In this theoretical paper Lenneberg asserts that man's ability to use language as a species specific function is due more to general deep-seated cognitive characteristics than to a specific ability for vocal auditory exchange of thought. He argues that man's ability for mathematical thinking arises from the same cognitive sources as language. 'For every mathematical notion there is a homologous one in the sphere of language.' Lenneberg illustrates certain formal similarities in the structure of mathematics (especially arithmetic) and language. A comparison of animal communication with man's language is not possible without an intimate knowledge of the nature of the structure of human languages. Both language and arithmetic are processes of relations that combine into integrating systems. Although the ontogenetic characteristics of these integrating systems are known, we do not know what the homologous phylogenetic systems are. 'By characterizing language and arithmetic simultaneously, it is also possible