Paradoxical "Paradox"

The formal way to say paradox in Mandarin is "矛盾"。　　It literally translates to "spear shield".

For instance, instead of saying "Serving breakfast for dinner is paradoxical, "Serving breakfast for dinner is spear shield."  (If you serve breakfast food at dinner, it's still dinner!)

Sometimes words in Chinese are too antiquated.

Here's one of the earliest uses of  矛盾：

《韓非子》

Han Feizi

Translated by YoYo

楚人有鬻矛與盾者

Of the State of Chu there one who sold spears and one who sold shields

譽之曰：「吾盾之堅，物莫能陷也。」

[One] boastfully said, "My shield is tough, nothing can penetrate it."

又譽其矛曰：「吾矛之利，於物無不陷也。」

Another boastfully said, "My spear is sharp, there is nothing it can't penetrate."

或 曰："以子之矛陷子之盾，何如？」

Someone said, "With his spear and his shield, what would happen?"

其人弗能應也。

They were unable to answer.

夫不可陷之盾與無不陷之矛,

An impenetrable shield and a spear that can pierce anything,

不可同世而立。

cannot be on earth at the same time.