Saturday, September 24, 2022

Links of Note

 * Justin E. H. Smith, Re-entering the Vampire Castle, on the history of the vampire

* Carissa Phillips-Garrett, Why Aristotle's Virtuous Agent Won't Forgive: Aristotle on Syngnome, Praotes, and Megalopsychia (PDF)

* Marc Morris, Normans and Slavery: Breaking the Bonds

* Eric Brown and Clerk Shaw, Socrates and Coherent Desire (Gorgias 466a-468e) (PDF)

* Sarah Karp looks at the Peace Warriors, an organization devoted to training for nonviolent campaigns

* Wenjin Liu, Ignorance in Plato's Protagoras (PDF)

* Meira Levinson, Tatiana Geron, and Harry Brighouse, Conceptions of Educational Equity

* David MacPherson, Transfiguring the Unborn: Abortion, Human Equality, and Moral Perception, at "Public Discourse"

Friday, September 23, 2022

Till Time Seemed Fiction, Past and Present One

 Rome: On the Palatine
by Thomas Hardy


 (April 1887) 

 We walked where Victor Jove was shrined awhile,
 And passed to Livia's rich red mural show,
 Whence, thridding cave and Criptoportico,
 We gained Caligula's dissolving pile.
 And each ranked ruin tended to beguile
 The outer sense, and shape itself as though
 It wore its marble gleams, its pristine glow
 Of scenic frieze and pompous peristyle.
 When lo, swift hands, on strings nigh overhead,
 Began to melodize a waltz by Strauss :
 It stirred me as I stood, in Cæsar's house,
 Raised the old routs Imperial lyres had led,
 And blended pulsing life with lives long done,
 Till Time seemed fiction, Past and Present one.

Thursday, September 22, 2022

Possible World Semantics

 Saul Kripke died last week (September 15), so there have been various obituaries slowly coming out. One of his major contributions was laying the foundations of possible world semantics, it's unsurprising that the obituaries and tributes make an attempt to explain the concept of a possible world to a lay audience. Unfortunately, they often make elementary mistakes in doing so. I don't intend this particularly as a criticism, since I think this is very easy to do when trying to explain things for those who are not familiar with them already; and, in addition, since analytic philosophers often don't read up on the history of the concepts they use, it's easy for mutations to develop and errors to propagate even among professional philosophers. Some of these are relatively harmless, but with respect to possible worlds, I think one error in particular has a tendency to cause no end of confusion. It is, more or less, this. A possible world, the error goes, helps us explain possibility statements by thinking in terms of other worlds; for instance, if you didn't eat breakfast, we can cash out the statement that you could have eaten breakfast by thinking of you as eating breakfast in another world. This is precisely how Kripke held we were not to think of possible worlds; in later times, reflecting on the confusion that this error caused, he wondered if he should have used a different phrase, like 'counterfactual situation'. Thus it seems reasonable to put up a very, very elementary guide to how possible world semantics is supposed to work.

We can start how Kripke would, with something that is familiar to most people with a basic mathematics education. If we talk about probabilities, we can do so in terms of what are sometimes known as microstates, particular configurations. For instance, a regular die has six microstates, depending on whether 1, 2, 3, 4, 5, or 6 come up. Since nothing differentiates the numbers on the face of the die, in a well-made die, each of these is equiprobable, and thus each has a 1/6 probability of being the result of a given roll of the die. 'Possible world' is just a generalization of this idea for cases in which we are more interested in possibilities than probabilities.

If we stick with our single die, we can think of each possible result of a roll as represented by a list of yes/no questions with their answers. For instance, the result in which one pip comes up could be represented as:

Does 1 come up on the die? Yes
Does 2 come up on the die? No
Does 3 come up on the die? No
Does 4 come up on the die? No
Does 5 come up on the die? No
Does 6 come up on the die? No

If nothing whatsoever exists or is relevant to the situation except the faces of the die, such a list specifies a possible world: a possible world is a logical object associated with a consistent list of yes/no questions with yes or no answers, which we can compare with similar logical objects. In this case we are interpreting the possible world as a roll of a die. If there were only two dice, and nothing else were relevant at all, we could capture the possibilities with lists that would cover all the new possibilities. For instance, this would be the list for the possible world for snake eyes:

Does 1 come up on die 1? Yes
Does 2 come up on die 1? No
Does 3 come up on die 1? No
Does 4 come up on die 1? No
Does 5 come up on die 1? No
Does 6 come up on die 1? No
Does 1 come up on die 2? Yes
Does 2 come up on die 2? No
Does 3 come up on die 2? No
Does 4 come up on die 2? No
Does 5 come up on die 2? No

We can even specify possibilities that have no well-defined probability. One of St. Olaf's miracles was rolling a 13 with two regular six-sided dice because one of the dice split in the middle of the roll. The possible world for St. Olaf's miracle roll, assuming that we call the die that actually split 'die 2', is described by the following list:

Does 1 come up on die 1? No
Does 2 come up on die 1? No
Does 3 come up on die 1? No
Does 4 come up on die 1? No
Does 5 come up on die 1? No
Does 6 come up on die 1? Yes
Does 1 come up on die 2? Yes
Does 2 come up on die 2? No
Does 3 come up on die 2? No
Does 4 come up on die 2? No
Does 5 come up on die 2? No
Does 6 come up on die 2? Yes

I said above that a possible world is a logical object associated with a consistent list of yes/no questions with their answers; the St. Olaf's miracle list is only consistent if we allow die-splitting to be relevant and possible, and even if we do, there are going to be question-answer lists that are not consistent -- they would require kinds of splitting that are not relevant or possible. Such lists designate, as you might expect, impossible worlds. Impossible worlds can be tricky to use; we will stick with possible worlds, that is, with cases designated by lists whose answers are all consistent with each other.

When we are talking about possible and necessary things, however, we usually want to handle more complicated things than dice rolls. Thus 'possible world' is usually reserved for cases in which our list of questions and answers are not just consistent but in some way complete, in the sense that they cover everything. This introduces additional complications; it means that we can't actually study each individual possible world by looking through all the items on its associated list, because we can't read through a list that covers everything. We need to handle these complicated cases in another way. The key is in another aspect of the description of possible worlds that we gave: possible worlds are things that can be compared with each other. That is, one possible world can be related to other possible worlds.

In principle, you could have all sorts of complicated and weird relations among possible worlds, but the relations in which we are particularly interested are binary relations, that is, relations that relate one particular possible world to another possible world by linking up their answers in some way. This is known as an accessibility relation: an accessibility relation is a binary relation between possible worlds that captures how the answers in the list for one possible world are related to the answers in the list for another possible world. Basically, what we're trying to do with accessibility relations is make sense of the fact that what we say about one situation may depend on what we say about another situation. For instance, I might interpret the possible worlds as moments in time and the list describing one includes the question and answer: "Is it 3:00 pm on Thursday, September 22, 2022? Yes." Then we would expect that it would also include things like, "When one minute passes, will it be 3:01 pm on Thursday, September 22, 2022? Yes." But the next minute also has its own list. On that list, both of those questions are answered with "No", but "Is it 3:01 pm on Thursday, September 22, 2022?" is answered with "Yes". The lists of the two times are related to each other, and the question & answer on the first, "When one minute passes, will it be 3:01 om on Thursday, September 22, 2022? Yes" tells us that that is the case. Therefore, the second moment is 'accessible' from the first, if we are talking about a relation of one moment being a minute in the future of another moment. The list describing one tells us a little bit about the list describing the other; they are linked by an accessibility relation.

With possible worlds and accessibility relations, we can define what are known as modal operators. Modal operators are the logical elements in the list-items that tell us about items on other lists. When dealing with times, for instance, 'at some point in the past', 'a minute in the future', 'at every point in the past', etc., are all modal operators. For instance 'at every point in the past, X' on a list for a possible world (call it W) tells us that if there are possible worlds accessible from W in the sense that their lists describe moments in the past for W, all of them have X (whatever X is) on their lists. There are many different kinds of modal operators; 'it is possible that X' (whatever X is) and 'it is necessary that X' (whatever X is) are common ones, for instance. And whenever we have a statement with a modal operator, we can translate it into discussion with possible worlds and accessibility relations. One reason you might do this is to see how one modal operator is related to another. There are many interesting kinds of research done in modal logic that look into the question of what kinds of accessibility relations go with what kinds of modal operators, and with that information you can learn a lot about how a modal operator works and its similarities and differences when compared to other modal operators. Another reason you might want to talk about possible worlds and accessibility relations rather than modal operators is that many modal operators are blunt instruments; they don't pick out particular alternatives, they just talk about them in a general way, and sometimes we want to talk about particular alternatives. There are other uses of possible world semantics, but these are probably the most common.

Those are the basics. Note that a possible world doesn't, strictly speaking, have to be a 'world'; that's just a figure of speech, although your lists could describe worlds. There are a few additional complications that are worth noting, although they aren't necessary for the basics. I already noted impossible worlds above. There are situations where using possible worlds can get very complicated  but if you allow yourself to use impossible worlds as well, you can simplify things a lot. Not everyone likes using them, though, and they are sometimes hard to interpret and relate to each other. Another complication is that people often assume that the list of questions for each possible world is always exactly the same. This is not strictly necessary, and there are times when you wouldn't want to make that assumption, but it simplifies things, so people often assume it. Another point worth noting is that, while I described the lists as being lists of yes/no questions linked with their answers, the more common way it is done is by describing them as lists of propositions linked with their truth values. For instance, instead of "Does 1 come up on die 1? Yes", the item on the list would be thought of as being, "1 comes up on die 1. True." But the two ways of talking (yes/no answers to questions and true/false evaluations of statements) are logically equivalent, so you can pick the one that you find easiest to use.

Ecstatic Heights in Thought and Rhyme

 Shelley's Skylark
by Thomas Hardy

(The neighbourhood of Leghorn: March 1887) 

Somewhere afield here something lies
 In Earth's oblivious eyeless trust
 That moved a poet to prophecies--
 A pinch of unseen, unguarded dust:
 The dust of the lark that Shelley heard,
 And made immortal through times to be;--
 Though it only lived like another bird,
 And knew not its immortality:
 Lived its meek life; then, one day, fell--
 A little ball of feather and bone;
 And how it perished, when piped farewell,
 And where it wastes, are alike unknown.
 Maybe it rests in the loam I view,
 Maybe it throbs in a myrtle’s green,
 Maybe it sleeps in the coming hue
 Of a grape on the slopes of yon inland scene.
 Go find it, faeries, go and find
 That tiny pinch of priceless dust,
 And bring a casket silver-lined,
 And framed of gold that gems encrust;
 And we will lay it safe therein,
 And consecrate it to endless time;
 For it inspired a bard to win
 Ecstatic heights in thought and rhyme.

Wednesday, September 21, 2022

Truth Will Be Truth Alway

 To a Lady
Offended by a Book of the Writer's
by Thomas Hardy 

Now that my page upcloses, doomed, maybe,
Never to press thy cosy cushions more,
Or wake thy ready Yeas as heretofore,
Or stir thy gentle vows of faith in me:

Knowing thy natural receptivity,
I figure that, as flambeaux banish eve,
My sombre image, warped by insidious heave
Of those less forthright, must lose place in thee.

So be it. I have borne such. Let thy dreams
Of me and mine diminish day by day,
And yield their space to shine of smugger things;
Till I shape to thee but in fitful gleams,
And then in far and feeble visitings,
And then surcease. Truth will be truth alway.

Tuesday, September 20, 2022

Three O'Clock on Friday I

 This is the first part of a short story draft.

*****


It was three o'clock in the afternoon on Friday, and the bell of Our Lady of Sorrows rang out with one low, dull tone. A pedestrian walked furtively along the street beside the basilica. He met no one and saw no one, for the people of the city usually avoided this neighborhood. From time to time, the pedestrian would glance behind him, as if afraid even to be seen. In the distance a sound like thunder rumbled, and it was hot and humid in the way it often is before a fierce summer rain, but the pedestrian walked with no expectation of rain, because there was never any rain. His footsteps echoed in the empty street.

He was a long, thin man, pale with sandy-brown hair wisping out from under a shabby fedora. He wore a trench coat that was equally shabby. But it is perhaps not right to say that he wore it; he slouched into it, hunched into it, and the hat on his head was pressed down so low that it might be said to slouch into him as he slouched into his trench. A more suspicious-looking person could hardly be imagined, short of also wearing dark glasses. He wore no dark glasses today, though. He had gambled his away at some point. He also did not care whether he looked suspicious. Everyone in the city looked suspicious, especially when they were doing something suspicious like walking outside. He only cared whether he was recognized.

As he pulled away from the church, he heard something like voices echoing in the distance. He stopped suddenly, his head tilted first this direction and then that, in an effort to ascertain, first, whether he had really heard them, and, second, from what direction. He heard them again, and quickened his pace, turning suddenly into a dingy alleyway whose sides were littered with refuse. He tried to walk softly, but the footsteps insisted on echoing, regardless of what he did.

From this point, he went through a maze of alleyways and side streets and wynds in a way that seemed almost without reason; but he knew his destination, and, after a quick and furtive look around, turned suddenly into a run-down close and knocked on a door with a little steel sliding-window in it. The little window slid open and an eye and part of a face peered with suspicion out at him.

"What do you want?" the eye and part of a face said to him in a surly tone. Said, not asked, for the tone was not really that of a question but of a challenge.

"Fish in newsprint," said the pedestrian.

The little steel window slid shut again and there was a sound of locks unlocking. One bolt, two bolt, three bolt, four bolt. Then the turning of a key in another lock. The door opened, and the eye and part of a face were fully displayed with the other eye and the rest of the face and, indeed, a whole body, a stout man with cold, narrow eyes and a scowly face that made his surly tone seem almost friendly in comparison. He stepped aside, the pedestrian stepped in, and the door shut behind the pedestrian as he proceeded immediately a narrow and badly lit stair. He went up three flights and then knocked on the door.

"Who is it?" asked a muffled voice from inside.

"The milkman," said the pedestrian.

There was a sound of a sliding deadbolt, then a fumbling at the lock on the doorknob, and the door opened. A man, about a head shorter than the pedestrian but equally pale, with strawy blond hair stood there and waved the pedestrian in. His face looked very tired, but he had a small smile that made him seem rather genial in comparison with either the pedestrian or the scowly-faced man. The door was closed behind the pedestrian, the deadbolt locked, the door locked, and only after this did the tired-looking man say anything.

"Well, Howard," he said, "how have you been?" His voice was pleasant and bland.

"Well enough, John," said the pedestrian in a dull tone, his voice slightly more gravelly than John's. "And you?"

"Well enough," said John with his tired smile. "Were you followed?"

Howard hated this question, which was always asked, and for no good reason, since no one would ever have said that they were followed, but he gave the same ritual answer, "No."

"Good," said John. "Everyone else is already here, so we can start. A beer?"

"Yes, please," said Howard dully.

The apartment in which they were standing was not much of an apartment, there was no proper hall, the hall, such as it was, being about one foot long before it opened on a living room with beige walls and a horrid lime green carpet. In the middle of the room was a card table with four folding chairs around it, two currently occupied. John went into an adjoining room and came back with a bottle of beer as Howard draped his trench coat over one of the unoccupied chairs and sat in it, putting his hat on the table beside him. Howard looked across from him at a man with dark skin and curly hair, whose high-cheekboned facial features might have made him look haughty if it weren't for the fact that his wide green eyes made him look perpetually as if he were surprised, or had recently been dazed by something.

"Hello, Sam," said Howard dully. "How are you?"

"Well enough, Howard," said Sam. He had a warm voice, much as one would expect from a radio presenter. "And how are you?"

"Well enough," said Howard in his usual dull tone. He turned his head to the other man, who was tanned and had an unruly shock of red hair. It was dangerous hair, hair that would certainly get one recognized in the street, and all the more so because the man never wore any hat. He was a dangerous man to be with, a man who would surely increase anyone's chances of being recognized, and he had the mocking smile of a dangerous man to be with. He always made everyone nervous because he had narrow, sarcastic eyes that never seemed to look at anyone directly. He looked at Howard mockingly out of the corner of his eye.

"Hello, Howard," he said. His voice was, if anything, even more mocking than his smile. "How are you?"

"Well enough, Tom" said Howard dully. "And you?"

"Well enough, Howard," said Tom, and again his voice made the perfunctory answer sound like he was goading Howard rather than being polite.

John, who had been clearing and replacing the beers already on the table, sat down and said, pulling out a seventy-eight card deck. "Let's waste no time, gentlemen."

They drew for first deal and Sam got the low card and became the dealer. Tom, at his left, cut the deck, then Sam dealt out the cards three at a time to each, randomly each round throwing a card to the kitty in the center of the table, and so it went until all the cards had been dealt. They each threw a starter into the pot, then looked at the eighteen cards in their hand, and John, to Sam's right, began the bidding and the earnest part of the game.

"So Sam," said Tom in his mocking voice, looking at Sam out of the corner of his eye. "Are you still seeing that musician?" Tom liked to talk during the game itself, which irritated Howard to no end. But the man was a gossip and there was no stopping him.

"No," said Sam shortly, clearly not wanting to talk about it.

"She was a beauty," Tom said, and said truly, although his mocking tone might have misled anyone who did not know that into thinking otherwise. "And such a voice. And when she played!"

"Yes," said Sam.

"I heard she even played for the Duke in the Castle once," John said. "Is that true?"

"Yes," said Sam.

"What was that like?" asked John.

"I don't know," said Sam. "She always refused to talk about it."

"I have always wondered what the Castle is like," said John.

There was an uncomfortable pause, and Howard said, in a tone that for once was sharp rather than dull, "Don't wonder about such things. Better never to know."

Sam and Tom both agreed, and Tom said, "If any of us got pulled to the Castle, it certainly would not be for music. And you don't want to be brought before the Duke on the charge of gambling outside the casino and gambling tax evasion."

This went without saying, and Howard wished that Tom would shut up. But Tom was not the shutting-up kind, and his mocking voice went on, occasionally punctuated by a laugh that always reminded Howard somewhat of both a donkey's braying and a duck's quacking, probably because both sound sarcastic. It was only well into the game, with Howard now the dealer, that he brought it back to Sam's musical lady.

"I tell you, Sam, if you dropped your girl, let me know her number, because she was a beauty."

"I didn't drop her," said Sam. 

"But you aren't seeing her," said John, making the sentence a half-question.

"I've had a few relationships like that," said Tom with a sarcastic laugh. "Never with such a good-looking pair of legs, though."

"I'm not seeing her," said Sam, "and I didn't drop her. She was at the Obajdin party when it was broken up by the Ducal Guard. I haven't seen her since, and if anyone asks, I'm not seeing her in any other way."

There was an uncomfortable silence. Then Tom said, "Well, I knew a guy who was pulled to the Castle, and while he was never the same afterward, he did come back." Perhaps it was intended as a sympathetic comment, but 'sympathetic' is not one of the varieties of tones of mockery that Tom's voice could take.

"Shut up, Tom," said Howard.

"Stop talking about such things," said John, almost at the same time. His voice cracked slightly.

Tom looked at John, and despite the fact that John was sitting across from him, still managed to look at him out of the corner of his eye. What this look meant was anyone's guess, but he said nothing, and the game went on in relative silence until, to everyone's misfortune, Tom resoundingly won the next round with a bold bid backed by major trumps and kings in an improbably good hand.

"And the World wins it for me," Tom crowed. "It's too bad we weren't at the casino; I could have broken the bank. Instead, I have to settle for breaking your puny little wallets." And in the face of such an exultant victory, whatever silence Tom was capable of immediately evaporated away. 

Two rounds later, Sam suddenly said, "Do you guys hear something?"

They all froze, their ears straining in the sudden silence of Tom no longer talking, and they did indeed hear something. There was a sound, slightly, but only slightly, muffled, like one large object hitting another large object. Suddenly John said, "Quick! Into the bedroom."

They scrambled to grab money, coats, hats, knocking over their chairs and bumping cards onto the floor as they did so. There was a terrible banging and screeching as they rushed into the bedroom and, as John threw open the closet door, they heard the banging of a fist on the front door of the apartment, Bang! Bang!, and a shout, "Open up in the name of the Duke!" In the closet, John was trying to pull back a sliding panel disguised as a wall, and Sam stepped in to help him. There was banging again at the front door, this time not of a fist but of something far heavier. The panel slid aside to reveal a narrow stairway, and they hurried down it, first John, then Sam, then Tom, then Howard. At the bottom there was no door, only a kind of service hatchway or access panel through which they had to crawl on hands and feet. Above and behind them they heard  something like a splintering and shouting. Beyond the hatchway was a short tunnel, then another access panel to the outside. Out they each came, tumbling and stumbling a little, John, Sam, Tom, and Howard, and as they came out, they began to run in different directions.

Howard had had some difficulty squeezing through the last access panel, so he was considerably behind the others. As he ran, he heard more shouts behind him. He was being chased by the Ducal Guard. He was not chased long. The Ducal Guard are never patient, and the soon just shot him in the back as he ran. 

A searing pain coursed through him, like nothing he had ever felt before. A vivid flash of red and something like stars poured through his brain as he stumbled and fell, face-first, into the ground. His whole body seemed to be throbbing with pain. He could not think very clearly. The pain was horrible, and he did not like it, but he almost liked it; it was horrible but it was vivid. And at least he had been shot. His spinning brain grasped after the alternatives to being shot, looming like a nightmare at the edge of consciousness, but the alternatives all were swiftly spinning away, too, and nothing was left except this: At least he had been shot.

The pain itself seemed to be spinning away, although slowly, and darkness fell. He still heard voices in the darkness. Then, before it all went silent, he heard in the distance the bell of Our Lady of Sorrows strike one low tone, making clear to the whole city that it was three o'clock in the afternoon on Friday.

to be continued

Yea, I Have Wondered, Often Wondered

 To the Moon
by Thomas Hardy
 

“What have you looked at, Moon,
 In your time,
Now long past your prime?”
“O, I have looked at, often looked at
 Sweet, sublime,
Sore things, shudderful, night and noon
 In my time.” 

“What have you mused on, Moon,
In your day,
So aloof, so far away?
“O, I have mused on, often mused on
 Growth, decay,
 Nations alive, dead, mad, aswoon,
 In my day!”

 “Have you much wondered, Moon,
 On your rounds,
Self-wrapt, beyond Earth's bounds ? ”
“Yea, I have wondered, often wondered
 At the sounds
 Reaching me of the human tune
 On my rounds." 

 “What do you think of it, Moon,
 As you go?
 Is Life much, or no?”
 “O, I think of it, often think of it
 As a show
 God means surely to shut up soon,
 As I go."