On the theory of the infinite in modern thought : Two introductory studies

These two early‑twentieth‑century lectures were delivered first to a group of women science students at Oxford and later to a philosophical society, preserving the original spoken rhythm of the author. Though framed as academic talks, the prose reads like a guided tour through the shifting landscape of thought, inviting listeners to hear how a mathematician‑turned‑philosopher bridges disciplines that were once treated as strangers.

The first lecture tackles the age‑old contrast between the finite and the infinite, arguing that modern mathematics no longer depends on spatial or temporal intuition but on the bare prerequisites of thought expressed through symbolic logic. From this pivot, the speaker shows how metaphysics—once paired with ethics—draws fresh rigor from mathematical concepts, while pragmatism offers a practical lens for knowledge. Listeners will come away with a clearer picture of why the “new” definition of mathematics matters for philosophy’s deepest questions, and how this intellectual partnership reshaped the way scholars conceive reality.