Dictionary:

nonsensical

  (nŏn-sĕn'sĭ-kəl)

1. Lacking intelligible meaning: a nonsensical jumble of words.
2. Foolish; absurd: nonsensical ideas.

adjective

So senseless as to be laughable: absurd, foolish, harebrained, idiotic, imbecilic, insane, lunatic, mad, moronic, preposterous, silly, softheaded, tomfool, unearthly, zany. Informal cockeyed, crazy, loony, loopy. Slang balmy², dippy, dopey, jerky, sappy, wacky. See ability/inability, knowledge/ignorance.

Definition: foolish
Antonyms: sane, sensible

adj

Definition: meaningless
Antonyms: logical, rational

The adjective has 2 meanings:

Meaning #1: completely devoid of wisdom or good sense
  Synonyms: absurd, derisory, laughable, ludicrous, preposterous, ridiculous

Meaning #2: having no intelligible meaning
  Synonym: nonsense