In this paper I shall address two main questions, namely: (1) Is Frege’s criticism against psychologism still relevant to the present debate on naturalism vs. anti-naturalism? And (2) Does Frege’s suggested alternative to reductive naturalism amount to a variety of supernaturalism? After having provided an answer to the above mentioned questions (a positive and a negative one respectively), I shall consider three possible non-Platonist proposals as regards the metaphysics of what Frege called the “unactual-objective realm”: (i) irrealism, (ii) objectivity without objects and (iii) objectuality without substantiality. I shall claim that, even though they all succeed in avoiding both Platonism and supernaturalism, it is the third that best fits Frege’s insight concerning the root of the reductive naturalist’s mistake.
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