Third letter to today's 9-year old kids!

THURSDAY, APRIL 2, 2020

An early glimpse of a method: After reviewing the moral and intellectual squalor of our nation's daily briefings—"in the darkness of this time"—it's hard to redirect one's sensibilities toward a loftier realm.

For that reason, we went outside and experienced sunshine and air. Let's consider how Wittgenstein entered the world of academic philosophy in 1911, at the age of 22.

Professor Goldstein described this history in her 2005 book about Godel's incompleteness theorems. The history involves a comical part of 20th century high-end "philosophy. It also gives us an early look at a certain Wittgensteinian method.

Goldstein sets the scene. For the moment, we're leaving the squalor of Donald J. Trump and the walking dead behind:

GOLDSTEIN (page 90-91): Wittgenstein came from one of the wealthiest and most culturally elite families of Vienna, "the Austrian version of the Krupps, the Carnegies, the Rothschilds, whose lavish palace on Alleegasse had hosted concerts by Brahms and Mahler"...While studying aeronautical engineering at the Technische Hochschule in Berlin, he had learned of Russell's paradox, and became interested in the foundations of mathematics.

(The quotation comes from Professor Monk.)

Wittgenstein "became interested in the foundations of mathematics," whatever that might mean. In October 1911, therefore, he presented himself, unannounced, at (Bertrand) Russell's lodgings in Cambridge.

Before the decade was done, he was one of the foremost figures in the world of English-language academic philosophy.

We'll examine "Russell's Paradox" at some point in the future. Suffice to say that it concerns "the set of all sets not members of themselves," a silly theoretical construct which, to this very day, provokes the laughter of the gods lounging about on Olympus.

Russell's Paradox will come a bit later. That said, Goldstein compares it to the ancient "liar's paradox," which she describes like this:

GOLDSTEIN (page 49-50): Paradoxes, in the technical sense, are those catastrophes of reason whereby the mind is compelled by logic itself to draw contradictory conclusions. Many are of the self-referential variety; troubles arise because some linguistic term—a description, a sentence—potentially refers to itself. The most ancient of these paradoxes is known as the "liar's paradox," its lineage going back to the ancient Greeks. It is centered on the self-referential sentence: "This very sentence is false." This sentence must be, like all sentences, either true or false. But if it is true, then it is false, since that is what it says; and if it false, well then, it is true, since, again, that is what it says. It must, therefore, be both true and false, and that is a severe problem. The mind crashes.

Should the mind of a sensible person "crash" when confronted with the liar's paradox? Should any sensible person regard the liar's paradox as "a catastrophe of reason?"

We'll have to say that the answer is no. Follow us down this byway:

"This very sentence is false!" So goes the liar's paradox. Professor Goldstein explains why it makes the mind crash. She starts with this assertion:

"This sentence must be, like all sentences, either true or false."

"Like all sentences," the liar's paradox must be true or false. On its face, that may seem to make perfect sense.

That said, the later Wittgenstein came to lodge a type of objection. Some collections of words which look like well-formed sentences are neither true nor false, he said, demonstrated or implied.

Those collections of words are incoherent. They don't make recognizable sense. They don't rise to the level of being false. They're neither true nor false.

Certain collections of words are simply incoherent. That said, these collections will often resemble other collections of words which do make perfect sense.

For that reason, they may seem to make sense. They may seem to make sense, but they actually don't in any established manner.

Consider some other collections of words which do make perfect sense. On the surface, these collections of words resemble the collection of words known as the liar's paradox:

Four collections of words:
1) The second sentence on page 98 of John Smith's book is false.
2) The very first thing you just said was false.
3) Every sentence out of your mouth last night was false.

4) This very sentence is false.

Those first three sentences can be said to share a "surface grammar" with the liar's paradox. That said, we all know how to evaluate such sentences. We look at the (pre-existing) sentence in question and decide if it's true or false.

On the surface, those first three sentences resemble the liar's paradox. That said, a major difference exists in what might be called their "depth grammar." Here's what we mean by that:

In each of those three sentences, we're told that some pre-existing sentence or statement is false. By the well-known rules of the game, we then examine that pre-existing sentence to determine whether we agree.

Everyone knows how to do this! But in the case of the liar's paradox, there is no pre-existing sentence for us to evaluate. No one has actually presented a statement. Nothing has been offered which could be true or false.

In that sense, the peculiar collection called "the liar's paradox" is fundamentally different from a wide array of very familiar statements. On the surface, the liar's paradox resembles those familiar statements, but it's fundamentally different.

The younger Wittgenstein was drawn to Cambridge by "Russell's Paradox." He bought the package Russell was selling. By the time of his later work, he had decided that vast amounts of his celebrated early work were just plain old wrong.

The later Wittgenstein decided that the early Wittgenstein was wrong. He might also be seen to have said something like this:

Much of traditional philosophy is comprised of statements which resemble perfectly reasonable statements. Because they resemble familiar statements, we may not notice that, in the depth of their logic (or "grammar"), they aren't like the familiar statements at all, and they don't make any obvious sense.

"The very sentence is false?" I have no idea why a sensible person would regard that as a "catastrophe of reason" which makes "the mind crash." It's just a bit of silly wordplay, apropos of nothing.

"Up is down" is rather odd too, but it's just a bunch of words. No one's mind should crash when they hear it said. So too with the ancient liar's paradox.

Shortly after the turn of the century, Bertrand Russell was wasting his time attempting to ponder "the set of all sets not members of themselves." He was trying to limn "the foundations of mathematics," whatever that might mean.

Russell was all tangled up in his eponymous "paradox." As a very young fellow from Vienna, Wittgenstein got sucked in.

Years later, he reconsidered. He ended up producing the book you shouldn't attempt to read.

Next: The preface and the first few pages of Philosophical Investigations. "Not a good book," he said.