But also, highly instructive: You think Charles Blow is losing out because of his selfless focus on Donald J. Trump? Consider the wonderfully entertaining instruction which could be provided by further excursions into the world of academic logic!
We abandoned our pursuit of such topics at the time of the Blasey Ford hearings. Up until then, we'd been entertaining ourselves with tales of the greatness of Kurt Godel, "who has often been called the greatest logician since Aristotle."
We're quoting science writer Jim Holt, who was reviewing Rebecca Goldstein's 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel. In an unintentionally entertaining passage, Holt described where academic logic resided as of the 1920s:
HOLT (2/28/05): Gödel entered the University of Vienna in 1924. He had intended to study physics, but he was soon seduced by the beauties of mathematics, and especially by the notion that abstractions like numbers and circles had a perfect, timeless existence independent of the human mind. This doctrine, which is called Platonism, because it descends from Plato’s theory of ideas, has always been popular among mathematicians. In the philosophical world of nineteen-twenties Vienna, however, it was considered distinctly old-fashioned. Among the many intellectual movements that flourished in the city’s rich café culture, one of the most prominent was the Vienna Circle, a group of thinkers united in their belief that philosophy must be cleansed of metaphysics and made over in the image of science. Under the influence of Ludwig Wittgenstein, their reluctant guru, the members of the Vienna Circle regarded mathematics as a game played with symbols, a more intricate version of chess. What made a proposition like “2 + 2 = 4” true, they held, was not that it correctly described some abstract world of numbers but that it could be derived in a logical system according to certain rules.According to Holt, the western world's greatest logician since Aristotle had been seduced at an early age by "the notion that abstractions like numbers and circles had a perfect, timeless existence independent of the human mind."
Gödel was introduced into the Vienna Circle by one of his professors, but he kept quiet about his Platonist views...
Reader, do you have even the slightest idea what that formulation could possibly mean? Of course you don't! But Holt just kept plowing ahead with his discussion of Godel. His review was published in The New Yorker, whose editors possibly couldn't see that this formulation didn't quite seem to make recognizable sense.
The review was republished this year as the title piece in a collection of Holt's essays. This new book is called When Einstein Walked with Gödel: Excursions to the Edge of Thought.
Friend, do you believe that numbers and circles have some sort of perfect, timeless existence? Do you have even the slightest idea what such a statement might mean?
Truthfully, no, you don't, but who gives a fig about that? And as if that formulation wasn't foolish enough on its own, Holt went on to say that Godel and the like were devoted to trying to determine "what made a proposition like '2 + 2 = 4' true."
What makes 2 + 2 = 4 true? Godel had one idea, the Vienna Circle had another! This is where formal logic stood 2500 years after Aristotle got everything started.
Do you believe that numbers and circles have some sort of perfect, timeless existence? If you're devoted to the practice of deference to authority, you may be prepared to swallow the claim that this presentation actually makes some sort of discernible sense.
We'll suggest a different possibility. We'll suggest the possibility that "notions" like these make no discernible sense at all. We'll guess that this incoherence, on the allegedly highest levels of thought, represents an anthropology lesson—a lesson about the mental capacities of our floundering species.
Eventually, we'll be inclined to float that idea, drawing on the work of the later Wittgenstein. But for now, let's consider the early Wittgenstein, the one who published the deftly-titled Tractatus Logico-Philosophicus in 1921, though it was written years earlier.
Decades later, the later Wittgenstein would largely throw this early work under the bus. In the wake of his later work, he came to be regarded, at least for a time, as the latest of our great logicians.
That was then, but what came earlier? In the past month or so, we've been marveling at an early passage from Professor Kenny's 1973 text, Wittgenstein. Needless to say, the publisher (Harvard University Press) and the reviewers said that Kenny's "lucid" text made Wittgenstein's work, early and late, accessible to "the general reader."
Over the past few months, we've marveled at Kenny's early capsule account of "the central doctrine" of the Tractatus. Chasing after worthier topics in the manner of a Blow, we'll look at some of Kenny's text, starting that labor tomorrow.
According to Kenny, what was the central doctrine of the early Wittgenstein's famous book? We think this work will be entertaining, but we'd also say it's highly instructive concerning the intellectual limitations of our human race.
How did we manage to get ourselves into our current political / journalistic mess? Let's start with this:
Throughout his life, history's second greatest logician struggled with the logic of 2 + 2 = 4! Tomorrow, we'll start exploring the early Wittgenstein, as explained by Kenny.
Concerning our species as a whole, Professor Harari has recently said that we're built around the ability to "gossip" and to promulgate potent group "fictions." That's what we've been saying here for the past twenty years!
How did we get to this dangerous place? Starting tomorrow, more of the work of the greatest logicians our species has brought to the fore...