Friday, May 28, 2021

The poverty of positivism/the poverty of originalism

"There is no better way of finding out what a writer meant than to attempt to state his meaning in different words, preferably in another language."

Gombrich, "Aby Warburg: His Aims and Methods"

We may accept the doctrine that associates having a language with having a conceptual scheme. The relation may be supposed to be this: if conceptual schemes differ, so do languages. But speakers of different languages may share a conceptual scheme provided there is a way of translating one language into the other. Studying the criteria of translation is therefore a way of focussing on criteria of identity for conceptual schemes. If conceptual schemes aren't associated with languages in this way, the original problem is needlessly doubled, for then we would have to imagine the mind, with its ordinary categories, operating with a language with its organizing structure. Under the circumstances we would certainly want to ask who is to be master. 

Donald Davidson, "On the Very Idea of a Conceptual Scheme" 

“When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I Choose it to mean—neither more nor less.”
“The question is,” said Alice, “whether you can make words mean so many different things." .
“The question is,” said Humpty Dumpty, “which is to be master—‘that’s all.”

I never paid much attention to Davidson—the argument itself was enough for me to laugh—but the Lewis Carroll connection above was clear. 

Carroll and Borges and Aaronson, Nabokov, Nino Scalia, and Scott Soames. Aesthetics is the manifestation of ethics. Hooray for induction.

I'd written "every writer knows language is the master", but that separates writers from philosophers and artists from illustrators: those who recognize that language is the master, and those who refuse to admit it. Writers are craftspeople.

"But art is not essentially content. Art is essentially form. Art is object, not subject." Ursula K. Le Guin
I know I repeat myself, but anyone finding one page would miss the full argument.

New Scientist, Alice's adventures in algebra. 
The 19th century was a turbulent time for mathematics, with many new and controversial concepts, like imaginary numbers, becoming widely accepted in the mathematical community. Putting Alice’s Adventures in Wonderland in this context, it becomes clear that Dodgson, a stubbornly conservative mathematician, used some of the missing scenes to satirise these radical new ideas.

Even Dodgson’s keenest admirers would admit he was a cautious mathematician who produced little original work. He was, however, a conscientious tutor, and, above everything, he valued the ancient Greek textbook Euclid’s Elements as the epitome of mathematical thinking. Broadly speaking, it covered the geometry of circles, quadrilaterals, parallel lines and some basic trigonometry. But what’s really striking about Elements is its rigorous reasoning: it starts with a few incontrovertible truths, or axioms, and builds up complex arguments through simple, logical steps. Each proposition is stated, proved and finally signed off with QED.

For centuries, this approach had been seen as the pinnacle of mathematical and logical reasoning. Yet to Dodgson’s dismay, contemporary mathematicians weren’t always as rigorous as Euclid. He dismissed their writing as “semi-colloquial” and even “semi-logical”. Worse still for Dodgson, this new mathematics departed from the physical reality that had grounded Euclid’s works.

By now, scholars had started routinely using seemingly nonsensical concepts such as imaginary numbers – the square root of a negative number – which don’t represent physical quantities in the same way that whole numbers or fractions do. No Victorian embraced these new concepts wholeheartedly, and all struggled to find a philosophical framework that would accommodate them. But they gave mathematicians a freedom to explore new ideas, and some were prepared to go along with these strange concepts as long as they were manipulated using a consistent framework of operations. To Dodgson, though, the new mathematics was absurd, and while he accepted it might be interesting to an advanced mathematician, he believed it would be impossible to teach to an undergraduate.

Outgunned in the specialist press, Dodgson took his mathematics to his fiction. Using a technique familiar from Euclid’s proofs, reductio ad absurdum, he picked apart the “semi-logic” of the new abstract mathematics, mocking its weakness by taking these premises to their logical conclusions, with mad results. The outcome is Alice’s Adventures in Wonderland.

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