This paper presents a new method of analysis by which structural similarities between brain data and linguistic data can be assessed at the semantic level. It shows how to measure the strength of these structural similarities and so determine the relatively better fit of the brain data with one semantic model over another. The first model is derived from WordNet, a lexical database of English compiled by language experts. The second is given by the corpus-based statistical technique of latent semantic analysis (LSA), which detects relations between words that are latent or hidden in text. The brain data are drawn from experiments in which statements about the geography of Europe were presented auditorily to participants who were asked to determine their truth or falsity while electroencephalographic (EEG) recordings were made. The theoretical framework for the analysis of the brain and semantic data derives from axiomatizations of theories such as the theory of differences in utility preference. Using brain-data samples from individual trials time-locked to the presentation of each word, ordinal relations of similarity differences are computed for the brain data and for the linguistic data. In each case those relations that are invariant with respect to the brain and linguistic data, and are correlated with sufficient statistical strength, amount to structural similarities between the brain and linguistic data. Results show that many more statistically significant structural similarities can be found between the brain data and the WordNet-derived data than the LSA-derived data. The work reported here is placed within the context of other recent studies of semantics and the brain. The main contribution of this paper is the new method it presents for the study of semantics and the brain and the focus it permits on networks of relations detected in brain data and represented by a semantic model.