On W. V. Quine's conception of a person's set of beliefs as a "seamless web," there is no proposition one could not in principle give up (if there were, there would be a "seam" in the web, protecting the principle from revision or rejection) or hold come what may. However, some beliefs may be more useful than others, or may be implied by a large number of beliefs. Examples might be laws of logic, or the belief in an external world of physical objects. Altering such portions of the web would have immense, ramifying consequences. It is better to alter auxilliary beliefs around the edges of the web in the face of new evidence unfriendly to one's central principles. Thus, while one might agree that there is no belief one can hold come what may, there are some for which there is ample practical ground to hold more stubbornly at least.
Hold more stubbornly at least
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