Little is known about Eubúlid's life. He was probably a pupil of Euclid of Megara and a member of the Megarian school of philosophy. He himself later had several pupils, including Euphant of Olynthus, Alexinus of Elymais and Apollonius of Cronus. Among his students was the famous orator Demosthenes.

Eubúlidês of Miletus wrote a treatise against Aristotle which dealt with fundamental logical questions.

But he is best known as the author of the seven famous logical paradoxes.

1) Liar - When I lie and say I am lying, am I lying or telling the truth?

2) The Hidden Identity Paradox - I'm asking someone: "Do you know your father?" He answers "yes." I ask further: "Now if I show you someone who is hidden behind a curtain, do you know him?" "No." - "But the man hidden behind the curtain is your father. Then you do not know your father.

3) Paradox of Identity - Eleuthera - Of the familiar Eleuthera, daughter of Agamemnon, who knows and does not know the same thing; for when Orestes, whom she does not yet know, stands beside her, she knows indeed that Orestes is her brother, but she does not know that the man beside her is Orestes.

4) The veiled paradox of identity - Do you know the one who approaches and is veiled? - No. - (Then they reveal the veil.) So what? Do you know this person? - I do. So you know the same person and you don't know the same person.

5) Paradox of Quantity - Pile - Do you think that a single grain of sand is a pile? It's not. What do you say about two grains? If you don't admit that two grains are a pile, I will continue to ask questions about grains of three, four, five, six, seven, eight, etc. If you do not say with respect to any number, as, for instance, of a hundred grains of wheat, that they form a heap, but after one grain has been added to it, you will say that now a heap has been formed, subsequently this quantity becomes a heap by the addition of one grain of wheat, and if one grain be taken away, the heap will cease. I know of nothing worse and more absurd than that the being and non-being of a heap is determined by one grain of wheat.

6) The paradox of quantity - Baldness - If we take away one hair, does that create baldness? No. And if we take another hair off? Also no. We continue on, and when we finally recognize that by taking away a particular hair, baldness has already occurred, then we actually recognize that the hair we took away last time caused baldness.

7) Horny - If you haven't lost something, you've got it. You haven't lost your horns, so you have horns.