We propose a method to quantify "semantic linguistic maturity" (SELMA) based on a high dimensional semantic representation of words created from the co-occurrence of words in a large text corpus. The method was applied to oral narratives from 108 children aged 4;0-12;10. By comparing the SELMA measure with maturity ratings made by human raters we found that SELMA predicted the rating of semantic maturity made by human raters over and above the prediction made using a child's age and number of words produced. We conclude that the semantic content of narratives changes in a predictable pattern with children's age and argue that SELMA is a measure quantifying semantic linguistic maturity. The study opens up the possibility of using quantitative measures for studying the development of semantic representation in children's narratives, and emphasizes the importance of word co-occurrences for understanding the development of meaning.