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Brentano's (1874 : 88–89) suggestion that intentionality is the mark of the mental is typically spelled out in terms of the thesis that all and only mental states are intentional. An influential objection is that intentionality is not necessary for mentality (McGinn 1982 ; Dretske 1995 ; Deonna and Teroni 2012 ; Bordini 2017). What about the idea that only mental states are intentional? In his 2008 paper published in Analysis, Nes shows that on a popular characterization of intentionality, notably defended by Crane (2014 [1998] , 2001), some non-mental states come out as intentional. Crane (2008) replies that the concept of representation solves the problem. In this paper, I argue that no representational account of intentionality meets Nes's challenge. After distinguishing between two notions of representation, I contend that there are two versions of Crane's representational account, but neither of them is able to solve the problem posed by Nes. [ABSTRACT FROM AUTHOR]