BC, and was present at his death. He he ...

and a contemporary of

Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...

. He is famous for his

logical paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

es.

Life

Eubulides was a pupil of

,Diogenes Laërtius, ii. 108 the founder of the

. He was a contemporary of

, against whom he wrote with great bitterness. He taught logic to

Demosthenes Demosthenes (; el, Δημοσθένης, translit=Dēmosthénēs; ; 384 – 12 October 322 BC) was a Greek statesman and orator in ancient Athens. His orations constitute a significant expression of contemporary Athenian intellectual prow ...

, and he is also said to have taught

Apollonius Cronus Apollonius Cronus ( el, Ἀπολλώνιος Κρόνος; fl. 4th century BCE) 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 Diodoru ...

, the teacher of

Diodorus Cronus Diodorus Cronus ( el, Διόδωρος Κρόνος; died c. 284 BC) was a Greek philosopher and dialectician connected to the Megarian school. He was most notable for logic innovations, including his master argument formulated in response to A ...

, and the historian

Euphantus Euphantus ( el, Εὔφαντος; floruit, fl. c. 320 BCE) of Olynthus was a philosopher of the Megarian school as well as an historian and tragic poet. He was the disciple of Eubulides, Eubulides of Miletus, and the instructor of Antigonus II Gona ...

. He may have been the author of a book about

Diogenes of Sinope Diogenes ( ; grc, Διογένης, Diogénēs ), also known as Diogenes the Cynic (, ) or Diogenes of Sinope, was a Greek philosopher and one of the founders of Cynicism (philosophy). He was born in Sinope, an Ionian colony on the Black Sea ...

Paradoxes of Eubulides

Eubulides is most famous for inventing the forms of seven famous

paradoxes A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

, some of which, however, are also ascribed to

: # 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 (''enkekalymmenos'') 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 In Greek mythology, Orestes or Orestis (; grc-gre, Ὀρέστης ) was the son of Clytemnestra and Agamemnon, and the brother of Electra. He is the subject of several Ancient Greek plays and of various myths connected with his madness and ...

. 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 (compare the

masked-man fallacy In philosophical logic, the masked-man fallacy (also known as the intensional fallacy or epistemic fallacy) is committed when one makes an illicit use of Leibniz's law in an argument. Leibniz's law states that if A and B are the same object, the ...

). 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 A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. ...

. These paradoxes were very well known in ancient times, some are alluded to by Eubulides' contemporary

and even partially by

Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...

Aulus Gellius Aulus Gellius (c. 125after 180 AD) was a Roman author and grammarian, who was probably born and certainly brought up in Rome. He was educated in Athens, after which he returned to Rome. He is famous for his ''Attic Nights'', a commonplace book, or ...

mentions how the discussion of such paradoxes was considered (for him) after-dinner entertainment at the

Saturnalia Saturnalia is an ancient Roman festival and holiday in honour of the god Saturn, held on 17 December of the Julian calendar and later expanded with festivities through to 23 December. The holiday was celebrated with a sacrifice at the Temple ...

, but

Seneca Seneca may refer to: People and language * Seneca (name), a list of people with either the given name or surname * Seneca people, one of the six Iroquois tribes of North America ** Seneca language, the language of the Seneca people Places Extrat ...

, on the other hand, considered them a waste of time: "Not to know them does no harm, and mastering them does no good."Seneca, ''Epistles'', 45. 8

Notes

References

Rescher Nicholas Rescher (; ; born 15 July 1928) is a German-American philosopher, polymath, and author, who has been a professor of philosophy at the University of Pittsburgh since 1961. He is chairman of the Center for Philosophy of Science and was fo ...

, 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. {{Authority control 4th-century BC Greek people 4th-century BC philosophers Ancient Greek philosophers of language Ancient Milesians Megarian philosophers Year of birth unknown Year of death unknown