Hold come what may
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.