Similar to this question, but slightly different. I am looking for a word or phrase to describe the act of adding in disclaimers or qualifications in sentences to not suggest a certain thing, especially if it is offensive. Take in mind that these phrases are often used in situations where one is scared of offending others, so it's likely there are ways of describing it with negative connotations.
Here are some examples:
"I admire Hitler's military tactics, not that I think he wasn't a bad person."
Notice for this one that the second half of the sentence doesn't change the implication of the first half, but not adding something to that effect at the end might have people come to other conclusions about the writer.
"Although I think women can do just as good as men in mathematics, there are few great female mathematicians."
Once again the first half is not really needed, it is put in to not offend people.
"If p, then q. Not that it should be that way and not that q implies p."
Again, the second sentence is not really adding more information about the subject, its purpose is to protect the writer or to stop the reader from forming conclusions that have no basis.
This question is different from this one because, in that one the statement that follows the caveat usually contradicts the caveat.