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Definition of incuriousness : Unconcernedness; incuriosity.

Synonyms:

lassitude, uninterest, feelings, lethargy, listlessness, insensibility, unresponsiveness, insensibleness, stolidness, phlegm, stolidity, impassivity

disinterest, carelessness, lack of interest, heedlessness, insouciance, incuriosity, detachment, indifference, dispassionateness, apathy, unconcern

Usage examples:

• But even at the height of their intimacy, the friendship seems to have remained more intellectual than personal, a fact due no doubt to Keats's reserve and Hunt's " incuriousness." - "Leigh Hunt's Relations with Byron, Shelley and Keats", Barnette Miller.
• It seemed rather to be a resolved incuriousness about things around her, a turning away of the face from life, as from something dreadful, that had only pain to offer her. - "Masterman and Son", W. J. Dawson.