I am not an native English speaker and I would like to know if the use of the word "vacuous" is offensive.

I am writing a reply to a request where I am asked to do something that has no sense at all in a mathematical context. Basically, I was requested to do some calculations on a mathematical object that is provably nonexistent. In my reply I want to be direct and say that trying to do so is useless. Then, I was planning to say that this is vacuous. I also want to be as polite as possible, then my hesitation on using this word. Any pointers to a more suitable word would also be appreciated.

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    If you are not sure of a word, do not use it. last time I heard this word it was used to describe a "dumb blond" type of person. Look at the synonyms: vacuous: having or showing a lack of thought or intelligence; mindless. "a vacuous smile" synonyms: silly, inane, unintelligent, insipid, foolish, stupid, fatuous, idiotic, brainless, witless, vapid, vacant, empty-headed – mplungjan Dec 9 '13 at 12:27
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    @EdwinAshworth Sorry but I do not get your point. – Baco Dec 9 '13 at 12:32
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    Maybe wait longer than 1 hour before concluding no one is willing to answer the question. – GEdgar Dec 9 '13 at 14:11
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    And I was just about to answer before seeing that comment... ah well. – GregRos Dec 9 '13 at 14:14
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    'vacuous', like 'trivial' or 'false' or 'wrong', has a mathematical meaning. It's not the overt meaning that is problematic. None of these is offensive either explicitly or by connotation. But they do imply things, and those implications might be upsetting to others, maybe even offensive. "Gas attacks killed thousands". None of those words is offensive, but the implications are. Which is to say the word 'vacuous' is not at all offensive but telling someone might turn out to be offensive. – Mitch Dec 9 '13 at 14:23

Vacuous definitely carries negative and/or offensive connotations in English, varying with the tone of voice employed when uttering the word. At best you'd sound flippant, at worst you'd sound extremely rude!

You'd probably be better served by sticking to simpler language - "performing these calculations is unnecessary because..." or something similar. At least that way you're avoiding the possible inference that the person who made the suggestion is in some way mindless or stupid.

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    Vacuous does have a specific meaning in a mathematical context, though -- using it that way, when talking to mathematicians, would not cause offense. – starwed Dec 9 '13 at 16:43
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    @starwed Not all mathematical contexts are the same! I don't think the OP is doing this kind of proof. This sense of a vacuous is used when working with empty sets, while he is trying to prove that some calculation needn't be done at all. – Hannele Dec 9 '13 at 16:49

As noted by @starwed, there is a very specific definition of vacuous in the context of mathematical sets:

A vacuous truth is a statement that asserts that all members of the empty set have a certain property.

However, if that is not your particular context, vacuous is more generally used to describe a subject in a derogatory fashion, to denote empty-headed-ness and a lack of deep thought.

Useless is a perfectly reasonable word to use, but if you're looking for a different term, you could use irrelevant:

Not related, not applicable, unimportant, not connected.

For example,

This calculation is irrelevant because the object will never exist.

Regardless, however, you're telling someone that they're wrong about something, which always has a little risk of coming off as offensive. Be careful with your tone of voice and body language!


Yes, except for certain arcane purposes, vacuous carries an offensive connotation.

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