Modern weather and climate prediction originated at the Institute for Advanced Study (IAS) in Princeton, New Jersey. Mathematician John von Neumann, a member of the IAS faculty, interacted with computing pioneer Alan Turing in the late 1930s and became involved in the construction of the first general-purpose digital computer, ENIAC, in the early 1940s. One of his goals was to use the computer to forecast weather using the equations of physics. He formed the Princeton Meteorology Group by hiring scientists with expertise in weather. In 1950, this group made the world’s first digital weather forecast. Two basic concepts from the philosophy of science – inductivism and deductivism – are introduced in the chapter to provide the context for the scientific developments being discussed. Von Neumann’s (thwarted) ambition of going beyond weather prediction to weather control is also discussed.

This chapter is the first of two exploring the idea that the core thought of the naïve conception – that there is an intimate connection between sets and properties – can be preserved as long as we build into the conception the idea that certain properties are pathological and, for this reason, do not determine a set. The chapter first uses a result from Incurvati and Murzi (2017) to show that restricting attention to those properties that do not give rise to inconsistency will not do. It then focuses on the limitation of size conception of set, according to which the pathological properties are those that apply to too many things. Various versions of the doctrine are distinguished. The chapter also discusses what it calls the definite conception, according to which the pathological properties are the indefinitely extensible ones. It is argued that the limitation of size fails to provide a complete explanation of the set-theoretic paradoxes. The definite conception faces the same problem and, in addition, it is unclear whether it has the resources to develop a reasonable amount of set theory.