 Now we can apply the local epoché to specify the noema of both veridical perceptions and hallucinations so as to bring out their singularity. Already in his 1894 essay “Intentional Objects” (cf. Husserliana, vol. XXII; English translation of a somewhat different version of the essay in: Rollinger 1999) Husserl stressed that objectless representations such as hallucinations can in a sense be characterized as “representing an intentional object”, provided that this characterization is understood to be made “under an existential assumption”, as follows: “If the act of hallucination were veridical, it would successfully represent such-and-such an object (under such-and-such aspects)”. Something similar goes with regard to the singularity of a hallucinatory experience’s noema: if such an experience were veridical, it would, in virtue of its noema, represent a particular perceptual object in all relevant possible worlds (see Section 3 above). Thus, we can provide an existentially neutral specification of the noema of a (veridical, illusory or hallucinatory) perceptual experience, just as local epoché demands, and still bring out the singular character of their content that Husserl has done so much to uncover, especially in his investigations into indexicality and the role of the determinable X in our constitution of spatio-temporal reality. The specification might run as follows: The noema of a perceptual experience i is such that either (1) there is an object x that i represents in virtue of its noema, where x is to be regarded as the referent of i in all relevant possible worlds, or (2) there would be an object meeting condition (1) if i were veridical. Condition (2) enables us to make sense of the behaviour of a speaker/thinker making counterfactual assumptions about an object which he, unknowingly, merely hallucinates, or of quantifying into modal statements about that alleged object (cf. Beyer 2000, pp. 26–31). Notice that on the above-proposed externalist reading of Husserl’s notion of intentional content, the noema will differ depending on whether condition (1) or (2) is satisfied. Nevertheless, our noematic specification meets the requirements of local epoché, as it does not rely on the existence of a particular perceptual object. If there is no such object, condition (2) will be satisfied—provided that we are dealing with a perceptual experience. The rationale behind condition (2) is that even in the non-veridical case an individual notion (a mental file) and consequently a unified series of intentional horizons gets activated, on the basis of the same sensory material, or hýle (see the following paragraph), as in the veridical case.