A key challenge for software engineering is to learn how to reconcile the formal world of the machine and its software with the non-formal real world. In this paper, we discuss elements of Problem Oriented Software Engineering (POSE), an approach that brings both nonformal and formal aspects of software development together in a single theoretical framework for software engineering design. POSE presents development as the representation and step-wise transformation of software problems. It allows for the identification and clarification of system requirements, the understanding and structuring of the problem world, the structuring and specification of a hardware/software machine that can ensure satisfaction of the requirements in the problem world, and the construction of adequacy arguments, convincing both to developers and to customers, users and other interested parties, that the system will provide what is needed. Examples are used throughout the paper to illustrate how formal and non-formal descriptions are reconciled under POSE.