I have seen a few Q&A's with this title but none really reflects my question. I am aware both are adverbs and so forth and how they syntactically can be used equivalently, but what about connotations? Are there places where "therefore" is preferred over thus and vice versa? Are there any fine differences in usage?
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Therefore is used in introducing a conclusion that follows from what has been said previously.
Thus means in this way. For example:
Extending that meaning, it can be used to introduce the intended consequences of an action:
And stretching that meaning further it can, like therefore, indicate the conclusion of an argument:
To me at least, in the cases where they have the same basic meaning, the effect of therefore and thus is slightly different: therefore emphasises that the conclusion is an inescapable logical consequence of what goes immediately before; thus puts more focus on the argument as a whole and the way it leads towards the conclusion.
From American Heritage Dictionary of the English Language, Fourth Edition
1 not same: you cannot say lay the pieces out therefore.
I am going to take a swing at this, because I just had a nice conversation with an Austrian about it. We came to the conclusion that the German ways of expressing them could be summarized like this:
folglich/in folge -> thus
deshalb -> therefore