"Nothing... compels us either to treat 'representations' as being inner mental entities, or to regard 'things-in-themselves' as external objects hidden from direct perception, beyond the sensory 'representations' formed within our cerebral mechanisms. Yet this is the sense in which Kant's position was widely understood... by physiologists and psychologists like Müller, Helmholtz and Fechner, and... philosophers like Schopenhuaer. ...The term Vorstellung came to refer simply to the 'ideas' brought into existence as an effect of repeated sensory 'impressions' (Empfindungen); the critical philosophy lost the transcendental character... and... Mach... confuse[d] the theories of Kant's Critiques with those of Berkeley and Hume, which Kant himself had been trying to supercede. ...[W]e can equally well state Kant's epistemic point... using... Darstellung—as used by Hertz, Bühler, and Boltzmann, and Kant himself... a 'representation', in the sense in which a theatrical representation... exhibition or recital provides a public... representation of works of art or music. To darstellen a phenomenon is then to 'demonstrate' or 'display' it... in an entirely public manner what it comprises, or how it operates: as when an hydraulic system... is used to provide a simplified... explanatory model, of a complex electrical circuit. (By contrast... Vorstellung suggests a 'representation' as private or personal... 'in the mind' of an individual. ...[It] carries the same burden as words like 'idea' and 'imagination': it is, in fact, the standard German translation for the Lockean term 'idea'...) ...When Hertz spoke of a dynamical theory as providing a Darstellung of the motions that it explains, and when Wittgenstein declared... propositions of a language darstellen the facts of the world, their assertions had nothing specifically 'mental' or 'inner' about them. ...[C]ollective intellectual functions of concepts and representation techniques in the explanatory activities of science... in terms of Darstellungen can sidetrack... Cartesian and Humean puzzles about the relationship between the 'inner' concepts and 'external' phenomena. At the same time it concedes to Frege all that his anti-psychologism legitimately claimed... that 'explaining' a phenomenon requires us not just to imagine inwardly... but to demonstrate publicly the nature of the relationships..."