Eubulides of Miletus

Miletus

Miletus was an ancient Greek city on the western coast of Anatolia , near the mouth of the Maeander River in ancient Caria...

 was a philosopher of the Megarian school, and a pupil of Euclid of Megara

Euclid of Megara

Euclid of Megara was a Greek Socratic philosopher who founded the Megarian school of philosophy. He was a pupil of Socrates in the late 5th century BCE, and was present at his death. He held the supreme good to be one, eternal and unchangeable, and denied the existence of anything contrary to the...

. He is famous for his paradox

Paradox

Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

es.

Life

Eubulides was a pupil of Euclid of Megara

Euclid of Megara

Euclid of Megara was a Greek Socratic philosopher who founded the Megarian school of philosophy. He was a pupil of Socrates in the late 5th century BCE, and was present at his death. He held the supreme good to be one, eternal and unchangeable, and denied the existence of anything contrary to the...

, the founder of the Megarian school. He was a contemporary of 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...

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

Demosthenes

Demosthenes was a prominent Greek statesman and orator of ancient Athens. His orations constitute a significant expression of contemporary Athenian intellectual prowess and provide an insight into the politics and culture of ancient Greece during the 4th century BC. Demosthenes learned rhetoric by...

, and he is also said to have taught 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, .....

, the teacher of Diodorus Cronus

Diodorus Cronus

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.-Life:...

, and the historian Euphantus

Euphantus

Euphantus of Olynthus was a philosopher of the Megarian school as well as an historian and tragic poet. He was the disciple of Eubulides of Miletus, and the instructor of Antigonus I Monophthalmus king of Macedonia. He wrote many tragedies, which were well received at the games...

. He may have been the author of a book about Diogenes of Sinope

Diogenes of Sinope

Diogenes the Cynic was a Greek philosopher and one of the founders of Cynic philosophy. Also known as Diogenes of Sinope , he was born in Sinope , an Ionian colony on the Black Sea , in 412 or 404 BCE and died at Corinth in 323 BCE.Diogenes of Sinope was a controversial figure...

.

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

Diodorus Cronus

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.-Life:...

:

1. The Liar (pseudomenos) paradox
   Liar paradox
   In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...
   
   :
   A man says: "What I am saying now is a lie
   Lie
   For other uses, see Lie A lie is a type of deception in the form of an untruthful statement, especially with the intention to deceive others....
   
   ." 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
   Electra
   In Greek mythology, Electra was an Argive princess and daughter of King Agamemnon and Queen Clytemnestra. She and her brother Orestes plotted revenge against their mother Clytemnestra and stepfather Aegisthus for the murder of their father Agamemnon...
   
    (Elektra) paradox:
   Electra doesn't know that the man approaching her is her brother, Orestes
   Orestes (mythology)
   In Greek mythology, Orestes was the son of Clytemnestra and Agamemnon. He is the subject of several Ancient Greek plays and of various myths connected with his madness and purification, which retain obscure threads of much older ones....
   
   . Electra knows her brother. Does Electra know the man who is approaching?
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 (sôritês) 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...
   
   :
   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 (keratinês) paradox:
   What you have not lost, you have. But you have not lost horns. Therefore you have horns.

The first paradox (the Liar

Liar paradox

In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...

) is probably the most famous, and is similar to the famous paradox of Epimenides the Cretan

Epimenides paradox

The Epimenides paradox is a problem in logic. It is named after the Cretan philosopher Epimenides of Knossos , There is no single statement of the problem; a typical variation is given in the book Gödel, Escher, Bach, by Douglas Hofstadter:...

. 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

Syllogistic fallacy

Syllogistic fallacies are logical fallacies that occur in syllogisms. They include:Any syllogism type :*fallacy of four termsOccurring in categorical syllogisms:*related to affirmative or negative premises:...

.

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

 and even partially by Plato

Plato

Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

. Aulus Gellius

Aulus Gellius

Aulus Gellius , was a Latin author and grammarian, who was probably born and certainly brought up in Rome. He was educated in Athens, after which he returned to Rome, where he held a judicial office...

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

Saturnalia

Saturnalia is an Ancient Roman festival/ celebration held in honour of Saturn , the youngest of the Titans, father of the major gods of the Greeks and Romans, and son of Uranus and Gaia...

, but Seneca

Seneca the Younger

Lucius Annaeus Seneca was a Roman Stoic philosopher, statesman, dramatist, and in one work humorist, of the Silver Age of Latin literature. He was tutor and later advisor to emperor Nero...

, 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.