Re: Is there a difference? (just alive / just living)
If you call it "I am just living", I would find it ambiguous. You could mean that you are really enjoying life, but you could also mean that you are merely, or only, living. You are doing no more than that. You are just living day to day. Usually, that situation would be worded "I am merely existing". As you said, "I am truly living" would be much better, as would "I am really living!" Why does it have to be one of the phrases you offered?
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