In current linguistics, non-objective (i.e. perspectival or construed) facets of linguistic meaning are often explained as properties or correlates of cognitive phenomena. Such outlook, exemplified by Langacker's (1987, 2008) Cognitive Grammar, stands in contrast vis-à-vis the necessary social character of language in general and linguistic meaning in particular. Accordingly, a viable semantic theory should seek to explain non-objective facets of meaning as an intersubjectively valid semantic resource that is an integral part of linguistic meaning at large. In this paper, such theory is proposed based on the phenomenological notions of intentionality and intersubjectivity. I will argue that the non-objectivity of linguistic meaning is most realistically explained as conventionalized intentionality, i.e. object-directedness of conscious experience. The conventionalization of intentionality, in turn, suggests a complex manner in which non-objective meaning motivates the selection of a linguistic expression within an intersubjective context. Finally, this intimate relationship between non-objective meaning and context suggests the feasibility of extending Cognitive Grammar's notion of construal into analysis of non-objective meaning as an intersubjective, context-sensitive facet of interaction (see Etelämäki et al. 2009 for a similar argument).