A Primer on Ernst Abbe for Frege Readers

1. Introduction

Setting out to understand Frege, the scholar confronts a roadblock at the outset: We just have little to go on. Much of the unpublished work and correspondence is lost, probably forever. Even the most basic task of imagining Frege's intellectual life is a challenge. The people he studied with and those he spent daily time with are little known to historians of philosophy and logic. To be sure, this makes it hard to answer broad questions like: 'Who influenced Frege?' But the information vacuum also creates local problems of textual interpretation. Say we encounter a sentence that may be read as alluding to a scientific dispute. Should it be read that way? To answer, we'd need to address prior questions. Is it reasonable to think Frege would be familiar with the issue? Deep or superficial familiarity? Would he expect his readers to catch the allusion? Can he be expected to anticipate certain objections? Can people he knows be expected to press those objections? A battery of such questions arise, demanding a richer understanding of Frege's environment.

Ernst Abbe might have been the only intellect of the first rank that Frege spent regular time with, apart from Frege's years of graduate study in Göttingen (about which time we know little).¹ Frege's 'revered teacher' (Frege 1984/1891, 127) Karl Snell was enthusiastic and engaged with philosophy but not profound. Hermann Schaeffer cared about mathematics education but made no contributions to mathematics as such. Later, Frege could talk to Otto Liebmann and Johannes Thomae — a productive philosopher and mathematician respectively, both of them respectably good. But they arrived later, and neither approached Abbe's intellectual power.

I will flesh out a story about Abbe and his work for anyone who is curious to know more about him, but the main audience will be those who are interested in Abbe's role in Frege's environment. I want to give a sense of Abbe's work, depth, and intellectual personality to make it plausible that he could have contributed to shaping the thoughts of someone as exacting as Frege. I have the impression that it is generally not appreciated what a profound, versatile, and charismatic thinker Abbe was. I hope a side benefit will be a sense of what a compelling person Abbe was to the people around him, of his warmth and humanness as well as the depth and energy he brought to his surroundings.

I'll anchor the general discussion in specific textual questions. A cluster of remarks in Frege's writings hint at a systematic view linking empirical induction, logic, probability theory, observation, fruitfulness of concepts, and a striking analogy relating the Begriffsschrift to a microscope. In a contextual vacuum, these may seem to be random and disconnected asides. We'll learn that Frege would have expected these remarks to have been seen as linked and salient by his most proximate readers and that he would have been well informed of the background required to make his remarks come to life.

2. Abbe as Frege's Mentor: A First Glimpse

2.1. Abbe's Life: Basic Facts

Ernst Abbe was born in 1840 into the family of a foreman in a textile mill. Though the economic circumstances were difficult, Abbe showed unusual academic promise from a young age, and his family, with help from his father's employers and money Ernst earned from tutoring and school competitions, managed to support him in attaining an education. After gymnasium he studied at Jena, attending lectures from Karl Snell and Ernst Apelt, among others. In 1858 he went to Göttingen, where he was especially impressed by the lectures of Bernhard Riemann. His PhD thesis on thermodynamics was completed under Wilhelm Weber in 1861, and, after two years during which he worked at the Göttingen observatory and a scientific society in Frankfurt, he returned to Jena in August 1863 to begin teaching physics and mathematics. When Frege arrived in 1869 Abbe, who appears to have been the person to appreciate his promise, guided him to Göttingen...