1. “Beg the question”
If you see this phrase in print, it’s likely to mean “to bring up an obvious question,” as in “That begs the question of how we are going to balance the budget” or “to prompt a question in response to something,” as in, “The new evidence begs the question of whether the defendant was guilty after all.”
To beg the question, however, originally meant to make a statement that assumes that the proposition in question is true; an example is, “Most scholars discount Smith’s theories because they don’t agree with him.” This original definition, however, is being overwhelmed by the new senses described above. They are so ubiquitous that they are coming to be accepted as valid, but such acceptance dilutes the value of the pure meaning. It’s best not to use the phrase at all. Try “raises the question” when that’s what is meant.
2. “I could care less.”