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"In 1971, John Rawls coined the term "reflective equilibrium" to denote "a state of balance or coherence among a set of beliefs arrived at by a process of deliberative mutual adjustment among general principles and particular judgments". In practical terms, reflective equilibrium is about how we identify and resolve logical inconsistencies in our prevailing moral compass. Examples such as the rejection of slavery and of innumerable "isms" (sexism, ageism, etc.) are quite clear: the arguments that worked best were those highlighting the hypocrisy of maintaining acceptance of existing attitudes in the face of already-established contrasting attitudes in matters that were indisputably analogous."
-Aubrey de Grey, The Overdue Demise Of Monogamy
This passage argues that reasoning does impact ethical behavior. Steven Pinker and Peter Singer make similar arguments, which I find convincing.
I find it quite arguable whether or not "reflective equilibrium" is a real thing that actually happens in our cognition, or a little game played by philosophy academics. Actual cognitive dissonance caused by holding mutually contradicting ideas in simultaneous salience is well-evidenced, but that's not exactly an equilibrium across all ideas we hold, merely across the ones we're holding in short-term verbal memory at the time.