nonsensical

• nonsensic (very rare)
• non-sensical

From nonsense +‎ -ical.

nonsensical (comparative more nonsensical, superlative most nonsensical)

1. Without sense; absurd.

   Synonyms: meaningless, unmeaning, absurd, foolish, irrational, preposterous

   Antonyms: comprehensible, commonsensical, logical, rational, sensible, sensical

   • 1837, L[etitia] E[lizabeth] L[andon], “Prudence in Politics”, in Ethel Churchill: Or, The Two Brides. , volume II, London: Henry Colburn, , →OCLC, page 179:

     Well, her very foolish grandmother has mixed herself up in some nonsensical correspondence with the court of St. Germains; or, rather, has let herself be made a tool by Mr. Trevanion, who, I am happy to say, is not Ethel's husband; they arrested him just in time.

• The form non-sensical is much less common while nonsensic is extremely rare.^[1]
• Webster 1828 defined this as "Unmeaning; absurd; foolish." Webster 1913 defined this as "Without sense; unmeaning; absurd; foolish; irrational; preposterous."

• nonsense
• nonsensible
• senseless

• “nonsensical”, in OneLook Dictionary Search.
• “nonsensical”, in The American Heritage Dictionary of the English Language, 5th edition, Boston, Mass.: Houghton Mifflin Harcourt, 2016, →ISBN.
• “nonsensical”, in Collins English Dictionary.
• “nonsensical” (US) / “nonsensical” (UK) in Macmillan English Dictionary.
• "nonsensical" in WordNet 3.1, Princeton University, 2011.