This paper takes issue with the view of conceptual structures as autonomous syntactic structures generated by syntactic formation rules. Instead, it adopts the position developed by Croft and Cruse (2004), in showing that linguistic knowledge -- knowledge of meaning and form -- is basically conceptual structure. In fact the, fundamental problem posed by the rules-based approach is that conceptual structures are treated as purely formal and devoid of any meaning. If we consider grammatical morphemes to be part of the conceptual structures of language, this position would hardly be applicable. As the instruments of thought, the meaning attached to grammatical morphemes is highly abstract and must be reconstructed based on attested uses. In line with the position adopted, the paper provides an explanation through the analysis of the uses of the -s morpheme and the -ø morpheme in English as well as the noun-class morpheme -m in Tagbana, about the fact that grammatical morphemes cannot be treated as abstract symbols devoid of intrinsic meaning. In fact the syntactic configurations which characterize the notions of plurality expressed by these morphemes evidence the types of conceptualization attached to them. The semantic representations denoted by these morphemes are, then, proven to be basically conceptual.