Discussions of the role of mathematics in software engineering are common and have probably not changed much over the last few decades. There is now much discussion about the "intuitive" nature of software construction and analogies are drawn (falsely) with graphic design, (conventional) architecture, etc. The conclusion is that mathematics is an unnecessary luxury and that, like these other disciplines, it is not needed in everyday practice. We attempt to refute these arguments by recourse to ideas from the philosophy of science developed over the past century. We demonstrate why these ideas are applicable, why they establish a framework (in the sense of Carnap) in which many central ideas in software engineering can be formalised and organised, why they refute the simplistic recourse to "intuition", and why they provide a scientific/engineering framework in which contributions to the theory and practice of software engineering can be judged.

For the last three years the authors have been building an instantiation of a system development paradigm, called ARTS. The paradigm consists of a view of what a system development environment is, in general terms, and a methodology for instantiating the paradigm for particular and specific domains of application. The motivation for and the explanation of the paradigm are derived from extant epistemological models of the method of natural science. They assert that these models are directly applicable to the domain of software and systems construction, and that, from them, one can derive principles and explanations for what a software development environment should be. They present briefly the statement view of scientific theories, a conceptual architecture for software development environments whose rationale is given in terms of the statement view and some examples of how the present version of ARTS realises this conceptual architecture.

Since the main themes at the Helena Rasiowa memorial were algebra, logic and computer science, we will present a survey of results on fork algebras from these points of view. In this paper we study fork algebras from the points of view of their algebraic and logical properties and applications. These results will prove to be essential, in a future work, for the definition of a wide-spectrum calculus for program construction.