The Principle of Permanence of Forms

The Principle of Permanence of Forms (PPF) stipulates that the forms of certain statements, such as the statements expressing the rules or laws of a scientific theory, should be preserved when extending or generalizing the theory, or when changing its domain of objects. It expresses a fundamental feature of science, a perseverance that has long been presupposed and often tacitly applied by the practitioners of
science. The PPF played a crucial role in the development of mathematics, for example in the works of De Morgan, Boole, and Dedekind, among many others. It was instrumental in articulating formalism – a cluster of philosophical views about mathematics, including that defended by Hilbert. The PPF was central to the
development of modern physics, especially in the work of Bohr, Dirac, and von Neumann, where it was taken to support the transition from classical to quantum mechanics, as well as further generalizations of the latter. It has been an essential element in Robinson's nonstandard analysis, justifying the transfer of certain
properties between distinct models of the theory. More recently, a version of the PPF has become extremely important in the foundations of logic and mathematics, such as in McGee’s attempt to secure the semantic determinacy of their languages.
The project will provide a philosophically illuminating account of the PPF, focused on its historical development, on its role(s) in the foundational debates about logic, mathematics, and physics, and on its scientific and philosophical applications. This account will show that ideas underlying contemporary science and philosophy (i.e., conservativity, transfer, open-endedness) are conceptual developments of the historical interpretations of the PPF. These ideas will not only help us appreciate how influential and fruitful this was, but they will provide rigorous conceptual means for the rational reconstructions of the PPF that will be offered in the project.
The project will apply the following methods: historical analysis, philosophical explanation, conceptual analysis, and logical reconstruction.
The project formulates highly original research questions and hypotheses, and pursues several lines of investigation that have never been approached before. It focuses, in part, on Ada Lovelace, one of the most interesting female scholars of the 19th century, whose work has been so far insufficiently well-studied. The
expected results will provide a rich source of historical data and philosophical arguments, which will throw light on topics of general philosophical interest.