It is possible.

Robert Anton Wilson in one or two of his books gives an exercise similar to this - consciously choosing to remove all absolutes from your conversations. Something like never saying "I am tired" but rather "I feel tired" and not saying "That is bad" but rather "That activity has badness in it" or something like that! Edits - it's called E-Prime and mentioned in another comment in this thread.

The point is that it would be possible to do it, but it would be very difficult and initially very strange.