I reconstruct Aristotle’s reasons for thinking that the intellect cannot have a bodily organ. I present Aristotle’s account of the aboutness or intentionality of cognitive states, both perceptual and intellectual. On my interpretation, Aristotle’s account is based around the notion of cognitive powers taking on forms in a special preservative way. Based on this account, Aristotle argues that no physical structure could enable a bodily part or combination of bodily parts to produce or determine the full range of forms that the human intellect can understand. For Aristotle, cognitive powers with bodily organs are always spatiotemporally limited, but the understanding is not. Aristotle claims that our understanding applies to all instances of the thing understood wherever and whenever they exist. On Aristotle’s own account the intellect in its nature is only “potential,” it does not actually possess any form. Thus nothing prevents it from possessing all forms.