The Principle of Permanence of Forms

This project concerns the history and philosophy of mathematics, more specifically the so-called Principle of Permanence of Forms. This principle states that the form of a theorys laws should be preserved when extending or generalizing the theory. It expresses a fundamental feature of science, a kind of perseverance that has long been tacitly applied by scientists. It played a crucial role in the development of mathematics, it was instrumental in articulating philosophical views about mathematics, and central to some developments in nonstandard analysis and modern physics. It has recently also been applied in the philosophy of language. The project will provide a philosophically illuminating account of this all important principle, showing that several ideas underlying contemporary science and philosophy are conceptual developments of the historical interpretations of the principle. These ideas will not only help us appreciate how influential and fruitful this was, but they will provide rigorous conceptual means for our understanding of the principle.