From the perspective of matters' properties and the world itself, and by using mathematical logic method, this paper discusses matters' both non-metricity and recognizability, the world's incomputability and the completeness of analytical method. The results show that analyzing the world and matters is necessary, but that attempting to fully understand all analytical methods concerning the world and matters is incomplete, and that there is no absolutely complete intelligent system. Based on the relationship between the matters and the cognition concerning them, this paper establishes a unified model about recognition, knowledge, and information, revealing that recognition is the image of mapping, and knowledge is the mapping from matters to their recognition on which the uncertainty of knowing is eliminated. It also points out that information is a projection of matters in a certain space and the nature of all matters as spirits, and reveals the inherent relationship among these concepts. The analysis of direct and indirect mappings shows that direct mappings and direct cognition are single, deterministic, mechanical, non-generic and incomplete in nature, and the complete knowledge of matters must be and must have indirect mapping paths.