A lame lemma from Kaushik Basu

What would be the distribution of shops selling a particular commodity which everybody needs on a globe where population is

 uniformly distributed, that is, the number of people living within any two square kilometer spaces is the same?

The answer depends on the cost of travel and information acquisition. If both are zero, Location doesn't matter. If information is slightly costly and entry is sequential, all shops will locate in the same place. Why risk setting up in the boondocks if everybody thinks that all the shops are in the shopping metropole? After all travel isn't costly. If we assume that travel cost is a function of distance to the shop then what matters is whether travel cost is 'material' relative to expenditure. Suppose I am buying an aircraft carrier. The cost of visiting shipyards is not 'material' given the budget. Ceteris paribus, if entry is sequential and there is some information cost or other external economy, we will still see concentration. This is like 'Hotelling's law' which gets reinforced because of external economies of scope and scale. 

Basu, cretin that he is, takes a different view- 

Suppose on this globe there is a rotary or a circle.

The shortest path between two points on a sphere- called the geodesic- is always a segment of a 'great circle' (i.e. one which would cut the sphere in two equal parts) 

There are n stores that have to be located on this rotary,

is it a 'great circle' ? Basu does not say

and all customers prefer to go to the store nearest to their location (traveling along the globe)

in which case, if the rotary is a 'great circle', choice of store is uniquely determined. The relevant geodesic is orthogonal to the rotary. There is always one and only one 'shortest path' save at the two relevant poles. But it is unlikely that any person happens to be constantly hovering exactly over one or other pole  

and, when indifferent between k stores in terms of distance, each person chooses to buy from a store chosen by applying equal probability to all k stores.

This is nonsense. Basu is forgetting that there is a unique great circle between any two points on a globe. That segment which is is shortest is the geodesic. A few years after publishing this nonsense, Basu claimed that there would be no concentration because it is impossible for two stores to be at the same location. He should have used a notion of 'materiality'. Then, he would have seen that, for all practical purposes, a number of stores can be said to share a location.

The aim of each store is to maximize the number of customers, that is, the people who shop from the store. This paper is an analysis of where the stores will locate themselves. After all stores have chosen a location, I shall refer to that as a ‘placement’ of stores. A placement of stores is an equilibrium if, given the location of the other stores, no single store in that placement can do better by changing its location unilaterally.

But if changing your location can't worsen the outcome for you, why bother with location or 'placement'? The thing doesn't matter in the slightest. It isn't a Nash or other type of equilibrium any more than you deciding when to scratch your arse. 

There is literature investigating similar questions for cases where people live on a line or a plane. In some ways, it dates back to the early contributions to economic geography, such as von Thunen (1826).

which does not deal with a homogeneous terrain. 

Recently, in Basu and Mitra (2016), we tried to provide a characterization of Nash equilibria on a circle.

Anything at all can be a Nash equilibria if there is reason to fear that if you change your behavior somebody or everybody will fuck you up. The fact is that this is a 'optimal transport problem' (Monge-Kantorovich Transportation problem) and that will the basis of Muth Rational Expectations. 

Suppose the free market doesn't get to the cost minimizing solution, then, absent non-market constraints, there will be a process of merger and acquisition and 'internalization of externalities' till that convergence occurs- if the game is worth the candle.

The main aim of the present paper is to extend the analysis to the globe and develop a methodology for translating the globe to the circle,

In which case, you need to talk about geodesics.  

and then to establish some simple properties of Nash equilibria.

Absent market failure, the system will solve the Transportation problem- if it is worth doing. In this case, if travel costs are 'material', then you'd have distribution hubs and home delivery. 

Given that location problems and the analysis of electoral voting have some common mathematical foundations,

But Chichilnisky & Heal showed that there will be no coordination device- market based, voting based, administrative or otherwise- if there is no preference or endowment diversity. Basu assumed a homogenous population distribution and, implicitly, made geodesic distance the only item of diversity.  There would be literally nothing for a population of this sort to vote about.

it is hoped that this exercise will be of interest to those analyzing voting patterns and electoral politics, even though the problem is presented in this paper as an abstract exercise in geometry.

This is ignorant shit. 

The result established in the paper tells us about the largest stretch of consumers who may be left unattended by a nearby store in equilibrium

Either this doesn't matter to anybody, or else population won't remain homogeneously distributed.  

and, by analogy, the stretch of voters who may be left without any candidate offering a platform close to their ideal.

This is stupid shit. It would be like a very tall or short person complaining that the average or the median does not pander to their notion of what is a proper and respectable height. It is a separate point that a minority might be slaughtered by the majority. But in that case, there is a discoordination game- some people should be selling up and running away. Politics, in such cases, is a waste of time. A Bengali Hindu should understand that. 

The location problem described in the opening section has people staying all over a globe or a sphere and buying from the nearest store located on a rotary or a circle. The first result I want to establish is an equivalence. If the people, instead of being uniformly distributed on the sphere, were instead uniformly distributed on the rotary or circle where the stores are located, with the rest of the sphere uninhabited, the mathematical problem would be exactly the same. Indeed, there is a general principle regarding how any distribution (not necessarily uniform) on a sphere can be converted to an equivalent distribution on a circle and then for the analysis to be done on a circle.

There is a unique geodesic (save at the poles) to the 'rotary'. This is the one whose great circle is exactly orthogonal to the rotary. One can then see which shop is closest. 

How stupid are Basu's students if they don't know this? The following scarcely deserves the grand name of 

 general equivalence result. Start with any distribution of population on the sphere. It does not have to be uniform. It is easy to convert this to an equivalent distribution on the circle on which the stores are to be located so that a Nash equilibrium based on the distribution on the circle will be identical to the Nash equilibrium using the original distribution on the sphere. For this, the rule is the following. Move all the people on each relative longitude line to the 5 point of intersection of this line with the original circle. In Figure 1, this means moving all those on the circle through NJP to be relocated at J. If this is done for all points, the new distribution of population on the circle AJIB is, for purposes of Nash equilibrium analysis, identical to when people were living all over the sphere. In other words, we can, from now on, convert all location problems where people live all over the globe to a two‐dimensional analysis.

This is unnecessary. The 'rotary is one dimensional and every inhabitant (save at the relevant poles) has a unique mapping on to it. But firms don't have to locate on the same great circle. The actual solution to the transportation problem involves some sort of 'tessellation' or tiling pattern.  (e.g the multiplicatively weighted Voronoi diagram which is also called circular Dirichlet tessellation). But this is useful stuff- Bezos probably hires guys with PhDs in such things so as to make yet more money- not the useless shite that is Basu's stock in trade. Come to think of it, the billionaire Engineering & OR savant Purnendu Chatterjee must be about Basu's age. 

Fortunately, location analysis in two dimensions

or three since about the time of Gauss or, at least, Lobachevski 

has a long history, from Hotelling (1929) to recent times, such as Gulati and Ray (2015), Basu and Mitra (2016), and many contributions in between.1 Now, using this equivalence between the sphere and the circle,

The thing could be a straight line if the cut is made at the right place (i.e. equidistant between two store locations). But this is just the unique distance function. 

I shall prove two results, one new and one that appears in Basu and Mitra (2016) but is done somewhat differently here.

They are both nonsense. 

Given the result in the previous section, we can now pretend that all people live uniformly distributed along the circle, where the stores have to choose their location. We shall, for simplicity, assume that the length of the circle, that is, of the circumference, is 1 and the total population living on the circle is 1. So the number of people or customers living on an arc of length x is x. People buy from the nearest store. Each store’s aim is to maximize the number of customers, i.e., people who buy from the store. A ‘Nash equilibrium’ is a choice of location by all firms such that no firm can do better by making a unilateral move to another location on the circle.

Why the fuck would all stores locate on the same great circle? Either they all locate at the same spot or else there is convergence to the Muth Rational solution to the Transportation problem. 

Given a placement of stores on the circle and given any point, we refer to the maximum arc of the circle around that point with no stores (except possibly some stores at that point itself) as the ‘customer neighborhood’ of that point. A store is described as ‘isolated’ if there is no other store at the same point. It is useful for the uninitiated to hone intuition by checking that all locations are Nash equilibria when n=2. Suppose there are two stores, 1 and 2, located on the circle. If they are at the same point, everybody is indifferent between the two stores and so each store will get an expected half the customers.

But, by relocating to the 'antipode', that expectation- in this model- turns into a certainty (assuming travel cost is 'material') Even minimal risk-aversion does the rest. 

Let us now consider the case where 1 and 2 are in different places, as in Figure 2.

Then each expects half the total custom no matter where they are located. All that matters in this model is the geodesic distance which is unique and gives exactly half the population one and only one 'nearest' store. 

Let A and B be the midpoints on the two arcs between 1 and 2. Clearly, half the people living on the stretch between 1 and 2 on the eastern arc (the halfway point being marked by A) will go to 1 and half to 2. And half the people on the western arc will go to 1 and half to 2. Hence, half the entire population will go to 1 and half to 2.

This analysis is otiose. We arrive at the conclusion on the basis of the principle of maximal uncertainty or what obtains when we have no relevant information.  

Basu now gives us a foolish lemma

Lemma. If there is a placement of stores such that 3 or more stores are located at one point, then that placement cannot be a Nash equilibrium.

All stores can be located at one point.  What happens when a third store enters a market where the existing two firms are separated? The answer is that expected market share is one third provided the new entrant is equi-distant between the two existing firms & on a great circle orthogonal to the center of the geodesic between then . The fourth should also have this property and so on an so forth. There is a problem where entry is 'cascading' rather than sequential but the steady state involves tessellation.

Basu is writing nonsense because he didn't take the trouble to define geodesics and made the absurd stipulation that firms can only locate on the same great circle. Basu's proof relies on this arbitrary and foolish assumption. Furthermore, he is assuming sequential entry- which is silly. If you can enter a market so can anyone like you.  If entry is turbulent, there are certain conditions under which the right tessellation will be achieved quite quickly. If this is not the case there is a Muth Rational correlated equilibrium which can be implemented in different ways. It is foolish to think that Nash is the right solution concept here. The fact is, if there is net entry or exit then there is no steady state- least of all a Nash equilibrium. What Basu has written is puerile nonsense. Why has the World Bank published it?

The paper is meant to demonstrate the elegance and aesthetics of geometry on a sphere,

Calculating the shortest route 'as the crow flies' between two places on Earth is very very fucking useful. Elegance and aesthetics certainly characterize Algebraic geometry. Most kids find tessellation beautiful. Teachers often show slides of the Alhambra or the paintings of Escher to motivate their students.  

which can be used to understand the economics of location or economic geography.

Basu has understood nothing. He would later claim to have disproved Hotelling's law because two firms can't locate at the same point. He doesn't get that a few hundred yards distance is not 'material'.  

The one theorem that was proved, though new, is sufficiently easy not to constitute a challenge. This is one area where one does not need pre‐established results. I wanted to demonstrate that with one’s school geometry honed, one can be ready to take on problems as and when they come along.

Only if you make crazy assumptions- e.g all shops must be on exactly the same great circle. 

What was important was the equivalence claims in section 3, which shows that a large class of location problems on a sphere can be converted to a two‐dimensional exercise on a circle.

This is not true. There is a 'representation' of anything in the mathematical universe as anything else. But such conversions are only useful if they represent 'natural transformations' or solve a specific optimization problem.  

Honing the technique of analysis used here is important because it constitutes the abstract backdrop of understanding location economics and the political economy of electoral democracy.  

But Basu, in his long career, has learned nothing, understood nothing, illumined nothing. India , being an electoral democracy, has got the message. Mathsy Bengali economists know neither Math nor Econ. Moreover, even if the Dynasty puts in a Punjabi Economist as a figurehead PM, the markets won't be fooled by the hiring of Cornel Professors as 'Chief Economics Advisors'. 

James Wood on Martin Amis

This is James Wood on Martin Amis-

"Drop me down anywhere in America and I’ll tell you where I am: in America.”

America is vast. Large swathes of it are almost empty. How could one tell if one were in Alaska rather than Canada or Siberia?  What great difference in topography obtains across the Mexican border? Do the stars shine brighter or is the Moon a different shape? 

Perhaps Amis meant that he was ignorant of America and wished to stay that way. He didn't care to learn anything about it. Drop him down anywhere- Mount Rushmore, the Niagara falls, the Grand Canyon- and he'd shrug his shoulders and say 'how banal! Must America insist on being so tediously American?'

Perhaps you need to be a slight stranger to this country to formulate American ubiquity in this way—as comic tautology, as wry Q.E.D.

No. You'd need to be a shithead who thinks that just because all Americans- to some supercilious European snobs- seem alike, therefore that vast land must also be homogeneous in some declasse, if not vulgar or meretricious, manner.

Quite often, in the last twenty years, I’ve found myself driving along some strip development in Massachusetts or New York State, or Indiana or Nevada

or a British motorway or German autobahn

for that matter, and as the repetitive commercial furniture passes by—the Hampton Inn, the kindergarten pink-and-orange of Dunkin’ Donuts, Chick-fil-A’s chirpy red rooster—I’m suddenly seized by panic, because for a second I don’t know where I am.

Because, unless you are a highway patrolman, chances are you don't know precisely where you are. I frequently get lost on my morning walk down to the river at Hammersmith. For some reason I keep ending up at Parsons Green.  It's the sort of thing which makes you question your choice of Single Malt as a breakfast beverage. 

The placeless wallpaper keeps unfurling.

More particularly if you have been driving for hours and still haven't got out of the car park. 

And then Martin Amis’s sentence from his great early book of journalism,“The Moronic Inferno” (1986), appears in my mind, as both balm and further terror: well, wherever exactly I am, I’m certainly “in America.”

Though you may have crossed into Canada or Mexico- which isn't a clever thing to do if you are of my complexion and don't have your papers with you.

So at least I laugh.

White privilege! 

One definition of literary value might be the number of any given writer’s phrases or images that appear unbidden in the mind as you are just going about your day.

 That's not a definition. It is a metric. The Bible wins. 

For me, Amisian jokes and tags have for a long time made up part of the useful poetry of existence.

Amis believed that good poets are bad drivers. Novelists are good drivers. Amis didn't want to be remembered as a phrase maker like Fredrick Raphael. He had larger ambitions though what they were precisely none cared to discover.  

When I’m bored or otherwise unhappy about reviewing another book, those wicked lines about the book reviewer Richard Tull, from Amis’s novel “The Information” (1995), swing into view: “He was very good at book reviewing. When he reviewed a book, it stayed reviewed.”

Whereas when Woods now reviews a book what stays reviewed is our dim and fading memory of having thought he showed promise. 

I always wondered which Bengali Social Choice theorist Amis was sending up in that book. If it was Sen, Sen got the last laugh. 

Whenever I see a photograph of Saul Bellow, I recall, with a smile, Amis’s description of the American novelist as looking “like an omniscient tortoise.”

Bellow looked....light on his feet. Dapper, I suppose, would have been the mot juste.  

Still, a hunched nebbish wearing outsize horn-rimmed spectacles might- at one time- have answered to Kinglsey's mental image of James Michener or Arthur Hailey. 

Encountering smokers in contemporary novels or movies, I think often of John Self, the narrator of Amis’s novel “Money” (1984): “ ‘Yeah,’ I said, and started smoking another cigarette. Unless I specifically inform you otherwise, I’m always smoking another cigarette.”

I must admit I initially thought Will Self was an invention of Martin's. But Will thought he was an intellectual. The Amises may have had their faults, but that was a solecism they never committed. 

City pigeons, with their dirty gray necks like hoods? The wonderfully silly sentence from “London Fields” (1989) comes to mind: “The pigeons waddled by, in their criminal balaclavas.” Criminal balaclavas!

The SAS wore balaclavas. Thugs pulled nylon stockings over their faces and wore sheepskin jackets because they'd grown up watching the Sweeney. Amis had an international upbringing. He could easily have ended up as a big wheel in Hollywood. London was rather flattered that he chose to write about it. But he was less of it than Will Self.

Or what about that beautiful and complexly funny description, from the memoir “Experience” (2000), of how Amis’s large, ailing father, Kingsley Amis, fell to the ground on Edgware Road, in London: “And this was no brisk trip or tumble. It was a work of colossal administration.”

Colossal administrations collapse in slow motion- I suppose that is why the phrase is effective in context.  

Over the years, in our household, as my wife and I witnessed our own large, ailing fathers fail and fall, how many times did we recite to each other, as rueful comfort, as stinging recognition, and as saving comedy, those words: “a work of colossal administration”?

Colossal administrations are no match for God's mysterious economy. Economia, in this context, means management. I suppose the native English speaker catches nuances in the language which us Babus need spelt out. Sadly, 'White Guilt' means people like Wood will no longer help us in that regard. Instead they wax lyrical about stupid shit by the likes of Megha Mazumdar.  

Amis’s style combined many of the classic elements of English literary comedy:

or just comedy 

exaggeration,

monstrous exaggeration- i.e. a thing too big to serve its own purpose

and its dry parent, understatement;

dry nurse, maybe. A sense of weakness, of vulnerability, is what father's exaggeration. It is a childish quality which can be winsome. 

picaresque farce; caustic authorial intervention; caricature and grotesquerie; a wonderful ear for ironic registration.

you can have a ear for a particular vocal register and, by extension, a tone of voice. But registration- i.e. how somebody else is registering what is being said- is something we must intuit or guess at using 'theory of mind'. 

Take that phrase, “a work of colossal administration.” Sterne, Fielding, Austen—above all, Jane Austen—might have recognized its mixture of cruelty and mercy.

One may say to someone you love 'how did you manage to hurt yourself so badly?' The tenderness here is conveyed by suggesting that it would take considerable planning and coordination to defy Providence in so egregious a manner.  

The Austen of “Emma,” the satirist who describes the irritating Mrs. Elton’s large bonnet and basket as her “apparatus of happiness,”

her readers would have taken the use of the Latin word, rather than the more Gallic 'apparel', as itself putting the woman in her place- a job best left to another woman though, no doubt, there were plenty of good female Latinists at the time. 

would have seen exactly what Amis is doing here.

But so would everybody else.  

To fall to the ground massively, slowly, with great difficulty, is an act of labor that wins from the writer that cumbersome word “administration.”

But it fit well with the notion that colossal administrations collapse in a manner as monstrously slow and bureaucratic as the calamities they concoct. The Soviet Union collapsed. Sadly, the CDC did not. 

And the cool Latinate tease of it is funny. But it also hints, more tenderly, at what will be needed of us—our administration, as we struggle to lift the almost deadweight up off the street.

That is work, not administration. But God's mysterious economy is the invisible hand which does the real heavy lifting. Not bodies, it is our grief which no set of sturdy pallbearers can bear away.  

The entire drawling phrase ironically distances something that’s unbearably painful and intimate.

Unless irony is what we do for a living, in which case it is ready to hand as a small pleasure- like rage.  

Or take, as another example, a line from “Experience” that I often think smilingly of. It’s a sentence about travelling with Amis’s friend Christopher Hitchens, and how the two men had to stop regularly “for the many powerful drinks and the huge uneaten meal without which the Hitch could not long subsist.”

You're not an alcoholic if you order a big meal- right? You are a bon viveur, a gourmand, a Regency buck- not a deeply boring wino.   

That’s B-grade Amis, not especially flashy by his standards. But note the way that powerfully drinking

imbibing strong drink with shaking hands is not the powerful draining of the flagon by the bardic hero

and hugely not eating

If you aren't going to eat, why not show you can afford to order plenty of dishes?

comically balance and cancel each other out; and how the genius is all in that little word “long,” with its absurd logical contradiction of Hitchens subsisting—no, needing to subsist—on huge uneaten meals.

But the 'powerful drinks' were needful. It is often thus for those who outlive their promise.  

On page after page of Amis’s work, you find this kind of attention to the comic music, to the careful sardonic orchestration, sounded and built up word by word, that constituted his brilliant style.

Surely there is more to Amis than that? His style was influenced by the 'Martian' poetry of Craig Raine and Christopher Reid. But did it actually have anything to say? Nation may speak unto Nation to some good purpose but, as Reagan's America would discover, if Aliens make contact it is only to probe our rectums. 

But Amis was hard to make sense of as a literary presence, because he insisted on throwing fizzing decoys in the path of his reputation.

He insisted on being paid a fuck ton of money for a shitty book. 

The Englishman’s adoration of the foreignness of Saul Bellow and Vladimir Nabokov, the comedian’s yearning for seriousness and soul, the borrowing of deep “themes” (nuclear disarmament, the Holocaust, Stalinist terror, Islamic extremism)—these obsessions were all surplus to his true literary vitality, which was comic and farcical.

But none of his books was laugh out loud funny. Kingsley had Lucky Jim but Martin thought farce was beneath him.  For yucks you were welcome to go to Tom Sharpe. Clive James, I suppose, was witty and erudite. But, like Edmund Wilson, the guy learnt Russian. Come to think of it, Saki must have learned Russian. But he kept quiet about it. There's such a thing as trying too hard.

Like a number of postwar English writers, he chased after the things he flagrantly lacked,

whereas prewar English writers would chase after things they were desperate to get rid off 

idealizing the qualities he found most difficult, or was simply unwilling, to enact in his own literary practice.

Non Christians in this country find it difficult to understand how some native English writers can appear wholly immune to what is finest in their literature.  

(Iris Murdoch’s admiration for the vital and utterly free characterization of Tolstoy and Shakespeare might be another example of this odd English questing.)

It is very odd indeed to admire Tolstoy and Shakespeare unless, of course, you aren't English. Wood himself confines his adulation to the works of Benny Hill. Old Etonians can be very conventional in that way. 

How often, for instance, this most knowing, this least innocent of writers found himself praising—as if in mystified wonderment—the “innocence” of a Joyce or a Bellow.

Too often? Please Sir, is that the right answer?  

But Amis never sounded like a Jewish-American novelist who was almost born in Russia, or a Russian novelist who emigrated into his own estranged English.

who might that be? Nabakov? But Nabakov grew up knowing English. So did Madam Blavatsky. But she had a thick Yorkshire accent.  

He sounded like a funny English writer

who didn't want to be funny because that would be vulgar.  

very keen not to sound like his father, the comic novelist Kingsley Amis—

he wrote one funny book 

and this was all the delight his readers needed or wanted.

His readers suspected he might be smart. The sad thing is, he was smart. 

This writer who wrote so persistently about the “moronic inferno” of the modern (pornography, urban dreck, “America,” the brutal state of the British nation),

could at best aspire to the limbo of virtuosity 

whose novels seemed to abound in postmodern tricks (a novel told backward, walk-on parts for characters named Martin Amis, and so on) wasn’t really modern at all: stylistically, he came cackling and chortling right out of the eighteenth century.

No he didn't. The eighteenth century was a time of expanding horizons when ideas were being cast in Augustan marble. Amis's England was already too little to be usefully belittled.  

In fact, the modern writer that Amis most obviously resembled was quite far from the high pantheon of Bellow and Nabokov, though he was admired by both Amis and Hitchens.

and Waugh and T.H White. Rudyard Kipling praised 'Lord Emsworth and the girlfriend'. 

It was that muscleless magician, that popular purveyor of timeless comic fertility and posh silliness, P. G. Wodehouse.

This is foolish. Wodehouse owed much to WS Gilbert. His plots were all sinew and no fat. He was fond of egalitarian America but considered Dulwich a veritable Eden.  

The clues were littered all over Amis’s work. His first major novel, “Money,” posed as an Englishman’s wised-up attempt to “do” mid-nineteen-eighties New York, seen as a hellish but endlessly alluring island of strip clubs, pornography, and simmering racial unease. But the New York of “Money” isn’t Tom Wolfe’s painstakingly reported dystopia of the same era. It’s an endlessly amusing, wholly invented universe, a world stripped of actual reference and filled with in-jokes and mad wordplay.

It is shit.  

In “Money,” for instance, the city’s hotels are teasingly named after literary models (the Ashbery, the Bartleby, the Cymbeline).

It so happens that I am a very boring and stupid person. Nice English ladies would reproach me for my clumsy conversational overtures by suggesting I was being 'a tease' or, in one case, 'a wag'.  I suppose Wood is doing something similar here. 

Wodehouse invented a magical alternative slang for ordinary objects: in his Jeeves and Wooster stories, the head becomes the onion, the lemon, the bean, the coconut (“I was still massaging the coconut”); beard becomes fungus (“fumbling at the fungus”), and so on.

Wodehouse was doing musical comedy without the music. His Latinate syntax allowed the holding in place of complicated systems of assonance though the thing appeared as effortless as the warbling of a songbird intent on, as so many avians are, a career in Actuarial Science.  

Likewise, in “Money,” Amis swaps words for their sillier siblings: an apartment becomes “a sock” (“I peer through the spectral, polluted, nicotine-sodden windows of my sock”),

which is what good, corn-fed, American adolescents masturbate into 

hair becomes “a rug”

rug was always American slang for wig 

(“His hair was that special mad yellow, like an omelette, a rug omelette”), a bachelor pad (or bachelor sock, indeed) smells of “batch.” And so on.

Because Amis's style was so so.  

Amis wrote a great deal about the decay of the body, about violence, ill health, tawdriness, perversion, and historic nastiness of all kinds,

That's what happens when Narcissus becomes self-aware. His mother, it will be remembered, begged for him the boon of not knowing himself.  

but the atmosphere of systematic and high-spirited comic exaggeration always pulled the sting from his reality:

Otherwise he'd have been Tom Sharpe 

“Refreshed by a brief blackout, I got to my feet and went next door.” “Wearing only a cigarette, I fetched myself some orange juice.” There’s no real distress or danger

and thus no real comedy 

in Amis’s fictional worlds, only words: America is “America.”

and literature merely something that uses up office supplies.  

It’s why his best novel was also his most weightless, and the closest he got to replicating the campus farce made famous by his father in “Lucky Jim.” I mean “The Information,” his ridiculously funny book about literary rivalry and drudgery.

 Max Beerbohm understood mimetic rivalry. He said the last word on the subject back when books mattered and authors were as doves sent out from the Ark while yet waters covered the earth. 

In that novel, the hapless reviewer Richard Tull—he whose reviewed books stay firmly reviewed—finds himself on book tour with his old friend and rival Gwyn Barry, a much more successful writer. The two men are in America, and a stray, rapid, utterly gorgeous sentence is flourished to evoke the bewildering variety of bookshops that Richard will encounter in his swing through the States: “the bookshops he would come to know, the Muzaked and mallish, the underlit and wood-paneled and pseudo-Bodleiaic, the disco-Montparnassian.”

Disco-Montparnassian. . . . Only words? An Arden of words

Adam in Eden gave all things their names. It seems, what Ghalib said of India- that it is an Eden without an Adam- became true of an England shorn of its Empire- but only to its indigenous wits. But only if they didn't have no tits. J.K Rowling showed that the place was as ardent as ever for what Literature needs to save itself from becoming 'Literature'. Stories, good stories, stories which live and grow in the mind, are the hypokeimenon of the soul. Amis's oeuvre, at least in memory, was as but a horcrux of bile. No doubt, that is an unkind judgment. But being a couple of years older than Wood, I feel entitled to make it. The London Amis described was no 'stony-hearted stepmother' to those who possessed talent regardless of gender or color or class. We have all profited from their flourishing.  I myself, thanks to Amazon, can now sell you a book more toxic to read than any Amis could have fathered on Richard Tull. This may not seem a great achievement. The thing is little enough but it is mine and mine alone. 

Jason Stanley's context-independent cretinism.

Why did Jason Stanley turn into a virulently woke cretin?  Was it because of sinister forces operating on Campus? That may be part of the answer. However, bad logic- the 'intensional fallacy' in particular- had already vitiated the entire project of Analytical Philosophy. 

The fact is, when using a word whose meaning diverges- on the basis of our knowledge level or 'epistemic state', from all that it might be said to designate- claims re. sufficiency & necessity are vitiated for two different reasons. In the case of sufficiency, correlation or 'Granger causality' may provide an empirical or inductive justification for the claim. In the case of necessity, the thing is impossible for a sentential operator, unless there is a Truth predicate in the first order language. But, in that case, we have taken leave of  Tarski and are in an Intuitionist or Gentzen type realm. Nothing is gained over the formalism where Necessity is a predicate because the thing is otiose or an example of 'modal collapse'. One may as well be an Occassionalist and say, 'God is the only efficient cause. All that is, necessarily is, coz that's what God wants.' This is fine and dandy coz we know that nobody knows the mind of God. There is some spiritual humility to Occassionalism. But, if this essentially theological argument is used by atheists- you get a paranoid, totalitarian, ideology whose proponent gradually convinces herself that she and she alone has the  power of 'strong Kleene evaluation' or (δοκιμασία‎) dokimasiai, which determines eligibility for every class or category whatsoever.

If you believe this crazy shit, you will soon start thinking you can tell that all sorts of non-Fascists are actually Fascists and that they are probably setting up Gas Chambers all over the place even as we speak.

As a case in point, some 20 years ago, Jason Stanley wrote

Contextualism in epistemology is the doctrine that

the predicate 'knows' is context sensitive. The alternative is that 'knows' is either necessarily true or necessarily false regardless of context. But, for the reason given above, this can only be the case if there is 'modal collapse' in which case everything is necessarily necessarily necessarily true unless it is necessarily necessarily false. 

Alternatively, truth can be a first order predicate in a Gentzen type or other 'natural deduction system' with 'witnesses' or 'zero-knowledge' proofs (verifications). 

But any 'univalent foundations' or category theoretical approach will have this feature. The problem is that either 'knows' is 'primitive'- i.e. undefined rather than context sensitive- or else there is an infinite regress and so nobody 'knows' what contextualism really is. 

the proposition expressed by a knowledge attribution relative to a context is determined in part by the standards of justification salient in that context.

This is not contextualism. It is determinism of some sort. But 'standards of justification' only tell us what is justified not what is known. We know plenty of stuff which we wouldn't dream of going to the trouble and expense of justifying. Stanley is illicitly trying to replace 'contextualism'- which is fairly common sensical- with some absurd type of determinism whereby what can be justified magically determines what can be known. This means Jason can get to pretend that protocols of justification determine what is knowable. Thus if the law changes such that a particular type of evidence is no longer admissible, suddenly a rapist will no longer know he was raped by such and such Spice Girl despite having found a lot of evidence on Pornhub that something of that sort might well have happened.

The (non-skeptical) contextualist allows that in some context c, a speaker may truly attribute knowledge at a time of a proposition p to Hannah, despite her possession of only weak inductive evidence for the truth of that proposition.

No. A contextualist would not say 'truly'. They would qualify their assertion in some suitable manner- e.g. saying 'in a particular context or 'for a particular purpose', a speaker may consistently, or un-controversially, make such and such attribution.  

Relative to another context, someone may make the very same knowledge attribution to Hannah, yet be speaking falsely, because the epistemic standards in that context are higher.

Or lower or non-existent. In some context, every statement is true or false or meaningless or not a statement at all.  

Still, Jason is admitting that 'knowledge attribution' is 'intesional' and 'epistemic'- i.e. we don't know the 'extension' of the term because knowing is about discovering more about that extension. True, such knowledge may be arbitrarily 'buck stopped' by some particular system of protocols or else, be conjectured to have 'naturality' for some particular purpose.  But outside that specific context, 'knowledge attribution' does not obey Liebniz's law of identity. We can't perform any logical operation on it. To do so would be to commit the 'masked man' or 'intensional' fallacy. 

The reason this is possible, according to the contextualist, is that the two knowledge attributions express different propositions.

No. A contextualist is not committed to a belief that propositions are atomic or that they change when contexts change. Nor do they necessarily think justification matters at all save contextually and for some specific purpose.  It is a different matter that some person Jason considers a 'contextualist' believes, according to Jason, stupid shit. But this is an arbitrary assertion. 

The main advocates of contextualism

are not knowable till the end of time.  

have used the semantic doctrine of contextualism

which is that there is no sematic doctrine for contextualism. The thing may be pure pragmatics. 

to defend a certain response to the problem of skepticism. According to it, the force of the skeptical paradoxes is due to

our reluctance  to slap skeptics silly before telling them they imagined the whole thing and thus should not go crying to Mummy.  

the presence of unrecognized context-sensitivity in the language.

or our recognition that stupid people talk bollocks.  

When we are not discussing with skeptics, many of our ordinary knowledge attributions are true, because what is there at issue is a less demanding sense of knowledge.

No. What is at issue is utility. Pragmatics is about doing useful things.  

But the consequence of engagement with the skeptic is that the content of knowledge attributions shifts in a manner that is not recognized by the interlocutors.

Only if they are as stupid as shit. It is obvious that some sort of type theory applies. It just may not be worth our while to find out which one does.  

In such a “skeptical” context, knowledge attributions that may previously have expressed truths now express falsehoods.

Nope. They were propositions and propositions they remained. The predicate applied to the proposition may change from- 'true and verified as true', to 'true but not verified to be true', or 'probably true' etc, etc.  

The contextualist therefore seeks to explain the force of skeptical arguments by appeal to a feature of ordinary language.

Only if the contextualist is as stupid as shit or is being paid to talk bollocks. 

It is because knowledge-attributions are context-sensitive that we are fooled by skeptics into thinking that even in non-skeptical circumstances, many of our knowledge attributions are false.

No. There is no necessary connection between Knowledge and Justification or Proof or anything else. Why accept another's arbitrary stipulation when you can suggest that they only make it because they habitually devour dog shit?

Jason considers the following scenario created by Keith DeRose which does not deal with knowledge claims but rather with expectations.

Hannah and her husband are driving home on a Friday afternoon. They plan to stop at the bank on the way home to deposit their paychecks. But as they drive past the bank, they notice that the lines inside are very long, as they often are on Friday afternoons. Thinking that it isn’t very important that their paychecks are deposited right away, Hannah says “I know the bank will be open tomorrow, since I was there just two weeks ago on Saturday morning. So we can deposit them tomorrow morning.” But then Hannah’s husband reminds her that a very important bill comes due on Monday, and that they have to have enough money in our account to cover it. He says, “Banks do change their hours. Are you certain that’s not what is going to happen tomorrow?” Hannah concedes, uttering “I guess I don’t really know that the bank will be open tomorrow.”

Nobody does. The world may end tonight. Hannah's confidence in her expectations has decreased for a 'regret minimizing' reason. This is a story about expectations and risk aversion.  

This sort of example supports contextualism about knowledge ascriptions,

there are no 'knowledge ascriptions' here. It is obvious that we are merely speaking of expectations.  

because it suggests that the propositions expressed by one and the same knowledge-attribution may differ with respect to two different contexts of use, even though the two contexts are identical in all respects relevant for fixing the values of obvious indexicals. Here is the example in more detail. Consider a sentence like (1), as uttered by Hannah in the first situation: (1) I know that the bank is open tomorrow morning.

Nope. The sentence should be 'I know the bank was open last Saturday and all preceding Saturdays. I expect it will be open tomorrow'.  

Before she realizes the importance of having a bank account flush with resources by Monday, she utters (1). What she utters expresses a proposition that seems perfectly true.

No. We all know that the future hasn't yet happened and may not happen. We may expect something to happen but we don't know it will have happened.  

The proposition concerns a particular time, namely the next morning. She is then informed about the pressing need for a full bank account. She then utters: (2) I guess I don’t really know that the bank is open tomorrow morning. Again, it looks like Mary has expressed a proposition that seems perfectly true, one that concerns the same time as the proposition expressed by her previous utterance of (1). But (2) looks to be the denial of (1). If we take these intuitions at face-value, we obtain a contradiction.

No we don't. We know that the future hasn't happened yet. We don't know shit about it. But we do have expectations regarding it. For regret minimizing reasons we can alter our behavior even without any change in our 'Bayesian priors' simply because we are highly risk averse with respect to catastrophic outcomes. In this particular case, Hannah is also aware that the are all sorts of other reason why, even if the Bank is open tomorrow, she won't be able to deposit the check. Ultimately, if the couple drive back and wait in line at the Bank, it is because they want to avoid the discomfort of an anxious night.

Here are the two basic options one has to respond to this problem: (a) One can reject the semantic significance of one of the two intuitions. For example, one could deny semantic significance to the intuition that the proposition semantically expressed by Hannah’s utterance of (1) is true.

Words have been forced into Hannah's mouth. She is more likely to have said 'Hey, we can bank our checks tomorrow. I remember doing so on a Saturday morning.' She wouldn't have made a knowledge claim coz the rejoinder would have been 'who has seen tomorrow?' or words to that effect.  

 For the contextualist, then, knowledge relations come in higher or lower “strengths.”

No. Confidence in knowledge claims may have this property. Knowledge relations don't. 

Knowledge attributions are thus comparable to context-sensitive gradable adjectives, such as “tall” and “flat”.

But Epistemology is about knowledge attributions about knowledge attributions. The word fat isn't itself fat. We say 'x is fat' or 'x knows calculus' and that is fine if x is actually overweight and really knows calculus. There are grades of fatness and grades of knowledge of calculus. But there is no change in how fat relates to thin or 'knows' relates to 'ignorant of'. Thus knowledge relations aren't gradable. But some predicates have that feature. 

An attribution of tallness is sensitive to a contextually salient scale of height, as is an attribution to flatness. If what is at issue are basketball players, then that brings in one rather high standard for “tall”; if what is at issue are fifth-graders, then that brings in a considerably lower standard for “tall”. In this sense, one could speak of tallness relations coming in higher or lower “strengths” as well.

Nonsense! We don't compare fifth graders to basket ball players. A tall basket ball player stands in the same relation to a short baseball player as a tall fifth grader to a short fifth grader. 

IS “KNOW” GRADABLE? Contextualists typically tell us, when introducing the thesis, that it wouldn’t be at all surprising if predicates such as “knows that Bush is president” turned out to be context-sensitive in the ways they describe.

Sure. An old guy who thinks Bush Snr. is the current POTUS might be suffering from dementia.  

After all, we are told,

by homeless people- right?  

many natural language predicates are context-sensitive.

Coz that's how language works. 

As Stewart Cohen (1999, p. 60) writes: Many, if not most, predicates in natural language are such that the truth-value of sentences containing them depends on contextually determined standards, e.g. ‘flat’, ‘bald’, ‘rich’, ‘happy’, ‘sad’. ... These are all predicates that can be satisfied to varying degrees

not in natural language. There has to be some protocol bound discourse aiming at some specific objective for 'satisfiability' to arise. 

and that can also be satisfied simpliciter.

Nope.  Acceptation is not the same thing as satisfiability. 

So, e.g., we can talk about one surface being flatter than another and we can talk about a surface being flat simpliciter.

Nothing is perfectly flat. Einstein bent everything.  

For predicates of this kind, context will determine the degree to which the predicate must be satisfied in order for the predicate to apply simpliciter.

Nope. Context won't be enough. Knowing what coordination or discoordination game is going on is not enough to determine anything.  Knightian uncertainty is a feature of language. That's why semantics is shite. Still, the fact is we say 'I know Smith' if we've met Smith. We aren't saying we know much about him. Clearly that's 'gradeable'. But 'knowledge relations' aren't gradeable. Knowing Smith means saying Hi to Smith and Smith saying Hi to you. Knowing him well means something more- e.g. predicting what birthday present he'd like. 

So the context will determine how flat a surface must be in order to be flat.

No. We might ask 'how flat must a microchip be in order for it to simulate a particular type of anyon interaction?'. The context may be that of competitive enterprises in a high-tech branch of the engineering industry. But the answer might come from some arcane branch of String Theory.  On the other hand, it might turn out that the question is meaningless from the scientific point of view. Still the Marketing Department might latch on to it and run a campaign claiming that the superior flatness of the company's microchips means that it will very soon corner a lucrative market. This may boost the stock price. 

There is a great deal of evidence for Cohen’s claim that there is a kind of predicate, of which ‘flat’, ‘bald’, ‘rich’, “happy”, and “sad” may occur as a constituent, the semantics of which involve degrees or scales.

Only if there are specific purposes for which protocol bound metrics are established. But that is a utilitarian, not a semantic, consideration. Indeed, language may be wholly disintermediated from the validating process. A machine may reject microchips which aren't flat enough. Sad people may kill themselves without anybody ever describing them as sad. The fact may only become known at the inquest.  

The reason that contextualists appeal to such predicates is so that, given their frequency in the language, the claim that “know” is a predicate of this kind will be unsurprising.

These guys are academics. They set exams to discover how well their students 'know' the stupid shite they teach.  

How good is this prima facie case for contextualism about “know”?

It is as good as any other stupid shite these guys babble about.  

The predicates mentioned by Cohen – the “kind” of which he speaks in his second to last sentence, are not a disjunctive sort.

They can be disjunctive. In India we speak of 'tall leaders' who, generally speaking, are rather short and squat.  

They are gradable adjectives.

Anything can be gradable for some particular purpose. The Nicaraguan horcrux of my neighbor's cat is more clammy than its Guatemalan horcrux- which is actually quite surprising if you think about it.  

Most of the gradable adjectives listed by Cohen are (I believe) context-sensitive, such as “flat”, “tall”, and “rich”.

They may be interpreted as such. But they could also be seen to be a subpoenas issued by the DOJ to the Nicaraguan horcrux of my neighbor's cat.  

In talking about buildings, “is tall” may express a property that it doesn’t express when talking about people.

Or the reverse may be the case. 

Furthermore, this sub-class of gradable adjectives are context-sensitive in just the way that Cohen and DeRose claim that knowledge-ascriptions are.

An adjective is just a word. It isn't sensitive at all. It is a different matter that the word can be used with a degree of precision for some useful purpose. But, speaking generally, a loose, discretionary, 'economia' is better than rigid 'akreibia'.

According to Cohen and DeRose, knowledge-ascriptions come in varying degrees of strength.

No. A knowledge ascription is merely a bunch of words that is interpreted as such. There are people who say 'you know deep down that you want to suck me off. Why not just do so already? Must we play mind games?'  We don't consider them to be making 'knowledge-ascriptions'. They merely want a b.j. 

In other words, knowledge-ascriptions are intuitively gradable.

No. They are merely a bunch of words. Our intuition only comes into play where some purpose of our own is served.  

Contextualists speak, as their theory suggests, of higher and lower standards for knowledge.

But those standards are arbitrary assertions. The epistemology attached to a discipline is not itself part of that discipline.  It is stupid, arbitrary, shite.

Gradable adjectives are the model for gradable expressions.

Everything is gradable for some specific purpose. So what?  

It is therefore no surprise that epistemologists since Unger (1975, Chapter 2) and Lewis (1986) have been exploiting the analogy between “know” and context-sensitive gradable adjectives such as “flat” and “tall”.

Adjectives solve coordination games. They give information about Schelling focality. But hedging on discoordination games may also occur.  

But, as I will argue in this section, the attempt to treat “know” as a gradable expression fails.

Not if it is useful. Pragmatics matter. Semantics is stupid shite.  

This casts suspicion upon the contextualist semantics for knowledge ascriptions. First, it shows that one cannot appeal to the context-sensitivity of words like “tall”, “flat”, and “rich” to justify the context-dependence of knowledge-ascriptions.

But Jason just mentioned a couple of guys who do exactly that! I suppose he means 'one should not appeal to xyz'. But 'should not' does not mean 'can not'.  

Secondly, it casts doubt upon the claim that knowledge comes in varying degrees of strength, a core claim of contextualism.

Claims about knowledge aren't knowledge. They are stupid shit. The context is the utter cretinism that prevails in Jason's own branch of Psilosophy.  

There are two linguistic tests for gradability.

But grading can be done by machines! Jason & Co may have to hand out grades to cretins so as to get paid. Do they use 'linguistic tests'? Perhaps. But the test may involve asking for a b.j.  

First, if an expression is gradable, it should allow for modifiers.

Anything at all 'allows for modifiers'.  

For example, predicative uses of comparative adjectives allow for modification, as in: (5) a. That is very flat. b. That is really flat. c. John is very tall. d. John is really tall.

But the predicative use of meaningless terms also allows for modification- e.g. 'Uqwkqw is very tall' or 'tall is very uqwkqw'. 

Secondly, if an expression is gradable,

e.g  Uqwkqw which is less meaningful than Urquharty

it should be conceptually related to a natural comparative construction.

there are no 'natural comparative constructions'. Category theoretical 'naturality' is probably a chimera- we can't be sure. 

What obtain are focal solutions to coordination games. But it is sensible, or regret minimizing,  to hedge on a discoordination game.  

So, for “flat”, “tall”, and “small” we have “flatter than”, “taller than”, and “smaller than”.

just as we have more Urquharty or less Uqwkqwian. 

Both of these features are to be expected, if underlying the use of the relevant expression is a semantics involving degrees or intervals on a scale.

Semantics doesn't underlie shit. Utility does. For some specific purpose, the pragmatics of an expression- even one whose meaning is unknown or unassigned- may be protocol bound in a mertrizable manner. Thus an AI may look at the use of the word and come to formulate an 'intension' for it. It often happens that a term of disapprobation- e.g. 'Tory' which originally an Irish Catholic Rebel-  comes to have a positive meaning for those originally slandered by its use. 

For instance, the semantic effect of a modifier such as “very” on a word like “tall” is to increase the contextually salient degree on the scale of height that an object must exceed in order to satisfy the predicate.

Nonsense! We Indians may have said 'Kharge is a tall leader'. Now, since Kharge engineered a stunning victory in Karnataka, we say 'Kharge is a very tall leader. Sadly, Congress has a tall poppy syndrome. Who wants to bet the fellow won't be abandoned and ignored this time next year?' 

The claim that knowledge ascriptions are gradable fits elegantly into the contextualist explanation for, say, DeRose’s bank case discussed in the previous section.

What mattered in that case was ignorance ascriptions. Nobody knows what tomorrow will bring. Don't procrastinate.  

For in Hannah’s final utterance, she claims that she does not really know that the bank is

will be, not is 

open. It is natural to read “really” here as a degree modifier, as in the examples in (5).

Nobody really knows what will happen tomorrow. We have expectations, not knowledge.  

That is, it is natural to read this discourse as providing evidence for the gradeability of “know”. Over the course of the discourse, Hannah asserts that she knows that the bank is open,

will be open. Hannah is talking about the next day 

but also asserts that she doesn’t really know that the bank is open.

will be open. 

That is like someone asserting that Bill is tall, but conceding that Bill is not really tall.

No. It is like someone asserting that Bill is tall today. Tomorrow, he will be short because the person making the assertion is a maniac and plans to cut off Bill's legs tonight. 

But the explanation of the bank case that appeals to the gradability of knowledge is not correct.

Because we don't know the future. We have expectations about it.  

As the above example suggested,  negations of degree-modifier uses of “really” can be conjoined with assertions of the unmodified forms without inconsistency: (6) a. John is tall, but not really tall.

He is tall in one sense but not in another sense which is more 'real'.  

b. Michigan is flat, but not really flat.

because of the curvature of the earth. Also it does have some hills.  

In contrast, the same facts do not hold of the use of “really” when appended to a knowledge-ascription (“#” expresses oddity): (7) # If the bank is open, then John knows that the bank is open, but doesn’t really know that the bank is open. The sentences in (6) are perfectly natural. In contrast, (7) is very odd.

It may be or it may not be. It may be part of John's duties to verify that the Bank is open before sending his assistant with the day's cash receipts to the branch in question. Here 'really knows' means 'verified according to set protocols'. As a matter of fact, the Bank branch was open and so no great harm was done. Still, John may receive a rebuke from his Supervisor who warns him to be more scrupulous in future.  

This suggests that the “really” that occurs in the above description of the bank case is not a degree modifier.

Yet, there is an easily imaginable scenario where it was in fact a modifier.  

Indeed, prima facie, propositional knowledge ascriptions are not gradable.

The reverse is the case because of verification protocols. As a private individual, John is welcome to treat 'expectations' as 'knowledge'. But, his terms of employment, may require him to do verification in his official capacity.  

First, knowledge ascriptions do not seem to allow for modification: (8) a. *John very knows that penguins waddle.

This may not be grammatical but we understand that there has been an elision of 'well' after 'very'.  

b. *John knows very much that penguins waddle.

the elision is 'about penguins and thus knows'  

Second, there is no natural comparative conceptually related to “know”.

Yes there is. Knowledge and verification go together.  

The following locutions are deeply strained: (9) a. ??John knows that Bush is president more than Sally knows it.

But this is perfectly informative. John is passionate about American politics. Sally is currently off her head on ayahuasca and has been living in a commune in Brazil for the last twenty years.  

b. ??Hannah knows that Bush is president more than she knows that Clinton was president.

Coz Hannah is five years old. 

If the semantics of “know” did involve scales, it would be mystery why there wouldn’t be a comparative form of “know” available to exploit the scale.

but there was for the older, more inflected, Indo-European term from which it evolved. Some older folk still use terms like cannier or canniest. 

It has been noted before that ascriptions of propositional knowledge are not gradable (cf. Dretske, 1981, Chapter 5).

Yet Jason & Co spend a lot of time giving out grades on the basis of which student has more or less of the stuff.  

However, the data surrounding knowledge ascriptions is more complex than these prima facie considerations suggest.

No. Data is simpler than the inchoate notions with which we approach a subject. 

There are several constructions that suggest that knowledge ascriptions are, despite initial appearances, gradable. In the remainder of this section, I provide a complete case that knowledge ascriptions are not gradable,

but that case must be 'non-informative' or wholly imperative and arbitrary, otherwise it could itself be graded.  

and draw some morals for contextualism about “know”. One might think that knowledge-ascriptions are gradable on the basis of the obvious felicity of the following sort of construction: (10) a. John knows Bill better than Mary does. b. Hannah knows logic better than John does. But in the sentences in (10), “know” does not express a relation between a person and a proposition. These sentences are not propositional knowledge ascriptions; rather the occurrences of “know” in them express the acquaintance relation, what would be expressed in German by “kennen” rather than “wissen”.

This became 'ken' and 'wot' in older forms of English with the former relating to perception and the latter referring to understanding. But, in this case, neither is relevant.

There are a number of facts about Bill and there are a number of facts about Logic. John knows more facts about Bill while Hannah knows more facts about Logic than John. This is because John and Bill are sharing a prison cell. Hannah is a Professor of Logic and Epistemology. It may be that Hannah says 'I think Logic is completely empty. It has zero informativity. There is nothing in it to understand' whereas John thinks that logic can prove he was innocent of the murder for which he has been sent to jail. After all, Bill can testify that John was on a spaceship being anally probed by Aliens when the murder took place.  

It is only the gradeability of propositional knowledge ascriptions that is at issue in contextualism in epistemology.

If knowledge was 'extensional' and intrinsic to the subject of knowledge, we wouldn't need contextualism. It is right and proper to kill everybody from a particular minority because each and every one of them, regardless of any evidence to the contrary, is obliged by their detestable religion to kill and eat Christian children once every week. You may say, 'in the context of winning the war, why devote scarce resources to gas chambers?' This proves you are yourself descended from those evil cannibals.  

However, “know” can marginally occur with “very much” or less marginally with “very well”, as in: (11) a. ?I very much know that Bush is president. b. I know very well that Bush is president. But it is doubtful that these occurrences of “very much” and “very well” are genuine semantic modifiers of the knowing relation, rather than pragmatic indicators.

Pragmatic indicators can get baked into the semantics of the 'ideal speaker'.  

In this sense, these constructions are similar to: (12) 2 is very much an even number.

No. When it comes to such numbers, there is Kripkean 'buck stopping' and a well defined extension.  No number is more even than any other. Intensional objects have an epistemic component and can be graded on the basis of verification. 

Decisive evidence for this comes from several sources. First, note the unacceptability of negating the constructions in (13): (13) a. *I don’t know very much that Bush is president.

Again this is a case of elision. The person may be understood as saying 'I don't know very much about American Politics, Indeed, I'm not even sure Bush is the President. '  

b. *I don’t know very well that Bush is president. The unacceptability of the sentences in (13) contrasts with the naturalness of negating the verb phrase in a case in which “very much” is clearly modifying the verb: (14) I don’t like Bill very much.

Here 'very much' tones down the informational content. It makes you appear polite and civilized. It isn't that you dislike Bill. It's just that you don't lurve him as a Christian should.  

Secondly, “know” is only with great awkwardness combined with “very well” in non-assertoric speech acts. Contrast the sentences in (15) with (16): (15) a. ??Do you know very well that Bush is president?

I suppose there are some people in America who think Trump is the actual President. Biden is illegally squatting in the White House. People of this sort may know all sorts of things 'very well'. The mentally ill often do.  

b. *Do you know very much that Bush is president? (16) Do you like Bush very much? So, the sentences in (11) are clearly not cases where the degree of knowing is operated on by “very much” or “very well”.

There are people who know very much about how Biden stole the election from Trump who is the genuine POTUS.  

Defenders of contextualism might hold that “better than” rather than “more” is the comparative relevant to “know”, as in (17) Hannah knows better than anyone that she is poor. But here again, the construction means that Hannah is familiar with the fact more than anyone else – e.g. she lives with the consequences.

Not necessarily. Hannah has a PhD in Poverty Studies. She is currently working long hours for less than minimum wage in the hope of getting tenure. She actually knows better than anyone else that by every metric in current use, she is classed as 'poor as shit'.  

4 More importantly, “better than anyone” is idiomatic. For example, consider the oddity of: (18) a. ??Hannah knows better than three people that she is poor.

Those are the three people blocking the pay rise Hannah is demanding for people like herself. The irony is that they are all tenured Professors of Woke, Virtue Signaling, shite.  

b. *Hannah doesn’t know better than anyone that she is poor. So, “better than anyone” is an idiomatic construction, one from which we can infer little about the semantics of “know”.

The opposite is the case. We can infer that the semantics of know implies that it is gradable  

Furthermore, none of the non-philosopher informants I asked found the following acceptable, though they disagreed amongst themselves which was worst: (19) a. ??John knows that Bush is president better than Mary does. b. ??John knows that Bush is president better than Bill knows that Clinton is a Democrat. Furthermore, all of my informants reported a strong difference in acceptability between these sentences, on the one hand, and the perfectly acceptable: (20) a. John likes Bill more than Mary does. b. John likes Bill more than Mary likes John.

Physicists often ask non-physicist informants whether they think an anyon based String Theory would be better than one which features Cheese straws.  

So “better than” is not a natural way to express comparisons between levels of epistemic position with “know”.

It is perfectly natural to say 'I know x better than you'. Incidentally, philosophers are supposed to know philosophy better than non-philosophers. Then the discipline turned to shit. It became adversely selective.  

If the semantics of “know” did involve scales of epistemic strength, then there should be uncontroversially non-idiomatic comparisons and modifications.

Schools and Universities grade students on the basis of 'epistemic strength'. The thing isn't 'idiomatic'. It is nomothetic and protocol bound- though absurd in the case of worthless disciplines.  

6 One might think that these facts about ‘know’ have syntactic rather than semantic explanations. Perhaps sentences like (8) and (9) and those in (13) are deviant because verbs that take sentential complements grammatically do not allow for comparisons or intensifiers.

Syntax is about protocol observance. But protocols may be non-linguistic. For a specific purpose, everything may be gradable.  

But consider “regret”, a factive verb in the same syntactic category as “know”: (21) a. Hannah very much regrets that she is unemployed.

There is a large technical literature on 'regret minimization'. Hannah, sacked from the University for being a TERF- she used a Feminist pronoun to refer to herself- shows more regret than any of her colleagues who were also sacked for the same offense. How do we know? The answer is that Hannah alone is undergoing gender reassignment surgery. 

b. Hannah doesn’t regret very much that she is unemployed.

Because she is part of a class-action suit which will soon see her rolling in moolah. Also not having to teach cretins is a big relief.  

c. Hannah regrets very much that she is unemployed. d. Hannah regrets that she is unemployed very much. Here, the degree of regret clearly seems to be modified by “very much”. Furthermore, “regret” easily allows for comparisons:

Coz that's how words work. 

(22) Hannah regrets that she is unemployed more than she regrets that she is unpopular.

Hannah knows she is unemployed more than she knows she is unpopular because she smells like shit. Could somebody please have a quiet word with her?  

This shows that the lack of straightforward comparatives or degree modifiers has nothing to do with the syntax, or even the factivity, of “know”.

The reverse is the case. I know more about this than you. I regret this more than you do. This hurts me more than it hurts you. 

There are syntactically similar expressions whose link to degrees and scales is far more plausible.

There is always some scenario where it is plausible that to say 'John is more urquharty than Bill' is meaningful and will get you a reputation for sagacious and incisive social observation. 

It is also worth mentioning that other expressions upon which one might be tempted to base the context-sensitivity of “know” are, unlike “know”, also gradable. So consider epistemic modals.

Epistemic modality is the kind of necessity and possibility that is determined by epistemic constraints. Sadly, no such constraints are necessary or possible. Epistemology isn't knowledge. It isn't informative. It is a waste of time. 

A contextualist might understandably wish to appeal to the apparent context-sensitivity of epistemic modals to justify the apparent context-sensitivity of knowledge-ascriptions. But one problem with this strategy is that epistemic modals, unlike knowledge-ascriptions, are intuitively gradable:

No. They are useless and stupid. There are no synthetic a priori judgments. Phenomenology is tomfoolery.  

(23) a. It is very likely that I will publish more papers on this topic.

This is not an 'epistemic modal'. It is a statement about a future action which is not constrained by any epistemic considerations. Most philosophy papers are shit. Whether a particular shithead publishes more worthless shite has to do whether a particular Academic Ponzi scheme can keep drawing in suckers. 

b. It is more possible that Hannah will become a philosopher than it is that she will become a mathematician.

Because philosophy is adversely selective.  Also the subject lends itself to virulent wokeness. 

So the analogy between epistemic modals and “know” is almost as strained as the analogy between context-sensitive gradable adjectives and “know”.

We know epistemic modals are shit. We know that adjectives are 'context sensitive'. That's what makes them useful. 

The evidence concerning gradeability is more complicated when one considers the deverbal adjective “known”.

No. What was known is like what is known and what will be known. New data can throw anything into doubt.  

But even here, there does not appear to be a good case for a semantics involving a scale of epistemic strength.

Yet, we say things like 'it was well known in ancient Greece that a Tyrant might manage things better than a Democracy would have done'. New data may prove us wrong. A trove of Celtic runes is discovered in Galicia. It turned out that Celtic spies had been closely monitoring public opinion in various Greek polities. It turns out that the texts on whose authority we relied were known to have been composed for money by desperate savants.  

This adjective, unlike its verbal relative, does give rise to comparisons and modifications. But they are not of the relevant sort. So, for example, consider: (24) a. That broccoli is low-fat is better known than that broccoli prevents cancer. b. That broccoli is low-fat is well known.  (24a) does not mean that there is more evidence that broccoli is low-fat than that broccoli prevents cancer; rather, it means that the fact that broccoli is low-fat is more widely known than the fact that broccoli prevents cancer.

It may mean precisely that. What matters is the context. If a professional scientist is speaking, we assume that hard and fast scientific evidence is being discussed. If the remark is made by some vegan Trustafarian at a dinner party we assume that what is being remarked on is the beliefs of that section of the population which gives credence to the thaumaturgic powers of Crystals. 

Similarly, (24b) means, not that there is a lot of evidence that broccoli is low-fat, but that it is widely known that broccoli is low- fat. Evidence for this hypothesis comes from the fact that while (25a) is perfectly acceptable, (25b) sounds quite odd: (25) a. That broccoli prevents the flu is well-known, but illunderstood. b. ?That broccoli prevents the flu is well-known, though few people know it.

In context, we can repair the above sentence to read 'well established scientifically though few are aware of the result' possibly because of the mischievous activities of Big Meat, not to mention the scoundrels who sell Cough Syrup.  

Furthermore, as Tamar Gendler has pointed out to me, instances of (26) are quite odd: (26) It is well known that p, and less well-known that q, but more people know that q than know that p.

In context, we can repair the sentence to read 'p is well established' but this truth has been kept from most people  

This data is explicable on the assumption that the only available reading for “well-known” is widely known.

We are welcome to supply any reading we like. Epistemic modals don't actually exist.  

So, while the data is more complex here, the adjectival relative of ‘know’, on the rare use of it where it expresses propositional knowledge, does not

a word is missing here. Is it 'appear'? 

to be an obvious candidate for analysis via degrees on a scale of epistemic strength.

But if the thing can be usefully done for some specific purpose, it will be done. Suppose some justiciable matter is involved. A Court may 'read in' just such a scale so as to ensure justice is done.  

Another potential source of evidence for the gradability of “know” comes from its use in certain kinds of embedded questions. Consider, for example: (27) a. John knows how to swim well. b. John knows how to ride a bicycle better than Mary does.9 c. Hannah knows where Texas is better than John does. It is quite plausible that these are attributions of propositional knowledge.

 If propositional knowledge is involved in swimming (though fish do it) or bicycling (though BoJo does it) then- sure. Hannah is a homing pigeon from Dallas. Release her anywhere in the continental United States and she takes the most direct route to Texas. John, who belongs to the Bush dynasty, is the junior senator of the Lone Star State. He thinks Texas is just north of the Yale Campus. 

10 If so, one might think that this suggests that knowledge is gradable after all.

For any specific purpose, it- like everything else- is gradable. Jason's stupid shite is stupider than Tim Willamson's stupid shite.  

However, in these cases, what is being compared are answers to questions.

But everything can be an answer to a question- at least that is the case with my farts.  

In each case, one person is said to have a better answer to a certain question than another; the answer Hannah has to the question “Where is Texas?” is better, or more complete, than the answer John has.

Is it more useful? That is what matters. We release Hannah the pigeon and very soon we see her flying off in a South Westerly direction. Texas is that-a-way. John Bush, meanwhile, is headed towards the Canadian border.  

So, embedded questions do not provide evidence for the gradeability of knowledge claims.

If the question is asked for some useful purpose, then such evidence arises on the basis of verification. Hannah the pigeon has got to Texas while John Bush has been arrested by the Mounties for being coked to the gills.  

I don't know if Jason even pretends to being doing analtickle philosophy any more. Still, we can see that his turn towards 'Virulent Wokeness' was based on a belief that knowledge is context independent, 'natural' or 'non arbitrary', and lodged 'in rebus' in things themselves. This meant that Jason could identify as Fascist all sorts of people who were no such thing purely on the basis of his being 'woke' or 'antifa'. 

The poverty of Social Choice Theory

Less then ten years ago, Project Syndicate published the following- 

Social Choice and Social Welfare
Nov 26, 2014AMARTYA SEN

Human beings have always lived in groups, and their individual lives have invariably depended on group decisions.

No. Individual lives depend on individual decisions- including which group to live amongst and which group to run the fuck away from. Groups may not make any decisions whatsoever. Polities do make decisions- judicial, administrative, defense related, fiscal etc. But a Polity is not necessarily a collection of groups. It may be territorially defined and administered by one type of group while being defended by another group. Furthermore, groups may have a common resolve without having any collective decision making mechanism.

But, given the daunting challenges of group choice, owing to the divergent interests and concerns of the group’s members, how should collective decision-making be carried out?

The answer is that decision making should be delegated to those with ideographic, specialist, knowledge. At the least, those involved in collective decision making should have the opportunity to choose between the recommendations of experts.  

A dictator who wants to control every aspect of people’s lives will seek to ignore the preferences of everyone else.

No. A dictator will choose one strong preference and show herself to be better able to bring that situation about. Germans were actually anti-Semitic though German Jews were tremendously patriotic and productive. 

Dictators may use propaganda to artificially create  preferences but they would be foolish to ignore those that actually obtain.  This is because coercion is costly. The Dictator's Praetorian Guard or inner circle may be able to indulge themselves in various repugnant ways. But the pretense will be kept up that the opposite is the case. 

On the other hand, the Planning Commission- or some other bureaucratic body- may well ignore the preferences of everybody else. But, if the plan is not implemented there is no Dictator. There is only a waste of time. 

But that level of power is hard to achieve. More important, dictatorship of any kind can readily be seen to be a terrible way to govern a society.

No. A Dictatorship may be seen as the only way to govern a terrible society. But, equally, a Dictator may be appointed if that seems the best way to secure an important objective- e.g. National Defense, rapid Economic growth, securing the lives and property of minorities- etc.  

So, for both ethical and practical reasons, social scientists have long investigated how the concerns of a society’s members can be reflected in one way or another in its collective decisions, even if the society is not fully democratic.

No. There has been no such 'social science'. There is 'comparative politics' whereby existing polities are compared and ranked on how democratic they are. But, if the populations have different characteristics then there is little point to the exercise. The other point has to do with observer bias. In the mid-Sixties, some Western observers would have thought North Korea more 'democratic' (because less 'Fascist') than South Korea.  

For example, in the fourth century BC, Aristotle in Greece and Kautilya in India explored various possibilities of social choice in their classic books, Politics and Economics, respectively (the Sanskrit title of Kautilya’s book, Arthashastra, translates literally as “the discipline of material wellbeing”).

This is sheer nonsense. Aristotle thought that though the rule of the most able (timocracy) was a good thing. Democracy was evil because it was unlikely that those chosen by lot would be the most able.

 Kautilya served an Emperor and stressed the role of spies and a secret police keeping everybody under observation. On the other hand, he did consider Economic questions- e.g how to increase the tax yield without driving away productive classes- because that was what guys like him were paid to do. The choices made by Kings or Emperors are Sovereign rather than Social choices. The recommendations of priests or pedagogues are ethical and soteriological. They can be wholly independent of what obtains as Society.  

The two main insights of modern Social Choice theory- viz that no voting system is strategy proof and that 'agenda control'- i.e. the ability to decide the order in which issues are decided, can enable to implement any outcome you want even if you lack a majority for it- were always known to people since ancient times. Every ancient culture had instructors in rhetoric who taught students how to achieve their objective by exploiting 'cyclicity' by 'framing' the question differently. 

Pliny the Younger describes how he and his pals were able to get a freedman accused of killing a Senator acquitted by fits getting the issue of punishment addressed first. They disingenuously insisted that this should be execution, not banishment and got a majority for this result. This meant that people who would have voted for banishment, had to vote for acquittal. 

The arbitrary aspect of 'agenda control' is one reason why Social Choice via voting procedures is generally  subject to review or other types of countervailing power. Assemblies and Juries can do crazy shit. Rhetoric is a type of 'lawful magic' against which professional Politicians and Jurists are careful to find defenses. 

The study of social choice as a formal discipline first came into its own in the late eighteenth century, when the subject was pioneered by French mathematicians, particularly J. C. Borda and Marquis de Condorcet.

There had been plenty of very sophisticated voting systems in previous centuries. The Venetian one was particularly complicated. But who gets to be the Archbishop or the Doge or even the President of the Republic can be wholly irrelevant as far as the choices the Society is making is concerned. Voting rules are about avoiding conflict. They may attempt to 'bake in' a power-sharing arrangement of an elitist or undemocratic kind. But they still won't be 'strategy proof'. In any case, the really important decisions- how to defend the country or conquer other countries- aren't taken by rhetoricians or armchair philosophers. Either a 'Man of Destiny' rules the roost or else a particular coalition of vested interests prevails. 

Condorcet, it must be said, did have a vision of a utopian type of society. But it was Malthus's rejoinder to him which changed the direction of the Social and Life Sciences.  But this meant that the focus shifted from choices to the fitness landscape upon which choices are made. 

The intellectual climate of the time was greatly influenced by the European Enlightenment, with its interest in reasoned construction of a social order, and its commitment to the creation of a society responsive to people’s preferences.

The Enlightenment, sadly, was Racist. Even if it believed in Peace in Europe, the price would have to be paid by the conquest of non-European polities. Liebniz's 'perpetual peace' was based on France conquering Egypt. 

It should also be emphasized that though the Enlightenment was anti-Clerical and could be against Monarchical Absolutism, it was never for the 'great unwashed'. The people's preference was for more food and wine and holidays and killing Jews or other despised minorities- including fancy-shmancy intellectuals. 

But the theoretical investigations of Borda,

Borda merely rediscovered Cardinal Nicholas of Cusa's voting method which had been briefly considered in 1433 as a method for selecting the Holy Roman Emperor. There is nothing greatly wrong with the Borda method. It just isn't a panacea for anything because voting never is. 

Condorcet, and others often yielded rather pessimistic results.

But everybody already knew- just from playground debates at the age of 10- that voting doesn't have any magic powers. 

For example, the so-called “voting paradox” presented by Condorcet showed that majority rule can reach an impasse when every alternative is defeated in voting by some other alternative, so that no alternative is capable of standing up to the challenge of every other alternative.

But kids already know this by the time they are 10 years old. Once you get arguing over what game to play, the entire recess can pass without any game being played. All you have is a futile argument. Thus what happens is that a couple of kids start playing a particular game and there is a mimetic effect. Other kids join in. The arguers have to stand on the edge of the playground talking heatedly to each other. This gains them the reputation of being shit at games. The other kids say mean things about them.  

Social choice theory in its modern and systematic form owes its rigorous foundation to the work of Kenneth J. Arrow in his 1950 Columbia University PhD dissertation. Arrow’s thesis contained his famous “impossibility theorem,” an analytical result of breathtaking elegance and reach.

It was nonsense. Mathematically, it may be the case that a particular guy always votes for the winning candidate in every election. This does not mean he is 'decisive' over the outcome. The thing is a fluke. Arrow calls a guy of this sort a 'dictator' but he is no such thing. 

Arrow’s theorem shows that even very mild conditions of reasonableness in arriving at social decisions on the basis of simple preference rankings of a society’s individuals could not be simultaneously satisfied by any procedure.

It is unreasonable to think that anyone would accept a Social Choice rule. Alternatively, we could say 'the Social Choice rule we all accept has two components-

1) the Rule is to have no Rule

and

2) implementation of the Rule must occur when flying pigs prove the Reimann hypothesis , travel back in time, and give me a big sack of gold five minutes ago. 

When the book based on his dissertation, Social Choice and Individual Values, was published in 1951, it became an instant classic.

It was part and parcel of a rebellion against Government control of the Economy. Bureaucrats were making choices for the people and life had become grey. Eisenhower was elected President while, in England, the Tories returned to power.  

Economists, political theorists, moral and political philosophers, sociologists, and even the general public rapidly took notice of what seemed like – and indeed was – a devastating result.

Sen exaggerates the impact of Arrow's work. It was other writers- Ayn Rand, Raymond Aron, Arthur Koestler and even Karl Popper- who had an impact. Meanwhile, Anti Communist propaganda was becoming more and more sophisticated and better and better funded.  

Two centuries after visions of social rationality flowered in Enlightenment thinking, the project suddenly seemed, at least superficially, to be inescapably doomed.

Revolutions and 'Men of Destiny' now looked like a very bad idea. What people really wanted was affluence not some crazy type of enlightenment.  

It is important to understand why and how Arrow’s impossibility result comes about.

It comes about by telling a stupid lie- viz a guy who, by fluke, always votes for the winning candidate is secretly a Dictator.  

Scrutiny of the formal reasoning that establishes the theorem shows that relying only on the preference rankings of individuals

is stupid because no individual actually has such a preference ranking. There are billions of alternative social states and no individual has a knowledge of even a tiny fraction of them.  

makes it difficult to distinguish between very dissimilar social choice problems.

If you rely on something which does not and can not exist, your big problem is that you are a fucking moron.  

The usability of available information is further reduced by the combined effects of innocuous-seeming principles that are popular in informal discussions.

Each of those principles is crazy.  

It is essential, particularly for making judgments about social welfare, to compare different individuals’ gains and losses and to take note of their relative affluence, which cannot be immediately deduced only from people’s rankings of social alternatives.

But, if we actually had preferences over all social states then we would know what our judgments were. I could find out whether I believe String Theory could work by seeing what proportion of the Scientific Research budget I wanted allocated to that type of inquiry.  

It is also important to examine which types of clusters of preference rankings are problematic for different types of voting procedures.

But we would also have preferences over what proportion of the Social Choice Research budget should be spent on different 'problem areas'.  

Nonetheless, Arrow’s impossibility theorem ultimately played a hugely constructive role in investigating what democracy demands,

Nonsense! The thing was worthless. Democracy is the system of government which prevails if no other type of regime can be imposed. This is the case even if the majority would prefer a Monarchy or a Dictatorship. If would-be King or Dictator can kill off his rivals, we are stuck with Democracy.  

which goes well beyond counting votes (important as that is).

Sadly, Democracy does not disappear even if there is widespread electoral malpractice, voter suppression etc.  

Enriching the informational base of democracy and making greater use of interactive public reasoning can contribute significantly to making democracy more workable, and also allow reasoned assessment of social welfare.

But the same is true of Monarchy or Dictatorship.  

Social choice theory has thus become a broad discipline,

It has become an oubliette where useless tossers are dumped. Indian economists went in for it in a big way because India's economy had turned to shit thanks to Indian economists.  

covering a variety of distinct questions. Under what circumstances would majority rule yield unambiguous and consistent decisions?

Never. Decisions should not be 'consistent'- i.e. transitive- because the fitness landscape changes unpredictably and, in any case, is imperfectly known. The meaning of any decision will always be ambiguous because it could have been prompted by different considerations. We might say 'Country X decided to attack Country Y because X felt it was strong'. But it frequently happens that weakness sparks aggression. The hope is that the other side panics and yields.  

How robust are the different voting procedures for yielding cogent results?

All 'results' can be seen as cogent or utterly crazy depending on your point of view. Robustness simply means whether the thing survives when circumstances change. Britain and America have robust constitutions. France is on its Fifth Republic. Might Macron usher in a Sixth Republic?  

How can we judge how well a society as a whole is doing in light of its members’ disparate interests?

Are smart people entering or exiting that Society? If you compare the material standard of living of the median individual in different countries, you get an idea of how well different societies are doing. No doubt, some stupid Professor may claim that the people of Venezuela are much happier than the people of Canada. But Venezuelans want to emigrate to Canada. Canada may be boring but it is safe and prosperous. 

How, moreover, can we accommodate individuals’ rights and liberties while giving appropriate recognition to their overall preferences?

We only know about 'revealed preferences'. Are people running away from one place and flocking to another? Indians probably have more 'rights and liberties' than the people of some Oil rich states. Yet, Indians are very happy to relocate to where they will be better paid.  

How do we measure aggregate poverty in view of the varying predicaments and miseries of the diverse people who comprise the society?

If we are paid to say 'under this administration, poverty has risen', then we will fudge the numbers to prove that result.  

How do we arrive at social valuations of public goods such as the natural environment?

If we are paid to say that we are all going to die horribly within six months because of an ecological catastrophe, we will fudge the numbers to prove this assertion.  

Beyond these questions, a theory of justice can draw substantially on the insights and analytical results emerging from social choice theory (as I discussed in my 2009 book The Idea of Justice).

Sen confused 'Policy' with 'Justice'. The former is welcome to look at Market Research surveys of voters' preferences. The latter must not do so. It is enough if there is a Jury which makes determinations of facts on the basis of what reasonable people would consider to be true or right.  

Furthermore, the understanding generated by social choice theorists’ study of group decisions has helped some research that is not directly a part of social choice theory – for example, on the forms and consequences of gender inequality,

Male rapists should be sent to women's prisons if they say they feel they are actually women.  

or on the causation and prevention of famines.

Famines are caused by food availability deficit. Preventing them involves boosting the supply and transport of food. Sen's work is mischievous nonsense.  

The reach and relevance of social choice theory is extensive.

It is wholly useless.  

Rather than undermining the pursuit of social reasoning, Arrow’s deeply challenging impossibility theorem, and the large volume of literature that it has inspired, has immensely strengthened our ability to think rationally about the collective decision-making on which our survival and happiness depend.

While Sen-tentious cretins have been virtue signaling, China has risen and risen. It has made rational collective-decisions- e.g. imitate what more successful countries are doing- but it is an open question whether it can, sui generis, take the lead in technology. 

Thinking rationally involves rejecting stupid lies. Social Choice Theory is founded on the absurd proposition that everybody has a preference regarding everything. It ignores Knightian Uncertainty and the ubiquity of 'Tardean mimetics'. It refuses to recognize that what makes collective decisions possible is 'transferable utility'- i.e. bribes and threats.