• The first, from the beginning to around p. 39 (see ‘p39’ in the margin), is the most important for us, for it concerns the philosophical status of the non-standard assumptions about geometry that were used in special relativity to accommodate an absolute speed of light and in general relativity to eliminate the need for a gravitational force.

Einstein’s general approach to this philosophical issue is one he shared with the logical positivists (many of whom got their start in philosophy via discussions of the philosophical significance of Einstein’s work). His way of formulating it rests on his distinction between “purely axiomatic geometry” and “practical geometry” (p. 32) and is sharpened by contrast with the views of Poincaré (pp. 33-36).

• In the second section (pp. 39-45) is a brief discussion of the issues Einstein saw being raised by the project of determining the geometrical structure of the universe. (The “mass-density of negative sign, distributed uniformly” that Einstein speaks of on p. 44 is known as the “cosmological constant.” Einstein abandoned the suggestion later, when it was found not to serve the theoretical purpose he intended it for, but it has come to attract attention again in recent years for somewhat different reasons.)

• The final section (pp. 45-56) was added after the lecture on which this is based. Although its explicit purpose is pedagogical, suggesting ways of picturing the sort of large-scale geometrical structure he thought most likely, it also has a philosophical significance because one traditional argument for the priority of ordinary Euclidean geometry is the difficulty of picturing alternatives.