The notion of a human value system can be quantified as a cognitive map, the dimensions of which capture the semantics of concepts and the associated values. This can be done, if one knows (i) how to define the dimensions of the map, and (ii) how to allocate concepts in those dimensions. Regarding the first question, experimental studies with linguistic material using psychometrics have revealed that valence, arousal and dominance are primary dimensions characterizing human values. The same or similar dimensions are used in popular models of emotions and affects. In these studies, the choice of principal dimensions, as well as scoring concepts, was based on subjective reports or psycho-physiological measurements. Can a cognitive map of human values be constructed without testing human subjects? Here we show that the answer is positive, using generally available dictionaries of synonyms and antonyms. By applying a simple statistical-mechanic model to English and French dictionaries, we constructed multidimensional cognitive maps that capture the semantics of words. We calculated the principal dimensions of the resultant maps and found their semantics consistent across two languages as well as with previously known main cognitive dimensions. These results suggest that the linguistically derived cognitive map of the human value system is language-invariant and, being closely related to psychometrically derived maps, is likely to reflect fundamental aspects of the human mind.