A phrase popularized by the late Harvard
philosophy professor,
W. V. Quine.
Beliefs that are "
held come what may" are beliefs one is unwilling to give up, regardless of any evidence with which one might be presented.
Quine held (on a perhaps simplistic construal) that there are no beliefs that one ought to hold come what may--in other words, all beliefs are
rationally revisable.
Many philosophers are to the contrary, believing that, for example, the
laws of thought[?] cannot be revised and may be held come what may.
See also Hold more stubbornly at least.