If you say something weird or apparently unsupported, the savvy reader at that very moment is going to be thinking so. So it's helpful to orient them like:
> Here's a wild sentence. Here's why it's not actually that wild: reasons
Without the connecting phrase, the reader has to figure out from context that out of all the possible things the following text could be doing, what it's actually doing is explaining the previous claim.
You can rightly counterpoint that it's not strictly necessary, that a savvy reader can figure it out. But I think the moment right after a wild statement is a hotspot for readers getting ready to jettison, and having a little assurance is likely very helpful.
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Both phrases are used like this— let me explain:
Logic classes teach that "but" is just "and" in fancy clothing, and actual usage is quite different. A lot of language is signpost phrasing that "helps the medicine go down" by giving hints at how the following idea will connect to this one.
Something I'd wonder about is if usage of it has changed based on the medium people use over the years, whether that's in-person, telephone, writing letters, or computer/smartphone writing. Has using computers for short form conversations allowed conversational phrases to bleed into formal writing.
"To be honest" typically means "Here is an opinion that I'm embarrassed to share, and would rather lie about"
They're not lying about everything else, they're lying about that one thing, every other time.
e.g. "I tell people my favorite movie is 'The Godfather', but, to be honest, it's actually Ratatouille"
Supernatural highlights this on S1E08, at 27:28. Dean was talking with someone and starts saying "the truth is" but the other person instantly cuts him off saying "you know who starts their sentences with 'the truth is'? Liars".
I do if I'm looking to pad the essay or video to make it longer.