In this paper I am going to consider a class of adjectives that we can term deictic adjectives and three grammatical problems associated with these adjectives. The grammatical problems are 1) the selectional restriction problem, 2) the grammatical frame problem, and 3) the semantic substitutability problem. I am going to show that understanding how these adjectives combine with nouns semantically will allow us to explain these grammatical peculiarities and that conceptual graphs can account for the linguistic phenomenon systematically.