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Abstract: 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.