The difference in answering the question whether “a glass is half full or half empty” is only significant if the speaker of this statement is included. For the statement itself there is no difference, at least not in the mathematical or mathematical-logical sense. That is just the difference between a purely mathematical statement and a purely linguistic statement. And the logic mediates between the mathematical language and the linguistic language. You must use your words (your lexemes) correctly if your statement has to be logically correct; you must use your numbers correctly if your statement has to be logically correct. Only then, if you include yourself or another person (a subject) in your statement, you have to leave mathematics to this very part and to the other part you have to take care that you say what you want to say linguistically correct (well-formed) and logically correct.