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If I have a proven without a doubt that drinking cyanide means certain death, is it correct to write the following?

The result of the study implies that drinking cyanide leads to certain death.

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You could, sure. It's probably more accurate to say "The study demonstrates that drinking cyanide results in death." – Kit Z. Fox Apr 23 '13 at 18:54
Or proves. Using a word that is weaker than what you really mean is somewhat inaccurate, as Kit says. – Cerberus Apr 23 '13 at 19:13
Makes sense, thank you for the help. – Richard Nysater Apr 23 '13 at 19:27
@Cerberus I would be very careful with using "prove" in an academic context. – Zeta Two Apr 23 '13 at 19:28
I don't see why you couldn't use it as understatement, to drive home your point with a rhetorical twist. – Robusto Apr 23 '13 at 19:50

Imply is a word that has two confusingly different definitions:

im·ply (m-pl) tr.v. im·plied, im·ply·ing, im·plies 1. To involve by logical necessity; entail: (AHD)

imply [ɪmˈplaɪ] vb -plies, -plying, -plied (tr; may take a clause as object) 1. to express or indicate by a hint; suggest (Collins)

Note that these are the first senses listed by these two dictionaries.

In maths, we always took the 'implication sign' to mean 'necessarily leads to the conclusion that' (ie AHD's primary sense), but in conversational English, we usually meant / mean (UK) hint / suggest when we used / use imply.

You need to define your terms if you are to avoid confusion - will your audience be guaranteed to know which usage you intend?

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