In this paper information concepts will be roughly divided into two categories: The cybernetic and the semiotic-pragmatic. They are further divided into three and four subcategories, respectively. The cybernetic conception of information, which comprises both the mathematical-statistic and the logical-semantic approaches, misses some aspects of information and knowing, that are important in economics and technology studies, among others. The semiotic-pragmatic approach presumes the existence of several modes of being of information, as well as connects certainty and ambiguity to information in a different way from how the cybernetic approach does. These two general approaches to information and knowing are strikingly different, especially in their analysis of ignorance or incomplete knowledge. None of the cybernetic conceptions, and only some conceptions within the semiotic-pragmatic approach, can vindicate the elusive intuition of the potential positive role of ignorance. This comparative, philosophical discussion of the modes of ignorance may be taken as a challenge for cybernetics and computational philosophy to make better sense of incomplete knowledge.