The distinction between axiom and assumption is quite clear, so I'll assume you are referring to premise. The distinction already exists, which is the beauty o

The distinction between axiom and assumption is quite clear, so I'll assume you are referring to premise. The distinction already exists, which is the beauty of words. I am not making this distinction up. I am merely enforcing them as we do as speakers by the words we choose, based on the accuracy of our expressions. From Popper: > A theoretical system may be said to be axiomatized if ... (d) necessary, for the same purpose; which means that they should contain no superfluous assumptions [0]. So either Popper is wrong, or theories should not include unnecessary assumptions. But how do we know if an assumption is necessary without doing the science? And after we do it, are we still going to call necessary assumptions assumptions, even with its subjective implications? Only a person is capable of assuming. A theory with assumptions is still subjective. A premise on the other hand is objective and specific. It's "a proposition supporting or helping to support a conclusion" [1]. It's a simple device in logic that asserts a dependency. Or in other words, a "necessary assumption". So then would it not be safer to say axiomatized theories have premises, not assumptions? And in Popper's words, yet to be axiomatized theories have assumptions. That is what makes them hypotheses. And so all the words and their distinctions fall cleanly into place (I did not make anything up). The original article in Nature was written on the premise that science is based on assumptions and that scientists doing the science rely on assumptions. This is not the premise of science, and is incorrect. Refining our word selection to reflect this understanding would be of great service, particularly to the students. -- [0] https://books.google.com/books?id=cAKCAgAAQBAJ&pg=PA51&lpg=PA51&dq=%22no+superfluous+assumptions%22+popper&source=bl&ots=2SpoXnlniS&sig=hocFKDmxKzHeOFlKUoQ0mhOr1lE&hl=en&sa=X&ved=0CC0Q6AEwA2oVChMImc3VrtHSxwIVFCuICh3eywzT#v=onepage&q=%22no%20superfluous%20assumptions%22%20popper&f=false https://books.google.com/books?id=cAKCAgAAQBAJ&pg=PA51&lpg=P... [1] Just from the dictionary, as to avoid my own words. http://dictionary.reference.com/browse/premise http://dictionary.reference.com/browse/premise