Generalized statements, mostly political
Is there a term used for statements made by politicians (and others) that are nebulous and allow people to infer what they want from them?
For example, politicians speak about "Christian values", "family values", and "American values", but often seem to purposefully ignore giving examples which would precisify which values they are talking about. Or they speak about "making America great", without explaining what this greatness would consist in.
This vagueness seems like a rhetorical trick which allows listeners to project their own fantasies into the words of the speaker.
Is there a name for this kind of rhetorical device? Is there a term for these kinds of statements?
Glancing through Wikipedia's glossary of rhetorical terms does not seem to provide an answer.
This article in The Independent newspaper discusses how politicians use weasel words like :
[...] 'robust', 'remnants' and 'anecdotal' [... etc ...] to hide or mislead [...] and obscure terrible truths.
Here is an snippet but I recommend reading whole article:
"Remnants" in certain contexts has had a bad smell ever since US spokesmen started employing it after the invasion of Iraq in 2003: in phrases such as "remnants of Saddam Hussein's regime" or "remnants of al-Qa'ida". It was useful in trying to explain away how enemies that the US army claimed to have eliminated were still very much in business, blowing up American troops and generally creating mayhem.
And finally regarding the definition:
A weasel word (also, anonymous authority) is an informal term for words and phrases aimed at creating an impression that a specific and/or meaningful statement has been made, when only a vague or ambiguous claim has been communicated, enabling the specific meaning to be denied if the statement is challenged — Wikipedia
I would call such uses of language simply rhetoric, which has developed a pejorative sense:
"language designed to have a persuasive or impressive effect on its audience, but often regarded as lacking in sincerity or meaningful content" (here; my emphasis).
You could also use empty rhetoric for emphasis, as suggested by @AmI below.
verbiage
the use of language that is wordy or needlessly complicated, and often meaningless. [emphasis added]
Platitude
1: the quality or state of being dull or insipid
His speech was filled with familiar platitudes about the value of hard work and dedication.
"Platitude." Merriam-Webster.com. Merriam-Webster, n.d. Web. 7 June 2016.
Bromide
a statement that is intended to make people feel happier or calmer but that is not original or effective
His speech had nothing more to offer than the usual bromides about how everyone needs to work together.
"Bromide." Merriam-Webster.com. Merriam-Webster, n.d. Web. 7 June 2016.