On the Theory of the Infinite in Modern Thought: Two Introductory Studies

In 1911, a pioneering female mathematician attempted something daring: she asked what infinity actually means, and why the concept has driven philosophers to madness for millennia. Eleanor F. Jourdain's two studies trace the evolution of human understanding of the finite and infinite from ancient Greek thought through Cantor's revolutionary work on transfinite numbers. The first study maps how different eras grappled with these ideas, revealing that the boundary between mathematics and metaphysics has always been porous. The second turns to pragmatism and epistemology, asking how knowledge grows through human interaction with the world, and how mathematical logic illuminates philosophical inquiry. Jourdain argued forcefully that mathematics and philosophy must collaborate to grasp reality's deepest structures. This is not a dry academic exercise but a period document capturing a moment when the infinite was being reimagined, when Cantor's insights were still fresh and controversial. For readers curious about how we came to think about infinity, and why the infinite still troubles our intuitions, Jourdain offers a window into early twentieth-century attempts to make the unimaginable thinkable.