An Irish bull, or, less prejudicially, a bull, is defined in OED as "A self-contradictory proposition; in mod[ern] use, an expression containing a manifest contradiction in terms or involving a ludicrous inconsistency unperceived by the speaker. Now often with epithet Irish; but the word had been long in use before it came to be associated with Irishmen." Its origin is uncertain.
Some examples of Irish bulls can be found in nineteenth and early twentieth century issues of Punch, which had a more stereotyped view of mankind than is permissible these days, as in a cartoon of an Irishman replying to a question about directions from a passing motorist: "Sure, sorr, if I was going to Dublin, I wouldn't be starting from here." This shows the truth of "An Irish bull is always pregnant", which has punning truth in it. (The pun is on bull, the male animal as against bull 'an incongruous remark', and pregnant, 'carrying a child' (only applicable to female animals) as opposed to 'full of meaning': it is itself an 'Irish bull', carrying a truth (that an irish bull has a meaning) in words that appear nonsensical, palpably false: that a male animal is always with child.)
- You may be interested in the more in-depth article on bull.