Naive consequentialism is the view that, to comply with the requirements of consequentialism, an agent should at all times be motivated to perform the act that consequentialism requires. By contrast, sophisticated consequentialism holds that a consequentialist agent should adopt whichever set of motivations will cause her to in fact act in ways required by consequentialism.
Sometimes the terms "sophisticated consequentialism" and "naive consequentialism" are used to describe the contrast between applications of consequentialism that do and do not, respectively, consider less direct, less immediate, or otherwise less visible consequences into account.[1]
As for a concrete example, a naive conception of consequentialism may lead one to believe that it is right to break rules if it seems that the immediate effects on the world would be net-positive. Such rule-breaking normally has negative side-effects, however - e.g. it can lower the degree of trust in society, and for the rule-breaker’s group in particular - which means that sophisticated consequentialism tends to be more opposed to rule-breaking than naive consequentialism.
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