Is there a word that means nonsensical question?

Question

A friend of mine and I were joking about questions that are complete nonsense. Here are some examples:

True or false: How tall is the Empire State Building?

Is it further to Pittsburgh or by train?

How tall do you weigh?

I called them nonsensical questions. My friend said he thought there was a more descriptive word for them, but could not remember the word. Is there a word for questions that are complete nonsense? I am dubious of his claim.

Edit: I just suggested the word balderdash, but he said that is not the word he was trying to remember. He says he is thinking of a word that specifically implies a question is nonsense. It would not be used to describe other types of sentences, like statements.

Edit 2: Someone requested that I add the following question: "Which weighs more, a pound of bricks or a pound of feathers?" This question is a trick question, but not nonsensical. A similar question that is closer to being nonsensical would be

Which weighs more, a pound of gold or a pound of feathers?

Comparing the weight of gold to the weight of feathers is ambiguous. Both bricks and feathers are typically weighed using the standard scale. Gold, on the other hand, is typically weighed using the Troy scale. A troy pound weighs less than a standard avoirdupois pound. So, the question does not have as straightforward an answer due to the ambiguity of which scale is being used to weigh each.

Answer 1

Your original examples are called category mistakes:

A category mistake, or category error, or categorical mistake, or mistake of category, is a semantic or ontological error in which things belonging to a particular category are presented as if they belong to a different category, or, alternatively, a property is ascribed to a thing that could not possibly have that property. - wikipedia

The confusion arising from the two types of pounds is a form of 'overloading' or syntactic ambiguity that might be considered a very narrow case of polysemy, with the sentence itself being an example of zeugma.

Answer 2

I don't think this actually is the word your friend has in mind, but there is the Japanese borrowing, koan, which shares many qualities with your example nonsense questions, and is worth pointing out for that.

koan (noun)

A paradoxical anecdote or riddle, used in Zen Buddhism to demonstrate the inadequacy of logical reasoning and to provoke enlightenment.

Let's take a look at one of the classic Zen koans, the one about wild geese.

Don't think that the koan and its solution are themselves wisdom and truth.

The goal of the Zen koan is enlightenment, which is a profound change of heart.

Like the ponderer of a Zen koan, the viewer must come to terms with this paradox.

Zen masters often use nonsensical or unsolvable riddles, or koans, to bring about enlightenment.

Koan, often also called Zen riddles in English, are meant to shake the Zen acolyte out of their materialistic hang-ups and logical pretensions, and allow them to progress on their path, perhaps even provoking momentary satori - enlightenment. They are an antidote to overthinking and the egoistic excesses of morality and intellectualism. (There's more to it than that, of course: the Wikipedia article is quite comprehensive, if you're interested.)

Koan are deliberately self-contradictory, and, very often - though not always - phrased as questions.

Two famous examples of koan follow, both taken from the same Wikipedia article:

• Two hands clap and there is a sound, what is the sound of one hand?

• What is your original face before your mother and father were born?

Note that a koan has a specific purpose. And a koan may be a nonsense question. However, if it bears pointing out, not all nonsense questions are koan, as they lack that revelatory objective.

Hence, "Is it further to Pittsburgh or by train?" is definitely not a koan. You say you'd quite like it if your friend was right, so perhaps you can have your cake and eat it as he is kinda right... but also wrong.

Also, even if koan is the word your friend has in mind, it should be noted that the Western conception of koan is more than slightly out of kilter with that of its originators:

The popular western understanding sees kōan as referring to an unanswerable question or a meaningless statement. However, in Zen practice, a kōan is not meaningless, and not a riddle or a puzzle. Teachers do expect students to present an appropriate response when asked about a kōan.¹

Again, for you friend, if they were looking for the word koan, even in victory there is defeat. (Of course, someone may well come up with a better word - I, for one, would gladly upvote it!)