Owain Griffin

Thoralf Skolem (1887–1963) is rightly regarded as one of the most significant figures in modern logic, and is widely seen as the founding father of model theory. His groundbreaking results (most notably the jointly eponymous Löwenheim–Skolem Theorems) have shaped mathematical logic as we know it and have initiated ongoing philosophical debate for over 100 years. In this paper, we provide the first English translation of Sur la Porté du Théorème Löwenheim–Skolem. To accompany this translation, we also provide a foreword to help situate the paper in its proper historical and philosophical context.

Model-theoretic skepticism is a challenge to purported a priori mathematical knowledge. According to this challenge, elementary results from mathematical logic undermine our grasp of basic mathematical concepts such as finitude and countability. Despite generating rich discussion over the years, most philosophers don’t feel worried by model-theoretic skepticism, in part due to a number of notable anti-skeptical arguments. In this paper, I evaluate these arguments, and explore the question of whether (and to what extent) a skeptical threat remains.