Heidegger explicates the concepts of "ontic" and "ontological" through a consideration of science in section 3 of Being and Time. A field of study such as mathematics, for example, operates under normal conditions with a conception of the nature of its subject matter -- numbers or quantities -- that is taken as self-evident and beyond question by its practitioners. Mathematicians start from paradigm cases of numbers, presumably cardinal numbers. In the course of their work, however, they might encounter anomalous cases, such as zero, infinity, irrational numbers, negative numbers, three divided by zero, and so forth. When such anomalies arise, it becomes necessary to ask questions such as, "What are we talking about when we talk about numbers?" and "What exactly is a number?" For Heidegger, the ordinary busy-work of puzzle-solving in mathematics is called "ontic" inquiry, whereas deeper questions about the very nature of the subject matter of this domain are called "ontological."

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