From Wikipedia.

by Jonathan Kujawa

Approximately 1900 years ago Theon of Smyrna authored On Mathematics Useful for the Understanding of Plato. In it, Theon wrote:

For Eratosthenes says in his writing he Platonicus that when the god pronounced to the Delians in the matter of deliverance from a plague that they construct an alter the double of the one that existed, much bewilderment fell upon the builders who sought how one was to make a solid double of a solid. Then there arrived men to inquire of this from Plato. But he said to them that not for want of a double altar did the god prophecy this to the Delians, but to accuse and reproach them the Greeks for neglecting mathematics and making little of geometry.

Thus the problem of doubling the cube was born. If we are given a cube of a certain volume, can we construct a cube whose volume is exactly double? We might as well start with the cube as a practice problem and worry about the more complicated shape of an altar once we've got the cube sorted out. Also, up to changing our choice of units, we can safely assume the cube has volume exactly 1. We've now got a simple geometry problem: given a cube with volume 1, how to construct a cube with volume 2? Like many of the best questions, this seemingly innocuous problem opens a Pandora's box of interesting things to ponder.

Plato warns us not to neglect our mathematics. As mathematically minded folks we know we should first decide on ground rules. If we don't bother to first agree on clear, unambiguous definitions and axioms, then we'll just end up talking past each other. This might play on cable tv, but it's not mathematics. Besides, like writing a sonnet or a haiku, half the fun in math is in the constraints. Like Robert Frost said, "I'd sooner write free verse as play tennis with the net down".

In the case of the doubled cube, the Greeks allow us to use a straightedge (that is, an unmarked ruler which allows us to make any straight line we like) and a compass (those devices from elementary school with a point on one end and a pencil on the other which allows us to make any circle we like). Nowadays you can instead play the addictive free game Euclidea.

Since a cube is completely determined by its side length and the volume is just the side length cubed, doubling the cube comes down to the problem of using a straightedge, compass and a line segment of length 1 and, by hook or by crook, construct a line segment whose length is the cubed root of 2.

Doubling the Cube (from Wikipedia)

After fiddling with your straightedge and compass for a millennium or two you might start to suspect that the god was putting one over on the Delians (after all the Greek gods weren't known for playing fair). But how in the world could you ever know for certain that it wasn't possible? After all, tomorrow you might find That One Weird Trick Which Doubles the Cube!

Math is nearly unique in that you can show things are never, ever possible. I was blown away when I first saw the proof that the real numbers cannot be put into an order list numbered by the counting numbers and that the square root of two cannot be written as a fraction of two counting numbers. In retrospect, it was the proofs of impossibility which first converted me to math.

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The Free Exercise of

At its center is a tree
which wraps the garden
in its entirety

The roots of it run deep—
some say to a molten core
while some insist they exit the other side
to suck juices from a Southern Cross
and that its sweet and sour blooms
on this respiring side of dust
reach and blossom
beyond the north pole star
and meet the ends of far
in parts we'll never know
until we wake or break
to give or take
right here and now
in time and space
the bait of love
or snake

Jim Culleny
3/27/17

by Brooks Riley

I feel a stress disorder coming on. Call it Persistent Trump Stress Disorder. Or PTSD 2.0.

This is not about Trump himself, the ‘dingo’ here, whose many inadequacies, fallacies and prevarications are scrutinized, dissected, biopsied, and finally lampooned 24/7 in every corner of the fourth estate, reaching every corner of the globe.

This is not about the man who’s determined to crush the zeitgeist Obama left behind and replace it with a deceptively quaint, unworkable fantasy from the mid-20^th century when employment was analog, energy was black and endless, skies were ripe for pollution, white men called the shots, and inequality was just fine if you were white, even as America was nevertheless still basking in the glow of its victories in World War 2. Just what ‘great” is he talking about?

This is not about the First Narcissist, whose new Presidential Face must have been rehearsed in front of the mirror for weeks before the inauguration, the grimaces and goofy smirks now replaced by a parody of grim determination and implied gravitas that ends up projecting ‘grumpy old man’, with an emphasis on ‘old‘ that was probably not intended.

This is not about all the progress that this man wants to disassemble–revoking Obamacare, denying climate change, disabling the EPA, eliminating the Clean Water Rule, defunding Planned Parenthood, endangering workers in critical professions, slamming shut the doors to the American dream, undermining an economy that needs to function way beyond its shores.

This is not about the pathology of a vengeful egotist whose priorities verge on the absurd, for whom a chocolate cake, or the performance of Schwarzenegger on his former show, or a department store that drops his daughter’s label, all matter more to him than the names of countries to which he launches missiles, or of leaders he shakes his fist at.

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by Jalees Rehman

On 5 November 2015, an iron ore tailings dam burst in Bento Rodrigues near the Brazilian city of Mariana, releasing 60 million cubic meters of a reddish-brown mud-flood. This toxic flood buried neighboring villages and flowed into the Rio Doce, contaminating the river with several hazardous metals including mercury, arsenic and chromium as well as potentially harmful bacteria. The devastating and perhaps irreparable damage to the ecosystem and human health caused by this incident are the reason why it is seen as one of the biggest environmental disasters in the history of Brazil. The German sociologist Stephan Lessenich uses this catastrophe as a starting point to introduce the concept of the Externalisierungsgesellschaft(externalization society) in his book Neben uns die Sintflut: Die Externalisierungsgesellschaft und ihr Preis ("Around us, the deluge: The externalization society and its cost").

What is the externalization society? Lessenich uses this expression to describe how developed countries such as the United States, Japan and Germany transfer or externalize risks and burdens to developing countries in South America, Africa and Asia. The Bento Rodrigues disaster is an example of the environmental risk that is externalized. Extracting metals that are predominantly used by technology-hungry consumers in developed countries invariably generates toxic waste which poses a great risk for the indigenous population of many developing countries. The externalized environmental risks are not limited to those associated with mining raw materials. The developed world is increasingly exporting its trash into the third world.

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by Tamuira Reid

1. Theresa killed a man with her car. It wasn't her fault but still.

It was dark. The road was long. Oldies played on the radio. The kind of music people dance to when they think no one is watching and there is still that chance of something good happening.

He hit her, not the other way around.

Thought it was a deer, she told the police. Same kind of thud, thick and heavy. It was raining but not too hard. The impact dented the hood, busted the window, the glass splintered and folded in on itself.

The paper runs his photo with details for a memorial service at the Y on Harrisburg Street. He was nineteen, worked weekends at a Ford dealership. Best damn worker bee we had, his boss would tell reporters when they turned up at his store, on the hunt for details.

Theresa folds the story into a square and hides it under her mattress. Sometimes she feels him breathing but doesn't tell anyone.

2. A television crackles from a corner of the room where his two little sisters sleep, arms and legs locking. They always do this; try to wait up for their brother. Sometimes he brings home candy or soda or other deliciously bad things their mother will not let them have. Junior, I wish you'd stop bringing that crap into my house, she will say to his back as he opens the fridge and sighs.

Her first born. Her son. How secretly proud she is of the man he's becoming. The man his own father turned out not to be.

3. The last thing he saw was the glare of headlights. Like rays of sun coming straight towards him.

4. The silk blouse and the gray slacks from Macy's with the pleats down the front. They go into the washer with extra Woolite. Theresa studies the water for signs of death but it's all over at this point. She lets the lid down slowly, disappears into the kitchen for another cigarette.

People call and she tells them. Didn't see him coming. Out of nowhere. I held his hand. Sometimes the people who call are friends. Sometimes the people who call are strangers. Fucking drunk bitch, they'll say and then hang up.

5. She was sober when she hit him. Ninety five days without anything, she'd tell the police. But no one would believe her, even when the blood tests showed she was telling the truth.

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by Yohan J. John

Once, some years ago, I was attending a talk by the philosopher Slavoj Žižek at the Brattle Theatre in Cambridge, Massachusetts. He was engaged in his usual counterintuitive mix of lefty politics and pop culture references, and I found myself nodding vigorously. But at one point I asked myself: do I really understand what he is saying? Or do I simply have the feeling of understanding? As a neuroscientist, I am acutely aware of the mysterious and myriad ways in which brain areas are connected with each other and with the rest of the body. There are many pathways from point A to point B in the brain: perhaps Žižek’s words (and accent and crazed physical tics) had found a shortcut to the ‘understanding centers’ (whatever they might prove to be) in my brain? Perhaps my feeling of comprehension was a false alarm? Had I been intellectually hypnotized?

One way to check would be to try and explain Žižek’s ideas for myself. A handy sanity check might involve directing my explanations at other people, since I knew from first-hand experience that a set of ideas can seem perfectly coherent when they float free-form in one’s head, but when it comes time for the clouds of thought to condense into something communicable, very often no rain ensues. (This often happens when it’s time for me to translate my ruminations into a 3QD essay!)

Many of us like to see ourselves as members of a scientific society, where rational people subject ideas to rigorous scrutiny before filing them in the ‘justified true belief’ cabinet. But there are many sorts of ideas that can’t really be put to any kind of stringent test: my ‘social’ test of Žižek’s ideas doesn’t necessarily prove anything, since most of my friends are as left-wing (and susceptible to pop cultural analogies) as I am. This is the state of many of the ideas that seem most pressing for individuals and societies: there aren’t really any scientific or social tests that definitively establish ‘truth’ in politics, history or aesthetics.

To attempt an understanding of understanding, I think it might make sense to situate our verbal forms of knowledge-generation in the wider world of knowing: a world that includes the forms that we share with animals and even plants. To this end, I’ve come up with a taxonomy of understanding, which, for reasons that should become apparent eventually, I will organize in a ring. At the very outset I must stress that in humans these ways of knowing are very rarely employed in isolation. Moreover, they are not fixed faculties: they influence each other and gradually modify each other. Finally, I must stress that this ‘systematization’ is a work in progress. With these caveats in mind, I’d like to treat each of the ways of knowing in order, starting at the bottom and working my way around in a clockwise direction.

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Editor’s Note: My sister Azra has kindly given us permission to publish remarks that she delivered to The Citizen’s Foundation gala in Houston a few days ago. She will provide translations of the Urdu poetry soon.

by Azra Raza

Thank you Dr. Abdullah Jafari, thank you TCF, thank you Houston for giving me this opportunity to speak tonight. I am greatly honored. This evening, we are going to celebrate the women of Pakistan.

In the 1930s of Aligarh, my mother was sent to Merath for a vacation. She was barely ten years old. In Meerath, she became homesick in the house of her relatives. A few weeks later, she learnt that her father would be visiting a nearby town so she wrote begging her mother that her father should take her home to Aligarh when he returned. This one simple act of letter writing caused a major upheaval in Aijaz Manzil because the first thing my Naana wanted to know was how Naani Amman found out about Ammi’s unhappiness. Naani Amman had to produce the letter which was examined carefully. My Naana was scandalized by the idea that his daughter had secretly learned to read and write, an activity considered subversive and dangerous. While a good head and a good heart in a woman was a desirable combination, adding a pen to that was tantamount to outright rebellion.

I remembered this story because when my own daughter Sheherzad was ten years old and I asked her one day what she would do if she won the lottery and had millions of dollars, her instantaneous and forceful response was, “Finish my education, of course!” What a contrast between two 10-year olds separated by one single generation. Sheherzad did not have to think twice about her education because of the sacrifices made by my mother and by the women of her generation in the pre-partition subcontinent. So if we are going to celebrate the women of Pakistan, let us begin with the pioneers. Ms. Fatima Jinnah and Begum Rana Liaqat Ali Khan, Lady Haroon and Begum Shaista Ikramullah. My mother became deeply involved in women’s education in Karachi and through her tireless efforts, managed to provide for both primary and higher education to hundreds of underprivileged students. When she died 15 years ago, my epitaph for her was the famous Faiz sher:

Karo kaj jabeen pay sar e kafan
Meray qaatiloun ko gumaan na ho
Kay ghuroor e ishq ka baankpan
Pas e marg ham nay bhula diya!

(Faiz)

(Keep the shroud tilted on my forehead as a sign of defiance and pride. Let not my assassins have the misapprehension that in death, they succeeded in crushing the honor and pride I took in my passions).

The first University open to women was in Bombay in 1882 while Harvard Medical School admitted women for the first time in 1945. As far as Pakistan is concerned, let us do a little math. The population is roughly 186 million. There are 296,832 students enrolled in degree level education which comes to 0.1% population. Despite these dire statistics, the good news is that 62% of them are women and the level of achievement of girls is consistently higher than that of the boys. Girls outclass boys in examination, and they are also higher achievers. And yet, when it comes to the work-force, their efforts are not rewarded equally. I was horrified to hear the goal announced at the International Women’s Conference last year: 50-50 by 2030 meaning equal pay by 2030. Why?

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by Paul Braterman

R: Sagan warns us against fallacies. But is exposing fallacies enough to shield us from the demons?

I had been waiting for a quiet moment to write about this, but there isn't going to be a quiet moment, so now will have to do.

Debaters regularly accuse their opponents of using fallacies. These can be formal fallacies, such as simple errors of logic, or informal fallacies, such as appeal to authority, ad hominem and strawman arguments, among others. If a piece of reasoning depends on any of these fallacies, so it is claimed, the conclusion does not really follow from the premises, and while it might still be true we have not been given any good reason to believe it.[1] And so books that discuss logic, and science-promoting blogs (including one I follow), regularly include descriptions of informal fallacies, with stern instructions to avoid committing them.

In an article entitled The Fake, the Flimsy, and the Fallacious: Demarcating Arguments in Real Life, Maarten Boudry, Fabio Paglieri and Massimo Pigliucci (henceforth BPP) challenge this view. BPP is written for the perusal of trained philosophers, which I am not, but I use it here as a jumping off point, while mixing in further content of my own.

BPP apply what they call the fallacy fork test to accusations of informal fallacy; either the reasoning is obviously erroneous, in which case no one would really use it, or else it is not obviously erroneous in context, and we still have all the work to do. In the first case, formal analysis is redundant; in the second, the facts of the matter need further consideration. So naming and shaming the particular kind of fallacy is either unnecessary or uncalled for. I agree, and suggest that we drop the label "fallacy" for such informal arguments, since to make the label stick we have to show on other grounds that the argument as used really is fallacious. The discussion made me think of my own reflections on formally valid logical arguments, which only work because the conclusion has actually been accepted in advance, otherwise we would not have accepted the premises. In both cases, the formal or semi-formal reasoning, while seemingly at the heart of the argument, is an unnecessary elaboration, and we can cut out the middleman.

Going beyond this, it is becoming increasingly clear that the logical is only one aspect, and not usually the most important aspect, of an argument. More important are the heuristic and rhetorical aspects; will the reasoning point us towards a way of acquiring new knowledge, and how useful is it in the attempt to persuade our opponents to change their minds. (In passing, I suggest that if our objective is to persuade others to change their minds, we are not arguing in good faith, unless we are at least in principle open to the possibility that we too might change ours.)

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by Katrin Trüstedt

While the murder series of the right-wing terror trio National Socialist Underground (NSU) has generally escaped major international attention (especially in comparison with Islamist terror attacks), one of the assassinations continues to come up. The murder of Halit Yozgat, the 9^th assassination of the NSU, resists the fate of the others, because of one rather delicate detail: a secret service agent was present at the crime scene at the time of the murder. When Halit Yozgat was shot in the head by two members of the NSU on April 6, 2006, from a close distance with a silenced Česká CZ 83 pistol (the signature style of the NSU assassinations), Andreas Temme, an agent of the Hessian domestic intelligence service, was in the internet café in Kassel. When Halit Yozgat's father, İsmail Yozgat, found his son when he returned to the café a few minutes after the murder, Temme was gone.

The agent claimed first to have been at the café the day before, and then that he had left the place right before the murder. He later changed his statement when confronted with overwhelming evidence placing him at the scene when the murder happened. He then claimed he didn't see or hear Yozgat getting shot while he was chatting with his online affair; that he put coins on the reception desk and left, not noticing that Yozgat was dying on the ground behind the desk; and that he didn't report back to the police like all the other witnesses in the café because he didn't want his pregnant wife to find out what he was doing there. The police, the court and his employers at the State Office for the Protection of the Constitution accepted his testimony. But his presence continues to raise suspicions that government agencies might in some way be involved in the murders, fueling conspiracy theories in various directions. Much justified criticism of the authorities' handling of the case came from the left, pointing out the general trivialization of right-wing violence by state agencies combined with racist prejudices when it comes to the victims, when the various agencies investigating the murders had disregarded the possibility of right-wing terror and rather investigated the victim's families for possible criminal ties, thereby doubling the crimes they were supposed to prevent. Against this background, the fact that an agent of the domestic intelligence service was present at the scene raised the suspicion that government agencies might have actively protected or enabled the NSU. Meanwhile there are, on the other hand, many rumors in the right-wing scene itself claiming the NSU murders were orchestrated by the state authorities in order to hurt the scene.

Forensic Architecture, a research agency based at Goldsmiths around the architect Eyal Weizman, have launched an independent investigation into the case and recently presented preliminary results.

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by Elise Hempel

I'm about to enter yet another poetry chapbook contest that I'll have little chance of winning. This one's cheap – only $10 to enter (compared to the usual $20 to $30), but that's because there's no monetary prize (most chapbook and full-length book contests award $1,000 to the winner), only publication and a contract for a certain percentage of the printed chapbook's sales.

Though we're now in the age of Trump, in the age of "winning," of loving winners and loving to win, I'm still the same person I was before November 8, 2016. Of course I'd love to win this chapbook contest, to have my 20 to 30 poems neatly packaged in a perfect-bound little book with a colorful glossy cover, to add one more publication to my résumé. But, like Anis Shivani, I also don't believe in poetry contests, and I resent the fact that this is what I, and other less-well-known poets, must do to even come close to getting just a chapbook published. And I continue to be baffled by the fact that most poetry contests (for both books and chapbooks, and for a single poem or group of poems) name only a single winner, awarding prize money and publication to the one "best" submission, though sometimes a few lucky finalists are also given publication and a lesser amount of cash.

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by Christopher Bacas

After any commercial job, I was a whirling particle; negatively charged. I wanted to appear simultaneously in a distant vector of the universe (preferably, garage level). Spooky action proved impossible. Quantum properties aren't conferred at loading docks. A single sound launched our universe, though. I wonder who was on that gig…

One band leader, obsessively germ-phobic, always brought food; peanut-butter and jelly sandwiches held tightly between layers of crinkled foil, fingers never touching bread. His musicianship so secure, he'd simultaneously walk impeccable left-hand bass, comp and go over details with the party planner. Preoccupied with himself, he never requested dinner service for sidemen, even when available. We usually got squashed sandwiches in clear folding trays. The potato chips inside, moistened by a pickle, bent a full 360 degrees without breaking. Once, a maitre'd bypassed him and asked the horn section if we wanted surf and turf. At break time, our boss fumed while staff uncovered our glistening plates and poured bubbly into elegant flutes.

We worked exclusively for a suburban Maryland office. They had high-end bar-mitzvah work sewn up. The chief drove a Porsche. He required us to make a new video at least once a year. The sound stage and audio/video team were part of his business; a club date version of the company store. Shoots dragged for needless hours as the "crew" struggled to properly mic and mix instruments and music they saw and heard weekly. While the smoke machine wafted saccharine clouds through skronking feedback and buzzing amps, grown-up high-school AV nerds, pocket protectors and cluttered tool belts included, scuttled around jabbering into wireless headsets.

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by Humera Afridi

I am the companion of the new Adam

Who has earned my self-assured love

(Fahmida Riaz)

“Mommy, when are you going to start dating? You’re not even trying!” complained my nine-year old on a sunny afternoon in February, two days before Valentine’s Day.

We’d just returned home from family day at Chelsea Piers, our cherished Sunday ritual. His words—incongruous in that moment and, certainly so, for his age—struck me with force. I dropped my gym bag, feigned horror. But the horror was as real as if I’d stumbled upon a nest of rodents as I breathed through a rush of emotions—alarm, sadness, mirth, shock.

These had suddenly appeared skittering and scampering, prodded by an innocent question which had penetrated, with the precision of an arrow, layers of social and cultural conditioning. My son’s words had spilled out, I noticed, in a single breath, question and complaint merged into an astutely observed assessment which he’d delivered with an air of impatience.

I threw my head back and laughed, pinched his chin. “Eeeks! Dating? I have zero interest. And, anyway, who has time?”

“Mom, there are apps, you know, where you can find a boyfriend.” He was adamant, unwilling to relinquish his position. “And that way I can have a stepdad,” he added, frowning now to conceal a tremor of self-consciousness.

This tragi-comic pronouncement in the elevator ride up to our apartment rapidly mounted into an existential crisis—I felt the urge to double over in reams of chronic laughter, I wanted to curl myself into a ball and weep, all at the same time.

Instead, I joked. “Hey, mister, how come you know about dating apps?”

The ground beneath my feet felt like quicksand. The mellow passage of domestic stability was suddenly under threat with the possibility of the new order that my son’s unsolicited and precocious ‘advice’ had raised. Stendhal’s words popped into my mind: “The most surprising thing of all about love is the first step, the violence of the change that takes place in a man’s mind.” Presumably, a woman’s mind, too. And I, comfortably ensconced in my routines, freedom, and independence desired no disruption, thank you. Motherhood is a gift I cherish; it has also, naturally, been my compass. But my child had now inadvertently made lucid the fact that I’d been occupying this station complacently, with inordinate fealty to an ideal of motherhood that upholds those who are settled in constancy, those spared the volatility and “violence” of new love—married mothers.

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by Richard King

Good news for US exports this month. Australia, my adoptive country, has also adopted the trigger warning. Taking its lead from US campuses, Melbourne's Monash University has obliged its academic staff to review their course materials with the aim of identifying content that may be "emotionally confronting" for students, and is set to attach fifteen advisory statements to subjects dealing with, inter alia, racism, torture, homophobia and colonialism. All very exotic in a country revered for its colourful language and casual racism, but that's the power of globalisation. And they say the American Century is over.

Not everyone is happy about the new arrival. Following their US counterparts (the reaction, too, has an imported feel), critics of "political correctness" have declared the adoption of trigger warnings to be a new front in the culture wars and the heir to such PC atrocities as affirmative action and university speech codes. According to this line of argument, trigger warnings are a Trojan horse from which the polo-necked Foucauldian foot-soldiers will emerge the moment Professor Tomnoddy brandishes his Amontillado-stained copy of Tractatus Logico-Philosophicus. "Sensitivity" is code for censorship and the imposition of radical values on the entire academic cohort.

Notwithstanding the muscular, male-menopausal, almost vaudevillian liberalism with which their animadversions come served, these critics aren't completely wrong. Trigger warnings are political and do derive, via a circuitous route, from the cultural "turn" in leftwing politics in the late 1960s and 1970s. But they are not political in the way conservatives or classical liberals think they're political, being neither an assault on "academic freedom" nor a Marcusean attempt to drive the sacred cows of tradition, "Western Civ." etc. towards the abattoir of Cultural Marxism. Possibly there's a bit of that, but my strong sense is that what we're dealing with here is a new form of subjectivity that regards the expression of personal hurt, not just as a form of political agency, but as the very stuff of politics itself. Like their close cousins "safe spaces" and "microaggressions", trigger warnings represent a new political epistemology.

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by Carl Pierer

I.

The old problem of induction raised the question of how we can justify inferences from singular observations to general statements. In the last century two newer problems were presented. The Ravens Paradox, which I will explain in section II, is due to Carl G. Hempel. The ‘grue problem' was put forth by Nelson Goodman and I shall present it in section III. In section IV I will first compare the two problems and then attempt to show that Hempel's paradox can be solved, whereas Goodman's ‘grue' points to a deeper problem.

II.

Carl Hempel focuses on the question of what counts as evidence for hypotheses. There are two principles of inductive reasoning that we seem to accept.

(i) If all Ps have been observed to be Qs, then this counts as evidence for "All Ps are Qs". Hempel writes: "(…) this hypothesis is confirmed by an object a if a is P and Q; and the hypothesis is disconfirmed by a if a is P, but not Q." (Hempel 1945, p. 18)

(ii) What counts as evidence for one statement, counts as evidence for all logically equivalent statements. So, if all non-B's have been observed to be non-A's, then this counts as evidence for the original statement. It seems plausible to accept the second principle. The statements are equivalent exactly because they are true under the same conditions.

Hempel thinks that this account entails a paradox, namely the Ravens Paradox. Say we start off with the hypothesis: "All ravens are black". We can then construct its logical equivalent: "All non-black things are non-ravens". By (i), everything that we can observe that is not a raven and not black will count as evidence for the second statement. By (ii) we are bound to accept these evidences as evidence for the initial hypothesis. But this seems absurd. We do not believe that my brown jumper does in any way affect the hypothesis that all ravens are black. This fact seems completely irrelevant.

III.

Nelson Goodman formulated a "new riddle of induction". In order to construe it, he needs to come up with a new predicate: the infamous "grue" (Goodman 1954, p 74). Objects are grue if they are observed before time t and are green, and if they are observed after t and they are blue. Now, t is some time in the future, say the 1^st November 2020. So, if we have a green emerald before time t, then this certainly supports the hypothesis "All emeralds are green". However, we can also take it as evidence for "All emeralds are grue". The issue, then, is to determine whether we have any reasonable grounds to prefer thinking of emeralds as green over emeralds as grue.

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