Saturday, April 29, 2017

Jane Austen, Sense and Sensibility

Introduction

Opening Passage:

The family of Dashwood had long been settled in Sussex. Their estate was large, and their residence was at Norland Park, in the centre of their property, where, for many generations, they had lived in so respectable a manner as to engage the general good opinion of their surrounding acquaintance. The late owner of this estate was a single man, who lived to a very advanced age, and who for many years of his life, had a constant companion and housekeeper in his sister. But her death, which happened ten years before his own, produced a great alteration in his home; for to supply her loss, he invited and received into his house the family of his nephew Mr. Henry Dashwood, the legal inheritor of the Norland estate, and the person to whom he intended to bequeath it. In the society of his nephew and niece, and their children, the old Gentleman's days were comfortably spent. His attachment to them all increased. The constant attention of Mr. and Mrs. Henry Dashwood to his wishes, which proceeded not merely from interest, but from goodness of heart, gave him every degree of solid comfort which his age could receive; and the cheerfulness of the children added a relish to his existence.

Summary: On the death of Henry Dashwood, the estate passes to the son by his first marriage, John Dashwood, who is always well situated; which leaves the second wife and her two daughters, Elinor and Marianne, dependent on his generosity. However, with the help of his wife, Fanny, he talks himself out of helping them, and Mrs. Dashwood and her daughters have to move to a cottage on the estate of her cousin, Sir John Middleton. While there, they meet Colonel Brandon, a bachelor in his mid-thirties who falls in love with Marianne -- but has secrets in his past. Marianne also meets the young, handsome, and personable John Willoughby, and they grow very attached. Elinor, in the meantime, has had what seemed to be the beginning of a relationship with Edward Ferrars, Fanny's brother, but he, too, has secrets in his past.

Sense and Sensibility is in many ways Austen's most relentlessly acidic novel. Most of the characters are hypocrites, or, if not hypocrites, foolish. The integrity of each of the main male characters is under a cloud at some point in the work, and most of the women are self-absorbed in one way or another. The petty malices of some of the characters are quite malicious, and the narrator does not in any way throw a veil over any of it. Both Chapter 34 and and the final chapter of the work are masterpieces of biting commentary:

Mrs. John Dashwood had so much confidence in her husband's judgment, that she waited the very next day both on Mrs. Jennings and her daughter; and her confidence was rewarded by finding even the former, even the woman with whom her sisters were staying, by no means unworthy her notice; and as for Lady Middleton, she found her one of the most charming women in the world!

Lady Middleton was equally pleased with Mrs. Dashwood. There was a kind of cold hearted selfishness on both sides, which mutually attracted them; and they sympathised with each other in an insipid propriety of demeanor, and a general want of understanding.

Yet the work is perhaps also the Austen novel that is most generous with its characters. The petty malices are often explained, and due to poor upbringing. The shadows over the characters of the men turn out to be not so dark as they seemed at first, although they do not always completely vanish away. The hypocrisy and selfishness turns mostly to be fairly harmless. And in many cases, we discover a deeper depth to a character than might at first be seen, even though the flaws remain in full view. Sir John Middleton is a bit silly and obsessed with hunting (all of the men are), not very bright or very educated, but he is a sociable man who loves to bring people together. Mrs. Jennings, the wife of Fanny Dashwood, is silly and vulgar and gossipy, without any elegance -- but she is also kind and generous. Mrs. Dashwood's imprudence is repeatedly highlighted, but she is shown as an amiable character, who truly loves her daughters, and all things told, has raised them fairly well. All of the significant characters, even the villains, get what they want in the end, or at least whatever happy ending they chose; good sense and sound judgment can see that some of these 'happy endings' are far better than others, but the author generously gives them all the triumph for which they strove.

It is perhaps not surprising that there is so much repentance in this novel, both genuine and false, and of the genuine, both of the sort that leads to true improvement and of the sort that is selfish. Marianne's brush with death brings her to a recognition of the need for "atonement to my God" and the importance of self-regulation by reason, religion, and work. The difference between prudence and the opposite is in part the ability not to be locked in the prison of one's own ideas, as Marianne's romanticism has narrowed her world, or of ceaseless self-regard. It has become common to suggest that perhaps the novel suggests that Elinor needs a bit of sensibility just as Marianne needs a bit of sense, and that the true message of the work is that we need both. But this is, I think, fairly obviously a case of reading with wishful thinking as one's guide. If by 'sensibility' we mean the power to feel, Elinor has it in spades; and Marianne's 'sensibility' is in fact acquired, not natural, passion, spurred on by ideas that demand excess rather than allowed to fall into their natural bounds. The modern world is Marianne-ish, or at least likes to flatter itself that it is so; naturally it would like to pretend that Marianne required only a little adjustment occasionally, and not a fundamental repentance of some of her leading ideas. But there is no remedy for a lack of prudence except repentance.

As a purely incidental matter, one of the things I was struck by on this reading was just how much the marriages of the men, as well as of the women, are front and center. Austen is sometimes treated as telling stories of women in a world in which women must marry well to do well; it is often overlooked, I think, that it's a world in which the same is true of men. It comes up in other novels, but with the central heroes often being quite wealthy it is not always obvious. But it is a central plot point in Sense and Sensibility.

In addition, I also watched the Tamil modernization, Kandukondain Kandukondain, which was quite good. India has quite a massive enthusiasm for Austen's work, so despite the fact that the movie modernizes it and sets it in India, it is in many ways very faithful to the original inspiration. (It likely helps that India, like Regency England, is still a culture in which marrying well is not uncommonly essential to doing well.) It tells the story of sensible Sowmya and romantic Meenakshi; Sowmya bears the burden of being considered unlucky in a culture that highly prizes luck, and Meenakshi insists she will only love a man who can sweep her away with Bharathiar, the great Tamil poet. (I'm not an expert on Bharathiar, by any means, but from what I have seen of his work, this is an inspired choice, since Bharathiar's work is often about freedom, fearlessness, and sincerity of feeling.) Sowmya meets Manohar, an aspiring director, and Meenu meets Srikanth, a Bharathiar-quoting finance executive; they also both meet Major Bala, who lost his leg in the war and now runs a business selling flowers. (Also an inspired choice, I think: the apparently prosaic former soldier makes a practical living doing something that has a poetic side.) And much of the structure of the tale works in the same way from there. Interestingly, they move the financial crisis from the beginning to somewhere closer to the middle; this gives more time to make the romantic interactions plausible on the screen. The big differences, I think, are (1) that Sowmya, though sensible, does not quite have the thorough self-command of Elinor, and one of the things she has to learn to do is not just bear the burden of being unlucky but let it go entirely; and (2) that we get less of a sense that Meenu's problem is her insistence on making everything fit with her ideas than we do with Marianne -- rather, she has to learn to focus on inner beauty rather than the superficial. All in all, though, it highlights some interesting facets of the story in a fascinating way -- exactly what a modernization should do.

Favorite Passage: From Chapter 34:

Mrs. Ferrars was a little, thin woman, upright, even to formality, in her figure, and serious, even to sourness, in her aspect. Her complexion was sallow; and her features small, without beauty, and naturally without expression; but a lucky contraction of the brow had rescued her countenance from the disgrace of insipidity, by giving it the strong characters of pride and ill nature. She was not a woman of many words; for, unlike people in general, she proportioned them to the number of her ideas; and of the few syllables that did escape her, not one fell to the share of Miss Dashwood, whom she eyed with the spirited determination of disliking her at all events.

The craftsmanship of this little description is utterly extraordinary; Austen takes everything that in an ordinary description would be used to mitigate the harshness of the description and turns it in the opposite direction, so that everything that would ordinarily have become a compliment, or at least a qualification, turns into a deeper razor-cut.

Recommendation: Highly Recommended, obviously. And Kandukondain Kandukondain is also Highly Recommended; Tabu and Mammootty in particular do an extraordinary job.

Prudent Charity

Today is the feast of Caterina di Giacomo di Benincasa, better known as St. Catherine of Siena (1347-1380), Virgin and Doctor of the Church. She entered the Third Order of the Dominicans, and attempted to live a secluded life, but later had a vision in which she was told that she must be more involved in the world. As a Dominican tertiary, she is currently the only female Doctor of the Church who was not a nun (indeed, unless I am mistaken, the only nonconsecrated layperson in the whole group). She was actively involved in ecclesiastical politics, both in person and by correspondence. She has always been a very popular saint. In 1866 she was declared one of the patron saints of Rome; in 1939 she was designated, with Francis of Assisi, patron saint of Italy; and in 1999 she was designated one of the six patron saints of Europe. From one of her letters, to Ristoro Canigiani, one of the people for whom she became spiritual director:

It seems to me that the Sweet Primal Truth teaches us what we ought to seek when in the holy Gospel, reproving man for the intemperate zeal which he bestows on gaining and holding the honours and riches of the world, He said: "Take no thought for the morrow. Its own care suffices for the day." Here He shows us that we should consider prudently the shortness of time. Then He adds: "Seek first the Kingdom of Heaven; for your heavenly Father knows well that you have need of these lesser things." What is this kingdom, and how is it sought? It is the kingdom of eternal life, and the kingdom of our own soul, for this kingdom of the soul, unless it is possessed through reason, never becomes part of the kingdom of God. With what is it sought? Not only with words—we have already said that such as these are not recognized by God—but with the yearning of true and real virtues. Virtue is what seeks and possesses this kingdom of heaven; virtue, which makes a man prudent, so that he works for the honour of God and the salvation of himself and his neighbour, with prudence and maturity. Prudently he endures his neighbour's faults; prudently he rules the impulse of charity, loving God above everything, and his neighbour as himself. This is the rule: that he hold him ready to give bodily life for the salvation of souls, and temporal goods to help the body of his neighbour. Such a rule is set by prudent charity. Were he imprudent, it would be just the opposite as with many who use a foolish and crazy sort of charity, who many a time, to help their neighbour—I speak not of his soul, but of his body—are ready to betray their own souls, by publishing abroad lies, giving false witness. Such men as these lose charity, because it is not built upon prudence.


(Statue of St. Catherine of Siena in the Palazzio Vecchio in Florence)

Friday, April 28, 2017

The Ruling of Prudence

The proper end of each moral virtue consists precisely in conformity with right reason. For temperance intends that man should not stray from reason for the sake of his concupiscences; fortitude, that he should not stray from the right judgment of reason through fear or daring. Moreover this end is appointed to man according to natural reason, since natural reason dictates to each one that he should act according to reason.

But it belongs to the ruling of prudence to decide in what manner and by what means man shall obtain the mean of reason in his deeds. For though the attainment of the mean is the end of a moral virtue, yet this mean is found by the right disposition of these things that are directed to the end.

Thomas Aquinas, ST 2-2.47.7

Elements of Modal Logic, Part III

Part II.

Another, more complicated example. Suppose you are trying to work out your schedule, so you are putting together a to-do list. You can have a Reference Table summarizes your to-do list for a given week. This means that the Reference Table is not one of the tables described by itself, because your to-do list is not a day of the week! Suppose further that this is your Reference Table:

REFERENCE TABLE (Things I Have to Do This Week)
□ (If it is the day before trash collection day, take out the trash)
□ (Brush my teeth)
□ (Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen)
◇ (Do not mow the lawn and Do not weed the garden)
◇ (It is the day before trash collection day)
◇ (Do not clean the kitchen)
◇ (Do not take out the trash)
◇ (Do not weed the garden and Do not clean the kitchen)
◇ (Do not clean the kitchen and Do not mow the lawn)
◇ (It is Monday and it is not the day before trash collection day)
◇ (Go to the movies)

The Box statements are like standing rules that I always have to keep in mind every day and not forget; and the Diamond statements are things I have to get done at some point this week or, in some cases, things that I should not do on at least some days. For instance, we can see that I should have some day on which I don't weed the garden and don't clean the kitchen.

So what should our schedule be like, if we just go off the information in our Reference Table? Although I only stated half of each rule in the previous post, our reasoning gives us a complete rule for each modal operator. We have a rule for Box:

(1) □ on the Reference Table means the thing to which it is applied can be found on any table there might be.

Or we could state this more simply as "□ tells us something that is constant for any table."

And we have a rule for Diamond:

(2) ◇ on the Reference Table means that there is a table on which we can find the thing to which it applies.

Or we could state this more simply as "◇ tells us there is a table with something on it."

If we apply these rules, we get eight tables, in no particular order, indicated by our Diamond-ed statements (more on the number in a bit), and each of these will have that Diamond-ed statement on it and will also have every statement that is Box-ed. I'll label each one with a letter.

TABLE A: Some Day or Other in the Week
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
Do not mow the lawn and Do not weed the garden

TABLE B: Some Day or Other in the Week
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
It is the day before trash collection day

TABLE C: Some Day or Other in the Week
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
Do not clean the kitchen

TABLE D: Some Day or Other in the Week
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
Do not take out the trash

TABLE E: Some Day or Other in the Week
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
Do not weed the garden and Do not clean the kitchen

TABLE F: Some Day or Other in the Week
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
Do not clean the kitchen and Do not mow the lawn

TABLE G: Monday
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
It is Monday and it is not the day before trash collection day

TABLE H: Some Day or Other in the Week
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
Go to the movies

Note that we know that Table G is Monday, because Table G is the one created by "◇ (It is Monday and it is not the day before trash collection day)"!

Let's look a little more closely at Table A. One of our statements in Table A is "I mow the lawn, or I weed the garden, or I clean the kitchen," while another statement is "I do not mow the lawn and I do not weed the garden". If we put these two together, we can see that the only way they can both be put together as part of our schedule for the day is if, on whatever day A may be, I clean the kitchen. So this follows as a conclusion on Table A, and we can write it down as something we know about A; to indicate that it's a conclusion, I'll put it below a line.

TABLE A: Some Day or Other in the Week
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
Do not mow the lawn and Do not weed the garden
------------------------------------
Clean the kitchen

We can do the same thing with other tables: look to see if what the Reference Table requires for that day gives us a conclusion specific to that day. For instance, with Table B:

TABLE B: Some Day or Other in the Week
If it is the day before trash collection day, take out the trash
Brush my teeth
Do at least one of these three: Mow the lawn, or Weed the garden, or Clean the kitchen
It is the day before trash collection day
------------------------------------
Take out the trash

The conclusions you can get may vary from table to table. On some tables we might not have enough information to derive these kinds of additional conclusions, but this is just a matter of how much we're told by the Reference Table.

One thing that I've glossed over so far is an additional bit of information that's not on our Reference Table but would likely be assumed in the real world: a week has only seven days. Let's assume this little bit of information. We already knew that our tables could be all the tables or only some of them; and we already knew that some of our tables could actually be describing the same thing without our knowing it. Knowing that there are only seven days in a week, and that our tables describe days in a week, and that there are eight tables, we know that at least two tables (maybe more, but at least two) describe the same day. What is more, we can see by the statements that some tables cannot be describing the same day, because they say contradictory things.

The following pairs of tables cannot describe the same day: A and C, A and E, B and D, B and G, C and E, C and F, E and F. If we wanted to, we could add this as an extra conclusion to all of the relevant tables (e.g., we could add 'Today is not Monday' to Table B). Any of the others might be describing the same day. And, again, at least two tables, whichever ones they might be, definitely are describing the same day. And (a little harder to see, but also true)note that H could be describing the same day as any other table -- it's not inconsistent with any of them. Given our to-do list, we still have a lot of flexibility with our schedule, but thinking through the rules for our schedule gives us a sense of what kind of schedule makes sense and what kind of schedule doesn't. None of this is difficult -- it is just a big logic puzzle -- but it's worth taking some time to get a sense of how it works, and all the kinds of conclusions you can draw, and enjoy the fact that you are doing modal logic.

**********

But where do we go from here?

Modal logic is often called intensional logic, which is just a fancy way of saying that it's a logic in which it can matter to the logic what you're talking about. In this case, since we already know that a week has seven days, we can take that into account in our reasoning, because we're talking about days in the week.

There's no limit to what assumptions you could add in this way, or to what number of assumptions you can add in this way. It just depends on what you're doing. Adding assumptions in this way usually keeps our modal reasoning very simple and very weak. There are assumptions, however, that you can add that make your modal reasoning much more powerful, capable of doing much more, and there are kinds of situations where the assumptions make sense, and kinds of problems where you need that extra power. These assumptions are assumptions about Box and Diamond themselves. Many of the most useful fall into two groups:

1. assumptions about how Box and Diamond are related to each other
2. assumptions about what it means if you have a modal operator (either Box or Diamond) for a statement that already has a modal operator (either Box or Diamond)

We'll set the second assumption aside for right now, and focus on the first kind of assumption. So far we only have a rule for Box and a rule for Diamond; they don't really have anything directly to do with each other, at least as far as we know. But what if we could get information about Box from Diamond and/or information about Diamond from Box? This would let us do a lot more, so that's what we need to consider next.

It Comes, It Comes, as Holy Darkness Can

A Ballade of the First Rain
by G. K. Chesterton


The sky is blue with summer and the sun,
The woods are brown as autumn with the tan,
It might as well be Tropics and be done,
I might as well be born a copper Khan;
I fashion me an oriental fan
Made of the wholly unreceipted bills
Brought by the ice-man, sleeping in his van
(A storm is coming on the Chiltern Hills).

I read the Young Philosophers for fun
—Fresh as our sorrow for the late Queen Anne—
The Dionysians whom a pint would stun,
The Pantheists who never heard of Pan.
—But through my hair electric needles ran,
And on my book a gout of water spills,
And on the skirts of heaven the guns began
(A storm is coming on the Chiltern Hills).

O fields of England, cracked and dry and dun,
O soul of England, sick of words, and wan!—
The clouds grow dark;—the down-rush has begun.
—It comes, it comes, as holy darkness can,
Black as with banners, ban and arriere-ban;
A falling laughter all the valley fills,
Deep as God's thunder and the thirst of man:
(A storm is coming on the Chiltern Hills).

ENVOI

Prince, Prince-Elective on the modern plan
Fulfilling such a lot of People's Wills,
You take the Chiltern Hundreds while you can—
A storm is coming on the Chiltern Hills.

Thursday, April 27, 2017

Elements of Modal Logic, Part II

Part I

Let's do a little more carefully what we did in the previous post. We are taking inventories of universes of discourse and keeping track of these inventories with tables; these need to be compared, but also to be kept distinct. We need to keep track of what's going on in these comparisons of different tables, and the easiest way is also to put it in a table. We can call this the Reference Table. It's where we'll find our modal information. The Reference Table can describe different things, depending on what we are doing. The second most important things in modal logic is usually to know what your Reference Table is and how you are using it; a lot of mistakes in modal logic are caused by switching Reference Tables, or forgetting to track things consistently with it.

(Is the Reference Table just like the tables it is keeping track of? Depending on what you are doing, the Reference Table is sometimes set apart, but it can also be one of the tables we are keeping track of. For instance, you could be doing something with times, and want to make the Reference Table 'now' -- then the Reference Table is one of the tables of times. We could also set things up so that any table can be the Reference Table for other tables. There are lots of ways we can do it, and we will have to consider some of them eventually. But we need to start with the easiest case. In the example that follows, the Reference Table is just a different sort of thing from the tables it describes.)

The single most important thing in modal logic, however, is to know exactly what all your other tables are supposed to describe. Suppose you want to compare the Tolkien books on the top shelf of your bookcase; and, as it happens, you have three: The Hobbit, The Lord of the Rings, and The Silmarillion. We will therefore have one table for each of these. We can make a table for each of these, and put down some of the things we know about the characters in those books.

Characters mentioned in the Tolkien books on the top shelf of my bookcase
TABLE 1: The Hobbit TABLE 2: The Lord of the Rings TABLE 3: The Silmarillion
Bilbo BagginsBilbo BagginsGaladriel
GandalfGandalfElrond
ElrondElrondGandalf
Frodo BagginsFrodo Baggins
Galadriel

Now, if this is all we know about the characters, we still can put some information on our Reference Table. We could have a lot of different rules, depending on exactly what we want to track. Let's make these our rules:

(1) If we would find something on any table there might be, we can list it in our Reference Table as Box (□).

(2) If there's something definitely on some table somewhere, we can list it as Diamond (◇).

(Note that rule 1 is tentative in a way rule 2 is not, since it doesn't actually tell us that there are any other tables besides the Reference Table, while rule 2 always gives us a table; the reason for this difference is complicated, and somewhat arbitrary, but it's the way many systems are set up, so we'll go with it for now.) The Box tells us that, for the things we are talking about, something is found always or everywhere or necessarily or without exception or invariably, no matter what table we might be looking at; the Diamond tells us that something is on some table. How we translate Box or Diamond -- what it represents in practice -- depends on what we're talking about and what comparison we are making. In the above example, Box tells us about every Tolkien book on the top shelf and Diamond tells us about some Tolkien book or other among those on the top shelf.

REFERENCE TABLE: Tolkien Books on the Top Shelf
□(Elrond is a character)
□(Gandalf is a character)
◇(Bilbo Baggins is a character)
◇(Frodo Baggins is a character)
◇(Galdriel is a character)

This is not an exhaustive list of statements we could make, since there are lots of others, like ◇(Elrond and Gandalf and Bilbo Baggins and Galadriel and Frodo Baggins are characters), which is a description of Table 2, but this will do for our purposes, since we're keeping things simple for now. (Note, too, why our Reference Table is separate from the other tables: the Reference Table talks about specific Tolkien books on the top shelf. But there is no Tolkien book on the top shelf that is called 'Tolkien Books on the Top Shelf'.)

So now we've taken our original tables, where there are no modal statements, and created a table of modal statements out of them. But in many cases of modal reasoning, we aren't just summing up our information with modal statements; we are working backwards from modal statements to try to see what they tell us about the things they describe.

So let's forget our first three tables for a moment, and suppose that someone else did all the work to get the Reference Table, and we are trying to reconstruct the information in the other tables just from what the Reference Table tells us, without knowing anything about what the books are. Because our Reference Table does not describe the other tables in exact terms, we will not be able to reconstruct them exactly. Let's see how close we can get, though.

REFERENCE TABLE: Tolkien Books on the Top Shelf
□(Elrond is a character)
□(Gandalf is a character)
◇(Bilbo Baggins is a character)
◇(Frodo Baggins is a character)
◇(Galdriel is a character)

We'll do the Diamond statements first, because each one tells us something about some table somewhere. But, they don't tell us which tables. The statements might be true for the same table, but they might not be. And since we have three Diamond statements, we get three tables, which might be different or might not, and which might be all of the original tables or only some of them:

some table or other (1)
Bilbo Baggins is a character

some table or other (2)
Frodo Baggins is a character

some table or other (3)
Galadriel is a character

But our Box statements still need to be added! By rule 1, they tell us that any tables the Diamond statements give us have the other statements, too. So now our tables look like:

some table or other (1)
Bilbo Baggins is a character
Elrond is a character
Gandalf is a character

some table or other (2)
Frodo Baggins is a character
Elrond is a character
Gandalf is a character

some table or other (3)
Galadriel is a character
Elrond is a character
Gandalf is a character


And remember, just from what our Reference Table tells us, we don't know if these are all the same table, or if two of them are the same, or if none of them are the same; likewise, we don't know whether these are all the tables or just some of them. The information in our Reference Table was very incomplete and not very precise. But it still gave us enough information to reconstruct something about the Tolkien books on the top shelf.

Most reasoning in modal logic is like this last example: we have a Reference Table and are trying to see what its implications are. You can think of it like a puzzle, in which the Reference Table is a list of clues that someone else gave you, and you are trying to see what those clues tell you.

To move forward, we need to look at how some slightly more complicated cases work. What you'll find, though, is that we've pretty much covered all the essentials of basic modal reasoning -- it all works exactly like this, and more complicated cases are only more complicated because they give us more information to use.

Part III

Wednesday, April 26, 2017

Elements of Modal Logic, Part I

This is a reworking of an experiment I began but never quite finished a while back, on a different approach to modal logic. What is the simplest way to teach it that allows the greatest kind of flexibility for intelligent use of it? The idea is that instead of trying to jump into standard modal logic systems, one should actually get some sense of how one builds modal logic from scratch, without necessarily going into all the technicalities that are there are only to get a system of a particular shape for reasons of purely logical convenience. I actually think this is a problem with a lot of 'introductory' logic courses; they are usually actually courses in using technical formulae to solve narrow ranges of problems. This is an excellent thing to have. But it's not really introducing you to anything except very particular technical formulae.


Whenever we are reasoning, some things are relevant and some are not. The universe of discourse, in the sense we will use it here, is the category that includes all the things that are relevant and leaves out all the things that are not relevant. Everything in the reasoning presupposes it. For instance, if I say, "Dragons breathe fire," it matters considerably whether we are talking about characters in a story or real-life monitor lizards -- if I switch from one to the other, it is like we are in a completely different universe of topics. A universe of discourse can be any kind of thing that you can talk about -- a time, a place, a shelf, a ball, an animal, anything whatsoever.

Sometimes we want to take an inventory of things that are in a universe of discourse. For instance, your universe of discourse might be 'Things that are scheduled at 2 o'clock'; and it might be important to know what some of these things are. Imagine we had a table corresponding to this universe of discourse; on this table we could keep track of our inventory of the universe of discourse:

TABLE
Tom's party
Gabriel's job interview
The End of the World

But in real-life discussion, things can get more complicated than this. So, for instance, we might have a very simple table, for claims about Greek philosophers, on which we've written:

TABLE 1
Socrates is strange.
Plato is not strange, but elegant.
Aristotle is not strange, but bossy.

We could then put these together in ways logically implied by these premises, and say that these things are 'true for the Table 1 inventory' or just 'true at Table 1'.

But we aren't always considering only one category; sometimes it is necessary to compare things across categories while keeping clear about the fact that they are in different categories. For instance, Table 1 might correspond to Greek philosophers at a certain time, but we might then also be interested in the same Greek philosophers but at different times. So we could have different tables. If Table 1 is for Greek philosophers on Tuesday, perhaps another thing we are interested in is the same group on Wednesday, so we can make another table corresponding to that, e.g.:

TABLE 2
Socrates is strange.
Plato is strange.
Aristotle is not strange, but bossy.

Strictly speaking, each table works on its own. For instance, on Table 1, we can reasonably conclude that neither Plato nor Aristotle are strange; but on Table 2, this is false. This is not a contradiction, since in drawing each of these conclusions we only stay on the relevant table, and don't leap from one to the other.

But we may also be interested in how the universes of discourse compare to each other. And we certainly can say something about that. For instance, we can say, if these are our only two tables, "'Socrates is strange' is constant for all our inventories." We can also say, "We can find an inventory with the claim that Plato is strange." In our example, the tables in question are interpreted as days, but they could be anything else. We could have tables that represent cities, possible worlds, stories, or whatever we please, because the tables just list things in universes of discourse, and anything we can talk about can be a universe of discourse.

At its most crude and basic, this is all that modal logic is. "On any table, we would find that Socrates is strange" is a Box proposition; we could also say it has a strong modality. "We can find a table on which Plato is strange" is a Diamond proposition, which is a weak modality.

Even this on its own is, logically speaking, very important. But we can do so much more! For instance, we've been assuming that it's easy to know what you have to do to find the right information. But you might still be learning what's in the inventories for each universe of discourse! It could be that there are restrictions on what we can know. There might be tables that we can find if we start at one table but not if we start at another. Likewise, one table might be able to teach you about other tables. There are lots of possibilities, because there are endlessly many universes of discourse; and what we need to do is to start thinking about how to handle all of these possibilities.

Part II

The Sunbeams of Thy Face

Psalm 57
by Lady Mary Sidney


Thy mercy, Lord, Lord, now thy mercy show:
On thee I lie;
To thee I fly.
Hide me, hive me, as thine own,
Till these blasts be overblown,
Which now do fiercely blow.

To highest God I will erect my cry,
Who quickly shall
Dispatch this all.
He shall down from heaven send
From disgrace me to defend
His love and verity.

My soul encaged lies with lions’ brood,
Villains whose hands
Are fiery brands,
Teeth more sharp than shaft or spear,
Tongues far better edge do bear
Than swords to shed my blood.

As high as highest heav’n can give thee place,
O Lord, ascend,
And thence extend
With most bright, most glorious show
Over all the earth below,
The sunbeams of thy face.

Me to entangle every way I go
Their trap and net
Is ready set.
Holes they dig but their own holes
Pitfalls make for their own souls:
So, Lord, oh, serve them so.

My heart prepared, prepared is my heart
To spread thy praise
With tuned lays:
Wake my tongue, my lute awake,
Thou my harp the consort make,
Myself will bear a part.

Myself when first the morning shall appear,
With voice and string
So will thee sing:
That this earthly globe, and all
Treading on this earthly ball,
My praising notes shall hear.

For god, my only God, thy gracious love
Is mounted far
Above each star,
Thy unchanged verity
Heav’nly wings do lift as high
As clouds have room to move.

As high as highest heav’n can give thee place,
O Lord, ascend
And thence extend
With most bright, most glorious show
Over all the earth below,
The sunbeams of thy face.

Tuesday, April 25, 2017

Smith on Sensibility and Self-Command

As taste and good judgment, when they are considered as qualities which deserve praise and admiration, are supposed to imply a delicacy of sentiment and an acuteness of understanding not commonly to be met with; so the virtues of sensibility and self-command are not apprehended to consist in the ordinary, but in the uncommon degrees of those qualities. The amiable virtue of humanity requires, surely, a sensibility, much beyond what is possessed by the rude vulgar of mankind. The great and exalted virtue of magnanimity undoubtedly demands much more than that degree of self-command, which the weakest of mortals is capable of exerting. As in the common degree of the intellectual qualities, there is no abilities; so in the common degree of the moral, there is no virtue. Virtue is excellence, something uncommonly great and beautiful, which rises far above what is vulgar and ordinary. The amiable virtues consist in that degree of sensibility which surprises by its exquisite and unexpected delicacy and tenderness. The awful and respectable, in that degree of self-command which astonishes by its amazing superiority over the most ungovernable passions of human nature.

[Adam Smith, Theory of Moral Sentiments, I.1.45. It is interesting to find this juxtaposition outside of Sense and Sensibility, although it could just be a convergence or influence from the general ambience. But I'm not sure it is consistent with the general thrust of S&S to divide up virtues into sensibility-virtues and self-command-virtues like this.]

Monday, April 24, 2017

Evening Note for Monday, April 24

Thought for the Evening: Progymnasmata and Language-Learning

A comment by Cristina on the evening note about developing a treasury of ideas led me to think about the possibility of adapting classical rhetorical pedagogy to language-learning -- or, to be more exact, to learning of language fluency (since the basics would have been covered by grammar rather than rhetoric). It makes considerable sense, actually, if you think about it, since rhetoric is concerned with speaking and writing well.

Classical rhetoric is constituted by the five canons -- inventio or heuresis (discovery of appropriate things to say), dispositio or taxis (organizing what is said in a coherent way), elocutio or lexis (style in which it is said), memoria or mneme (vocabulary, patterns of discourse, and the like), pronuntiatio or hypokrisis (which includes pronunciation but is more broadly the whole acting-out of what is said, so would include things like gestures and tones, or punctuation in writing). These can operate more or less simultaneously in actual speaking and writing, so they can be considered the elements of speaking or writing well, and together constitute the goal of rhetorical pedagogy.

Actual classical rhetorical pedagogy usually broke up into two parts: progymnamsata and gymnasmata. Gymnasmata were full-scale rhetorical declamations on any topic, and thus practice for advanced students. Progymnasmata were more rudimentary exercises designed to focus on specific skills needed for the more advanced work, and thus slowly to get you to the point where declamation was a real possibility. They could vary, but there were twelve or thirteen that were traditionally standard. (There could be some overlap, but they were broadly speaking in sequential order.)

(1) Mythos: Students would be given a fable, usually from Aesop, and would have to adapt it -- both summarize it in simpler terms and expand upon it by adding descriptions. One can see the advantage of doing this in language-learning: the fable provides a sort of frame that the student can rely on while exercising their skills. They can use the same patterns of speech, the same phrases, and like, but have to modify it to new use.

(2) Diegema: This exercise would go a bit further by having the students tell a complete story, and would be varied by telling the whole story from the beginning, or starting from the middle, or starting from the end.

(3) Chreia: Students would start with an anecdote with a precise point -- a specific action or saying, or the like; a wide variety of different kinds of anecdotes would be used, and they would be varied in different ways (rephrased as praises or condemnations, given brief explanations, or compared to other anecdotes). While the story would be simpler, the skill would be more advanced, since it requires both concision and precision, as you would have to do strictly what was required to fulfill the various tasks.

(4) Gnome: This would work the same way, but with proverbs and maxims.

(5) Anaskeue: Students would be given a myth or legend and argue that it was absurd, or doubtful, or useless, etc.

(6) Kataskeue: Students would take the other side and argue in favor of the myth or legend, that it was reasonable, or probable, or practically valuable, or the like.

(7) Koinos topos: Students would talk about general virtues or vices, qualities, or characteristics, or talk about general types of people.

(8) Enkomion: Students would go beyond (7) by praising virtues, abstract qualities, specific people, places, or all sorts of other things in close and varied detail.

(9) Psogos: This would work the same way, but from the opposite side, criticizing things in detail.

(10) Ethopoeia: Students would construct a speech for a historical or mythological character, speaking from that person's point of view, and in a way appropriate to that person. This would start getting quite advanced, because you would need to consider things like how polished or concise or florid a person's style might be, and, of course, you would have to change it up with different characters.

(11) Ekphrasis: Ekphrasis is basically word-painting, in which one uses all the resources of language to describe something (often a work of art, like a literal painting, or a sculpture) to give people who had not seen it a vivid imaginative picture of it.

(12) Thesis: With thesis one would develop precise, specific arguments for this or that being the correct answer to a general question (like whether it was beneficial to marry, or whether the world is spherical. At this level the exercises are starting to take the same form as the later declamations, with introductions, descriptions, arguments for and against, and conclusions. The exercises would be varied not only by questions but by different kinds of argument -- whether things were legal, or just, or useful, or beneficial, or possible, and the like.

(13) Nomou eisphora: While (12) is at a general level, this exercise (which literally means 'proposal of law') would go further by dealing with specific questions (specific laws, specific policies). At this point, the student is taking the first steps in full-scale declamation.

Throughout every stage, there would be a lot of imitation and borrowing -- full creativity would be one of the things that would distinguish progymnasmata from gymnasmata -- as well as detailed analysis of examples to see how they worked so that the student could do the same. One sees this to some extent in ordinary language-learning -- think of all the endless dialogue-fragments one gets in standard language textbooks -- but, of course, language textbooks tend to focus on grammar; rhetorical proficiency is another level of language-learning on its own.

Various Links of Note

* Samizdat is a form of political resistance involving the self-publishing of works to get around state censors. One of the more notable samizdat publications is the very long-running periodical, The Chronicle of the Catholic Church in Lithuania, also known as the LKB kronika, which ran from 1972-1989 and kept track of the oppression of the Catholic Church (as well as related oppressions) in the Lithuanian SSR. Copies would be handtyped and then smuggled around, and then out to where they could be read over Vatican Radio (thus giving it a much larger audience than most samizdat did). It makes interesting reading. Very grim, but also there are regular sparks of hope -- a poem smuggled around, a report of Catholics being confirmed despite Soviet inquiries, and the like. And, of course, it kept going and going and going. You can read a number of the issues translated into English online.

* Lydia Moland, Friedrich Schiller, at the SEP.

* Joe Gibes, How to Make Nazi Doctors

* James Hannam, Medieval Science in Medieval Fiction

* Andrew Loke, The resurrection of the Son of God: a reduction of the naturalistic alternatives

* An English translation of the Suan shu shu, which I believe is currently the oldest extant Chinese mathematical text, dating from about the second century BC.

Currently Reading

Jane Austen, Sense and Sensibility
Donald Ainslie, Hume's True Scepticism
Andrea Wulf, The Invention of Nature: Alexander von Humboldt's New World
Michael Flynn, Eifelheim

A Poem Translation Draft

Novel
by Arthur Rimbaud


I.

You are not serious when you are seventeen;
- a fair night, thick with stein and lemonade,
bright cafes, chandeliers in sheen,
- you walk the green linden promenade.

The lindens smell fine on fine June nights,
the eyes close from breeze sweet and clear,
the wind is charged with noise -- not far the city lights --
perfumed with vine and perfumed with beer....

II.

Here we see a somber blue on a little felt,
by a little branch set in frame,
quilted by malignant star that melts
with shivers soft, a small, fair flame.

June night! Seventeen! You drink deep;
youth's sap is a heady champagne....
You wander, on your lips still keep
a kiss; a quivering soul, it remains....

III.

Through novels the crazy heart robinsonades
when in the streetlight's clarity pale
a girl walks by with her charms displayed,
though partly by her father's collar veiled....

And, as she finds you all innocent,
while tapping by in little heels,
she sudden-turns, full of life up-pent;
- on your lips die melodic peals....

IV.

You are in love, till August placed.
You are in love. - Your poems she takes in fun.
Your friends have left; you are in poor taste.
- Then one night she writes, your worshiped one!

- That night... - you return to the cafe-sheen,
asking for the beer-stein and the lemonade.
You are not serious when you are seventeen
and you still have green lindens on the promenade.

Rimbaud is a challenge, always. Here is the French; here is an English translation by Wyatt Mason.

8values

In ancient days of yore, when blogging was relatively new, we did a lot of quizzes just to be doing things; but they are rare these days.

(Source)

Of course, with any sort of centrist designation, it is always difficult to tell whether it indicates an actual position in the center or a position that is not easily measured on the scale. I had several Neutral/Not Sure answers, usually because I thought the question too vague. And the Equality/Wealth numbers are heavily affected by the strength of my opposition to communism as a political ideology. (I think it is in practice at least as bad as fascism. I also think it's an error, tempting as it may be, to treat capitalism as the opposite of communism, an opposition that requires treating communism as labor-ism. It's unsurprising that communists do tend to put themselves forward as the champions of Labor over Capital, but this characterization doesn't survive any serious analysis, I think. The opposite of modern communism is something for which we have no definite name, a society in which people are not reduced to their political-economic role, one based on ethical principles rather than economic plans and in which civic friendship and shared traditions matter more than means of production.)

Sunday, April 23, 2017

Passages on Self-Command in Sense and Sensibility

Chapter 8:

"How strange this is! what can be the meaning of it! But the whole of their behaviour to each other has been unaccountable! How cold, how composed were their last adieus! How languid their conversation the last evening of their being together! In Edward's farewell there was no distinction between Elinor and me: it was the good wishes of an affectionate brother to both. Twice did I leave them purposely together in the course of the last morning, and each time did he most unaccountably follow me out of the room. And Elinor, in quitting Norland and Edward, cried not as I did. Even now her self-command is invariable. When is she dejected or melancholy? When does she try to avoid society, or appear restless and dissatisfied in it?"

Chapter 11:

Elinor could not be surprised at their attachment. She only wished that it were less openly shewn; and once or twice did venture to suggest the propriety of some self-command to Marianne. But Marianne abhorred all concealment where no real disgrace could attend unreserve; and to aim at the restraint of sentiments which were not in themselves illaudable, appeared to her not merely an unnecessary effort, but a disgraceful subjection of reason to common-place and mistaken notions. Willoughby thought the same; and their behaviour at all times, was an illustration of their opinions.

Chapter 19:

Elinor sat down to her drawing-table as soon as he was out of the house, busily employed herself the whole day, neither sought nor avoided the mention of his name, appeared to interest herself almost as much as ever in the general concerns of the family, and if, by this conduct, she did not lessen her own grief, it was at least prevented from unnecessary increase, and her mother and sisters were spared much solicitude on her account.

Such behaviour as this, so exactly the reverse of her own, appeared no more meritorious to Marianne, than her own had seemed faulty to her. The business of self-command she settled very easily;—with strong affections it was impossible, with calm ones it could have no merit. That her sister's affections WERE calm, she dared not deny, though she blushed to acknowledge it; and of the strength of her own, she gave a very striking proof, by still loving and respecting that sister, in spite of this mortifying conviction.

Chapter 22:
"It is strange," replied Elinor, in a most painful perplexity, "that I should never have heard him even mention your name."

"No; considering our situation, it was not strange. Our first care has been to keep the matter secret.— You knew nothing of me, or my family, and, therefore, there could be no OCCASION for ever mentioning my name to you; and, as he was always particularly afraid of his sister's suspecting any thing, THAT was reason enough for his not mentioning it."

She was silent.—Elinor's security sunk; but her self-command did not sink with it.

"Four years you have been engaged," said she with a firm voice.

Chapter 23:

The necessity of concealing from her mother and Marianne, what had been entrusted in confidence to herself, though it obliged her to unceasing exertion, was no aggravation of Elinor's distress. On the contrary it was a relief to her, to be spared the communication of what would give such affliction to them, and to be saved likewise from hearing that condemnation of Edward, which would probably flow from the excess of their partial affection for herself, and which was more than she felt equal to support.

From their counsel, or their conversation, she knew she could receive no assistance, their tenderness and sorrow must add to her distress, while her self-command would neither receive encouragement from their example nor from their praise. She was stronger alone, and her own good sense so well supported her, that her firmness was as unshaken, her appearance of cheerfulness as invariable, as with regrets so poignant and so fresh, it was possible for them to be.

Chapter 32:

Elinor only was sorry to see them. Their presence always gave her pain, and she hardly knew how to make a very gracious return to the overpowering delight of Lucy in finding her STILL in town.

"I should have been quite disappointed if I had not found you here STILL," said she repeatedly, with a strong emphasis on the word. "But I always thought I SHOULD. I was almost sure you would not leave London yet awhile; though you TOLD me, you know, at Barton, that you should not stay above a MONTH. But I thought, at the time, that you would most likely change your mind when it came to the point. It would have been such a great pity to have went away before your brother and sister came. And now to be sure you will be in no hurry to be gone. I am amazingly glad you did not keep to YOUR WORD."

Elinor perfectly understood her, and was forced to use all her self-command to make it appear that she did NOT.

Chapter 37:

She was very far from wishing to dwell on her own feelings, or to represent herself as suffering much, any otherwise than as the self-command she had practised since her first knowledge of Edward's engagement, might suggest a hint of what was practicable to Marianne. Her narration was clear and simple; and though it could not be given without emotion, it was not accompanied by violent agitation, nor impetuous grief.—THAT belonged rather to the hearer, for Marianne listened with horror, and cried excessively. Elinor was to be the comforter of others in her own distresses, no less than in theirs; and all the comfort that could be given by assurances of her own composure of mind, and a very earnest vindication of Edward from every charge but of imprudence, was readily offered.

Chapter 37:
"Yes. But I did not love only him;—and while the comfort of others was dear to me, I was glad to spare them from knowing how much I felt. Now, I can think and speak of it with little emotion. I would not have you suffer on my account; for I assure you I no longer suffer materially myself. I have many things to support me. I am not conscious of having provoked the disappointment by any imprudence of my own, I have borne it as much as possible without spreading it farther. I acquit Edward of essential misconduct. I wish him very happy; and I am so sure of his always doing his duty, that though now he may harbour some regret, in the end he must become so. Lucy does not want sense, and that is the foundation on which every thing good may be built.—And after all, Marianne, after all that is bewitching in the idea of a single and constant attachment, and all that can be said of one's happiness depending entirely on any particular person, it is not meant—it is not fit—it is not possible that it should be so.— Edward will marry Lucy; he will marry a woman superior in person and understanding to half her sex; and time and habit will teach him to forget that he ever thought another superior to HER."—

"If such is your way of thinking," said Marianne, "if the loss of what is most valued is so easily to be made up by something else, your resolution, your self-command, are, perhaps, a little less to be wondered at.—They are brought more within my comprehension."

"I understand you.—You do not suppose that I have ever felt much.—For four months, Marianne, I have had all this hanging on my mind, without being at liberty to speak of it to a single creature; knowing that it would make you and my mother most unhappy whenever it were explained to you, yet unable to prepare you for it in the least.— It was told me,—it was in a manner forced on me by the very person herself, whose prior engagement ruined all my prospects; and told me, as I thought, with triumph.— This person's suspicions, therefore, I have had to oppose, by endeavouring to appear indifferent where I have been most deeply interested;—and it has not been only once;—I have had her hopes and exultation to listen to again and again.— I have known myself to be divided from Edward for ever, without hearing one circumstance that could make me less desire the connection.—Nothing has proved him unworthy; nor has anything declared him indifferent to me.— I have had to contend against the unkindness of his sister, and the insolence of his mother; and have suffered the punishment of an attachment, without enjoying its advantages.— And all this has been going on at a time, when, as you know too well, it has not been my only unhappiness.— If you can think me capable of ever feeling—surely you may suppose that I have suffered NOW. The composure of mind with which I have brought myself at present to consider the matter, the consolation that I have been willing to admit, have been the effect of constant and painful exertion;—they did not spring up of themselves;—they did not occur to relieve my spirits at first.— No, Marianne.—THEN, if I had not been bound to silence, perhaps nothing could have kept me entirely—not even what I owed to my dearest friends—from openly shewing that I was VERY unhappy."—

'Self-command' is used once in Persuasion, once in Pride and Prejudice, three times in Mansfield Park, five times in Emma, and not at all in Northanger Abbey. It is notable that of the eight times it occurs in S&S it is only attributed to Elinor, and it is put center stage in Chapter 37, where it is used twice, and discussed specifically between the characters, rather than simply being a passing comment.

Flowers Laugh Before Thee on Their Beds

Ode to Duty
by William Wordsworth


Jam non consilio bonus, sed more eo perductus, ut non tantum recte facere possim, sed nisi recte facere non possim"

"I am no longer good through deliberate intent, but by long habit have reached a point where I am not only able to do right, but am unable to do anything but what is right."
(Seneca, Letters 120.10)

Stern Daughter of the Voice of God!
O Duty! if that name thou love
Who art a light to guide, a rod
To check the erring, and reprove;
Thou, who art victory and law
When empty terrors overawe;
From vain temptations dost set free;
And calm'st the weary strife of frail humanity!

There are who ask not if thine eye
Be on them; who, in love and truth,
Where no misgiving is, rely
Upon the genial sense of youth:
Glad Hearts! without reproach or blot;
Who do thy work, and know it not:
Oh! if through confidence misplaced
They fail, thy saving arms, dread Power! around them cast.

Serene will be our days and bright,
And happy will our nature be,
When love is an unerring light,
And joy its own security.
And they a blissful course may hold
Even now, who, not unwisely bold,
Live in the spirit of this creed;
Yet seek thy firm support, according to their need.

I, loving freedom, and untried;
No sport of every random gust,
Yet being to myself a guide,
Too blindly have reposed my trust:
And oft, when in my heart was heard
Thy timely mandate, I deferred
The task, in smoother walks to stray;
But thee I now would serve more strictly, if I may.

Through no disturbance of my soul,
Or strong compunction in me wrought,
I supplicate for thy control;
But in the quietness of thought:
Me this unchartered freedom tires;
I feel the weight of chance-desires:
My hopes no more must change their name,
I long for a repose that ever is the same.

Stern Lawgiver! yet thou dost wear
The Godhead's most benignant grace;
Nor know we anything so fair
As is the smile upon thy face:
Flowers laugh before thee on their beds
And fragrance in thy footing treads;
Thou dost preserve the stars from wrong;
And the most ancient heavens, through Thee, are fresh and strong.

To humbler functions, awful Power!
I call thee: I myself commend
Unto thy guidance from this hour;
Oh, let my weakness have an end!
Give unto me, made lowly wise,
The spirit of self-sacrifice;
The confidence of reason give;
And in the light of truth thy Bondman let me live!