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Someone reviewing an article of mine claims that this sentence begins with a dangling participle. Is that true? Is the meaning of the sentence ambiguous?

Before defining the derivative, it is useful to first define nullability.

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    cf these examples: not dangling: "before doing A, you should do B", and dangling: "before doing A, B should be done". – AmI Oct 8 '18 at 1:03
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No.

The sentence does not even begin with a participial phrase, but with a prepositional phrase.

Ask someone if they think that "Before dinner, it is useful to define nullability" is a dangling participle as well.

And even more to the point, tell them that a dangling participle is not a mistake. It is just a label for a figure of speech.

A dangling participle is a common and useful shorthand that exists (in English and a great many other languages) precisely because it is useful.

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    Maybe useful sometimes, but capable of leading to misunderstanding at other times: "Arising out of a collision between a car and a bus, the bus driver was charged with manslaughter" (adapted from The Complete Plain Words, Fraser, HMSO 1973). – JeremyC Oct 7 '18 at 21:30
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    But aren't other prepositional phrases regarded as including dangling participles? "Before blowing down the trees, I was already fed up with the storm", for example? – Araucaria Oct 7 '18 at 23:38
  • @Araucaria In Wikipedia dangling participle falls under "dangling modifier", I'm not sure if that's a general term for things that are left dangling en.wikipedia.org/wiki/Dangling_modifier It has an example of a sentence starting with a prepositional phrase under the heading "Non-participial modifier". Also at OLO: "It’s not only participial phrases that can dangle and come adrift from their subjects: they’re part of a wider issue that grammarians describe as ‘floating modifiers, ‘hanging modifiers’, ‘dangling modifiers’ or (again) ‘danglers’." Sorry can't fit link. – Zebrafish Oct 8 '18 at 0:45
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    @JimNewton You could explain to the reviewer that if the main clause is an It-extraposition (as this one is), then the subject of any participial in the modifying subordinate clause does not have to be co-referential. the simple reason for this is that the it in an extraposition has no meaning and no identity. So it is impossible for any participial clause to have a co-referential subject with it. If they doubt this then ask them what exactly the it in it is useful to refers to (the answer is nothing; it's non-refrential). Then explain to them that in such cases ... – Araucaria Oct 10 '18 at 13:51
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    @JimNewton ... such a participial clause would only be considered to be bad/dangling if its subject referred to a different entity from the subject of the extraposed clause. In this sentence both of these are unexpressed, but refer to the same people. The subject in each case is something like people. You could paraphrase the sentence like this "Before people define the derivative, it is useful [for those people to first define nullability]" . – Araucaria Oct 10 '18 at 14:09

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