3
  • Continue donc de te concentrer sur ~~~ !

In an imperative sentence, donc means "DO continue" as an emphasis, right? Instead of "so, therefore"?

If that is the case, how can you mean "so" in an imperative like this one? Should you use alors?

  • Alors continue donc de te concentrer sur ~~~ !

In another case, in a "let's do ~~~" sentence, does donc mean "so"? Or "LET'S do ~~~" as an emphasis?

  • Faisons donc un petit tour ~~~
4

That's what the TLF says about donc in imperative sentences:

II.− Particule servant à noter une réaction affective ou expressive devant une situation donnée, exprimée ou suggérée par le contexte (valeurs stylistiques en situation) [...]
4. [impérative] Entrez donc, asseyez-vous donc, faites donc! Il dit d'une voix engageante : « Viens donc dîner un de ces soirs à la maison » (Beauvoir, Mandarins,1954, p. 294).

The role of donc in an imperative sentence is to add feeling to your words. I read Simone de Beauvoir's sentence as expressing polite invites that could be rephrased as: Donnez vous la peine de rentrer1, Et si tu venais dîner2.
It is the same meaning in your sentence: Faisons donc un petit tour.3

In your other sentence:

(Alors) Continue donc de te concentrer sur ~~~ !

it is a firm exhortation to act in a certain way. We could rephrase the sentence like this: Veux-tu bien te concentrer... I don't understand what you mean when you say "how can you mean "so" in an imperative like this one?" I don't see what meaning of so it could have here... I would express the sentence in English as "Well then, will you please concentrate further on ~~~!"

I can't say donc will never express consequence in an imperative sentence, because one might find an instance where it does, but it doesn't to me in any of the sentences you gave.

1Do come in.
2What about coming to dinner...
3Let's go for a walk!/ What about going for a walk!

  • I'm thinking "in that case" may be a good translation for such sentences. – Igor Skochinsky Jul 15 '17 at 16:32

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