Vienna's greatest minds: Yesterday, when we left off, we were ruminating about a bit of modern upper-end logic.
Granted, it was only a footnote. The footnote is found on the first page of Chapter 3 of W. D. Hart's 2010 book, The Evolution of Logic.
Hart's book is part of the "Evolution of Modern Philosophy" series published by the Cambridge University Press. His footnote, which we basically picked at random, goes exactly like this:
Perhaps more generally a quantifier is a second-level function whose value at an (n + 1)-ary first-level concept is an n-ary concept, unless n is zero, in which case its value is a truth value, an object. In that case, quantifiers would be second-level functions sometimes having first-level concepts as values and sometimes objects as values. When the value of a first-level concept at an object is truth, Frege says the object falls under the concept. Perhaps the concept:falls-under is a binary second-level concept whose first argument is an object and whose second is a first-level concept. In that case, second-level concepts could also have arguments of different levels.Not that there's anything wrong with it! But that may give you some idea of what modern elite "logic" looks like.
Meanwhile, how about the logic of everyday public discourse—the logic of paraphrase, let's say, or the bungled logic which lay behind the endlessly bungled mid-1990s Clinton-Gingrich Medicare debate?
How about the logic (the semantics) of lies, false claims, errors, mistakes and misstatements? Such charges dominate the current debate. Has any logician ever stepped forward to address the logic of that?
Alas! When it comes to everyday logic, we the people (we the rubes) are pretty much left on our own. Rather, we're left to the mercies of the modern journalistic elite, who mainly like to talk about who may have had sex on one occasion with someone ten years in the past.
(In the end, it's what they care about.)
Our modern journalists enjoy discussing topics like earth tones and sex. They'll speculate, from morning to night, about who may end up in prison or jail, and of course for how long.
They'll quickly find ways to stop discussing the separation of kids at the border, or the deaths of children around the world in U.S.-linked wars. Much as Professor Harari has said, they seem to run on "fictions" and "gossip," and perhaps on little else.
That's the fuel on which our modern elite journalists run. By way of contrast, our elite logicians like discussing whether "the concept:falls-under is a binary second-level concept whose first argument is an object and whose second is a first-level concept," and other topics like that.
Not that there's anything wrong with it! Unless you think that something's been wrong with our public discourse for at least the past three decades—something which won't be fixed by the entertaining, exciting dreams of the Milbanks, the Lemons and the Dowds, or even by the O'Donnells and the Maddows.
We take it as obvious that something is wrong with the world of our elite "journalists." But how about our elite "logicians?" What can we say about them?
What about our elite logicians? Despite the deference we tend to display toward authority figures of various kinds, is it possible that our greatest logicians since Aristotle have possibly never been "all that?"
Ignore their flight from public service! Is it possible that our elite logicians just haven't been especially insightful or sharp, even on their own terms? In the next two days, we'll chuckle at two suggestions to that effect, suggestions drawn from Rebecca Goldstein's 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel.
Goldstein focuses on Kurt Godel, who she explicitly describes as "the greatest logician since Aristotle." Rather plainly, she draws a picture of a man who was mentally ill throughout his life, leading to a tragic death by self-starvation at the age of 71.
She also focused on Godel's array of weird ideas, weird ideas which isolated him within the Princeton community. When Jim Holt reviewed Goldstein's book for The New Yorker, he referred to other peculiar ideas, perhaps without realizing that he was doing so:
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.Do numbers and circles actually "have a perfect, timeless existence independent of the human mind?" More to the point, does anyone have the slightest idea what such a claim might mean?
Meanwhile, how about the mysteries of 2 plus 2? Should the greatest minds in Vienna have spent their time arguing about how we can know that it adds up to 4?
We'll say the answer may be no. In Vienna, the argument raged. To appearances, it was still being taken seriously in Goldstein's well-reviewed book.
In that chunk from Holt's review, an interesting part of Goldstein's book makes a brief appearance. Along the way, Goldstein spends a good chunk of time discussing the "thinkers" of the Vienna Circle, and especially "Ludwig Wittgenstein, their reluctant guru."
Eventually, the later Wittgenstein would try to leave the work of these elite logicians in the dust. Goldstein describes an earlier version of this guru, and she describes the comical way the greatest "thinkers" of Vienna let themselves be drawn under the spell of his "almost mystical influence."
Tomorrow, we'll run through Goldstein's eye-rolling account of the way these greatest thinkers responded to the eccentric mannerisms of this reluctant guru. Though we don't agree with Goldstein's overall stance, we'll agree with her on one point:
Forget their concerns about 2 plus 2! Goldstein's comical portraits suggest the possibility that these lofty Viennese thinkers may not have been "all that," despite their high academic standing.
Tomorrow, we'll look on as Europe's greatest minds ape Wittgenstein's various tics. We'll even wonder if we ourselves saw a version of that as the teaching assistant in our first-year "Problems in Philosophy" class agonized at a third-story window over 7 plus 5 making 12.
Tomorrow will be the aping of tics. Then, on Friday, well touch on a point from Professor Hart's book, at least as the book is described by the Cambridge University Press:
CAMBRIDGE UNIVERSITY PRESS: Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II...During the evolution of logic, Cantor and Frege achieved great things. But their achievements were "threatened by the paradoxes, like Russell's." What in the world does the publisher mean by that?
How in the world were achievements in logic threatened by paradoxes? On Friday, we'll establish the field of play. Next week, we'look at Goldtsein's treatment of this embarrassing part of the modern history of upper-end, high detached elite "logic."
Goldstein seems to buy this history all the way down. Somewhere, Professor Harari is mordantly chuckling as we see a major way in which our greatest "great ape" minds have never been all that sharp.
Tomorrow: Aping the tics