The axioms describe regularities in conscious experience, and IIT seeks to explain these regularities. So these notations do not guide readers to infer the regularities of English spelling. This is possible because human languages show certain linguistic regularities. Such idealized models can capture many of the statistical regularities of systems. Probability theory is also used to describe the underlying mechanics and regularities of complex systems. Schwann's notes suggest that he hoped to discover regularities and laws of physiological processes. Mathematics seeks to discover and explain abstract patterns or regularities of all kinds. Similarly in the sciences, theories explain and predict regularities in the world. Patterns in nature are visible regularities of form found in the natural world. Pattern recognition is the automated recognition of patterns and regularities in data. They serve merely to describe regularities and consistent relationships in nature. But this world is "out of phase" (Lawson) with the underlying ontology of economic regularities. Kepler used mathematics to discuss physics and described regularities of nature this way. Predictions are then based on these regularities or habits of mind. An "adequate grammar" should capture the basic regularities and the productive nature of a language.