Frege’s “Despondency” and Academic Writing

I was struck by a passage in Frege’s foreword to Volume 1 of the Grundgesetze der Arithmetik (Basic Laws of Arithmetic). I suspect also that I was only struck by the passage in light of my own experience with writing a dissertation, and so a book-length academic work, of my own.

Here is the context. In 1879, Frege published Begriffsschrift (Concept-Script). In 1884, Frege published Die Grundlagen der Arithmetik (The Foundations of Arithmetic). Loosely-speaking, these works may be viewed as formal and philosophical antecedents, respectively, for Frege’s Grundgesetze. But it was published in 1893, almost ten years later. Why did it take so long?

Frege goes on for a couple pages explaining how his new work has new primitive notions and how the passing years “have seen the work mature.” This is fairly typical: philosophers, especially honest and deeply thoughtful ones like Frege, rehash their views. Then Frege writes something that really struck me (page XI):

…I arrive at a second reason for the delay: the despondency that at times overcame me as a result of the cool reception, or rather, the lack of reception, by mathematicians of the writings mentioned above [Begriffsschrift andGrundlagen], and the unfavorable scientific currents against which my book [Grundgesetze] will have to struggle. The first impression alone can only be off-putting: strange signs, pages of nothing but alien formulae. Thus sometimes I concerned myself with other subjects. Yet as time passed, I simply could not contain these results of my thinking, which seemed to me valuable, locked up in my desk; and work expended always called for further work if it was not to be in vain. Thus the subject matter kept me captive. All that is left for me is to hope that someone may from the outset have sufficient confidence in the work to anticipate that his inner reward will be repayment enough, and will then publicize the results of a thorough examination.

A page later, Frege bluntly laments, “Otherwise [if I do not get such a reader], of course, the prospects for my book are dim.”

This cuts deep when I think about the reception that my dissertation is likely to receive, namely, none. Many individuals pour their work and closely-held beliefs into their dissertation. My uneducated guess is that most have yet to find a reader of the sort Frege sought. This can lead to melancholic thoughts, such as

Why am I spending my time doing this? Nobody will read it. It does not matter. I will not get a permanent academic position in which I can unpack the implications of this work anyway.

Thoughts like that can interfere with the writing. But the work keeps calling me back, as Frege’s called him. And Frege ends on a happy note that usually is enough to dispel such brooding moods (page XXV):

The distance [of my logical standpoint] from psychological logic seems to me to be as wide as the sky, so much so that there is no prospect that my book will have an effect on it immediately. My impression is that the tree that I have planted has to heave an incredible load of stone to make space and light for itself. Still, I will not give up all hope that my book will eventually aid the overthrow of psychological logic.

Hi-Story Time x 2!

It’s story time! (Rather, hi-story time!) Here is a retelling of two truly terrific tales from the history of logic. I hope you find them fun and engaging!

  • Story Time 1/2: Russell’s letter to Frege announcing the contradiction

On 16 June 1902, Bertrand Russell (1872-1970) wrote to Gottlob Frege (1848-1925). Russell had just discovered his famous paradox, and he wanted to inform Frege that an analogue was derivable in the logic of Grundgesetze (Basic Laws of Arithmetic, link). Meanwhile, Frege had just sent to press the second volume of Grundgesetze, his life’s work. Then Frege got the news of Russell’s contradiction.

Just to pump your sympathy for Frege: imagine you had just finished and sent off your book or dissertation, you were days from your publication or your defense, and then — somebody points out you contradicted yourself on some point that was fundamental to your argument. I reckon I would be pretty upset, and I reckon you would be, too.

How did Frege react? Like this:

“Dear colleague: Many thanks for your interesting letter of 16 June…Your discovery of the contradiction caused me the greatest surprise, and, I would almost say, consternation, since it has shaken the foundation on which I intended to build arithmetic…In any case your discovery is very remarkable and will perhaps result in a great advance in logic, unwelcome as it may seem at first glance.”

That is a powerful response to what must have been a monumental disappointment. And Russell thought as much, too. In a 23 November 1962 letter reflecting on the exchange about 50 years later, Russell commends Frege’s response to the contradiction:

“As I think about acts of integrity and grace, I realise that there is nothing in my knowledge to compare with Frege’s dedication to truth. His entire life’s work was on the verge of completion, much of his work had been ignored to the benefit of men infinitely less capable, his second volume was about to be published, and upon finding that his fundamental assumption was in error, he responded with intellectual pleasure clearly submerging any feelings of personal disappointment. It was almost superhuman and a telling indication of that of which men are capable if their dedication is to creative work and knowledge instead of cruder efforts to dominate and be known.”

Frege’s prediction was right, of course: the contradiction led Russell to collaborate with Whitehead to produce Principia Mathematica. And Principia was a direct inspiration of enormously fruitful work, including Gödel’s theorems, Church’s work on type theory, and computer scientists’ research on artificial intelligence and automated theorem-proving in the 1950s and 1960s (including Newell, Simon, and Shaw’s Logic Theorist). Speaking of Principia:

  • Story Time 2/2: Whitehead and Russell had to self-publish Principia Mathematica

Imagine you spent ten years — say, your entire 30s — reworking and fixing the very foundations of mathematics and logic. You invent type theory, solve the contradictions, and put mathematics back on a firm foundations. You also prove a ton of interesting theorems about cardinals and ordinals just for kicks. An academic publisher would beg to print that work, right?

Wrong! It turns out Cambridge University Press estimated they would lose £600 in publishing Principia. (That amounts to almost $100,000 in today’s dollars.) So Cambridge University Press told Whitehead and Russell they would assume half that risk. That meant Whitehead and Russell, after working for ten years to fix math for everyone else, had to scrounge about for £300 to tell everyone what they did to fix it.

Happily, they got a grant for £200. But Whitehead and Russell each had to fork over £50 (~$8,000 today) to self-publish their grand treatise on the foundations of mathematics. And Cambridge thought they would lose money: probably a copy now resides in every college and university library in the world.

A little more detail on the calculations from 1910 UK pounds to modern US dollars are given here (link). And you should definitely read Principia (link) — yes, all three volumes (or at least skip the introduction and skim **1-20, pp. 90-199). Enjoy!