What's a "phantom explanation?"

THURSDAY, JUNE 10, 2021

Afternoon delights: Yesterday afternoon, in award-winning fashion, we introduced an award-winning term—"phantom explanation."

We were thinking of the phenomenon known as "phantom limb." Somehow, an arm or a leg has been lost—but it may continue to feel like the missing limb is there.

A surprising amount of high-level academic communication involves phantom explanation. The phenomenon goes like this:

After some question has arisen, an apparent explanation is offered. In fact, the matter at issue hasn't been explained at all. The apparent explanation doesn't make sense, but the person receiving the apparent explanation can't tell. 

That person believes he's received an explanation. He believes he's understood it.

In fact, that hasn't happened at all. A few simple questions will reveal the fact that the recipient of the phantom explanation actually doesn't understand the matter in question at all.

A surprising amount of high-level academic and journalistic communication involves phantom explanation. The later Wittgenstein seemed to suggest that most academic philosophy comports to this awkward model.

A collection of words is emitted. It sounds like the words make sense—like something has been explained.

Nothing resembling that has occurred. In fact, the explanation is a phantom, but the recipient can't tell.

Phantom explanation will often occur in books about physics or math aimed at the general reader. If the person writing the book is highly regarded, journalists will enthusiastically say that the work in the book is amazingly clear, even though the work in the book is basically incomprehensible.

This question arises in the case of Stephen Budiansky's new biography of Kurt Gödel, Journey to The Edge of Reason. The book is written for the general reader. The problem we face is this:

Gödel is routinely cited as "the greatest logician since Aristotle." With that in mind, what did this greatest logician discover, prove or show?

More to the point, is Budiansky able to explain what Gödel discovered, proved or showed? Beyond that, a second question may even arise:

Are we completely sure that Gödel proved anything of value at all?

The later Wittgenstein might have said no to the latter question. Regarding Budiansky's efforts in his new book, we'll also go with a no. 

(We're not suggesting that anyone else could have done any better.)

In our view, no general reader will emerge from Budiansky's book with anything like an understanding of whatever it is Gödel is alleged to have proven.  The reader may think that he understands. Our prescription?

Let the (simple) questions begin!

We'll have much more in coming weeks about this fascinating topic. Decades after the start of our journey, the pointlessness of commenting on the mainstream public discourse has at last become abundantly clear, even at long last to us!

Meanwhile, what the heck did Gödel prove? Taking a further Wittgensteinian road, do we feel completely sure that he demonstrated, proved or showed anything at all? 

For entertainment purposes only: Budiansky occasionally offers a humorous look at what preceded Gödel. In the passage shown below, he describes the problems which arose when Bertrand Russell decided, at the turn of the century, that he should do whatever it is he did:

BUDIANSKY (page 108): In deciding to take on the fourth of the challenges Hilbert had put forward at the Congress of Mathematicians in 1928, Gödel placed himself at the very center of the storm over mathematical foundations, which had broken with a deeply unnerving discovery Bertrand Russell had made at the turn of the century while working on Principia Mathematica.

Russell's idea had been to establish the soundness of mathematics by showing how it could all be reduced to principles of logic so self-evident as to be beyond doubt. Defining even the simplest operations of arithmetic in terms of what Russell called such "primitive" notions, however, was far from an obvious task. Even the notion of what a number is raised immediate problems.

The laboriousness of the methodology and notation was all too evident in the (often remarked) fact that that it took more than seven hundred pages to reach the conclusion, "1 + 1 = 2," a result which Russell and Whitehead described as "occasionally useful."

It took Russell and Whitehead more than seven hundred pages to establish the fact that 1 + 1 = 2? The amusement only deepens as Russell makes his "deeply unnerving discovery," then later as the years lead on toward the 24-year-old Gödel.

The methodology had been laborious. Are we sure this fandango made sense?