Given the notion of empty concept, the IL conception of concepts is both flexible and powerful enough to assign meanings to lexical words of any kind. A conception is a mental state, and a perception a mental event, located in the brain of an individual. By identifying concepts not with such mental entities but with (extra-mental) properties of mental entities, Integrational Lexical Semantics can account for the potential intersubjectivity of concepts, a problem that any psychological meaning conception must face: while perceptions and conceptions are tied to an individual, a concept may well be a property shared by perceptions or conceptions located in different individuals. Lexical meaning composition is based on morphosemantic composition functions whose arguments are ("n"-tuples of) concepts and whose values are again concepts. Such semantic functions occur in the semantic content of morphological functions such as morphological complement, modifier, and nucleus, and operate on the basis of (morphological or semantic) application conditions. In Integrational Sentence Semantics, sentence meanings are construed as intensional relations between potential utterances and potential speakers. For any syntactic unit that has a sentence meaning, the meanings of the unit jointly represent a necessary condition for successful utterances of the unit. Each (simple) sentence meaning consists of at least (i) a referential part: a set containing exactly one 'referential meaning' for each referential expression of the syntactic unit; (ii) a propositional part: a pair consisting of a directive part (determining a speech act type) and a proposition; and (iii) a propositional background, consisting of what the speaker co-expresses with the proposition. The referential part and the propositional background of a sentence meaning may be empty. Syntactic meaning composition is based on semantic composition functions associated with (i) the syntactic functions in an idiolect system, by the 'syntactic function interpretation,' (ii) with syntactic categories like tense or definiteness categories, by the 'syntactic category interpretation' (both are components of the sentence-semantic part of the idiolect system). Syntactic meaning composition starts from the lexical meanings of the primitive constituents in a syntactic quadruple: 'basic syntactic meanings' are pairs of a concept, assigned to a primitive constituent by the lexical interpretation, and a 'contextual embedding' of the concept that involves potential speakers and utterances. Next, basic syntactic meanings are transformed into 'intermediate syntactic meanings' for non-primitive constituents by means of syntactic-semantic composition functions that are associated in the idiolect system with syntactic functions such as complement and modifier.