Tuesday, October 26, 2021

Not on Her Brow; Beneath Her Feet

 The White Witch
by G. K. Chesterton

The dark Diana of the groves
Whose name is Hecate in hell
Heaves up her awful horns to heaven
White with the light I know too well. 

The moon that broods upon her brows
Mirrors the monstrous hollow lands
In leprous silver; at the term
Of triple twisted roads she stands. 

Dreams are no sin or only sin
For them that waking dream they dream;
But I have learned what wiser knights
Follow the Grail and not the Gleam. 

I found One hidden in every home,
A voice that sings about the house,
A nurse that scares the nightmares off,
A mother nearer than a spouse, 

Whose picture once I saw; and there
Wild as of old and weird and sweet,
In sevenfold splendour blazed the moon
Not on her brow; beneath her feet.

Monday, October 25, 2021

Russell on Barriers to Entailment

 Gillian Russell has an interesting paper, How to Prove Hume's Law, which is probably the best thing I've read on the subject in a while. As I've noted before, there is actually no single thing that is Hume's Law, since different people use it to mean different things, all of which are different from what Hume clearly meant. Russell introduces the principle in a common way -- You can't get an Ought from an Is -- but the version that Russell actually considers is that you can't get a normative conclusion from a descriptive premise, which is not the same. In any case, the primary interest is less this than the logical contextualizing of the idea.

Russell takes the principle to be one of a family of principles, barriers to entailment, such as:

You can't deduce a universal conclusion from particular premises.
You can't deduce conclusions about the future from premises about the past or present.
You can't deduce conclusions about how the world must be from premises about how the world is.
You can't deduce indexical conclusions from non-indexical premises.

Russell -- and this is the fundamental value of the paper -- argues for a unified logical account of all of these and then, assuming standard assumptions in logical systems, proves a Limited General Barrier Theorem that handles some commonly proposed counterexamples to the above principles, especially to 'Hume's Law'.  There is a kind of curious twist in the argument -- what Russell actually shows is that all of the above principles are false, and that the major counterexamples (including some Russell does not consider but are analogous to those that are considered) are essentially right, but that the counterexamples each fall under a condition. 

Trying not to get too bogged down in logical technicalities, the essential idea is that we often have cases in which we are dealing with claims that can change truth value depending on context. We find many such cases in the matters with which the above barrier principles are concerned, and in ways that seem closely connected to why people think they are true. For instance, the indexical claim "I am Brandon" is true of me and false of most of you; the context shifts, and the truth value can shift with the context. If "I am Brandon" followed from non-indexical statements, the shift of truth value would not be possible: the truth of the non-indexical statements does not depend on the indexical context, so any conclusions that can be deduced from them will not depend on the indexical context. Thus the indexical shift will block certain kinds of inferences from non-indexicals to indexicals. However, it's obvious that this cannot be an absolute barrier. "All adult Americans have a name" is a non-indexical statement, and from this I can conclude, "If I am an adult American, I have a name", which is indexical. The reason is that, while the latter statement shifts its truth value in different contexts, if we look only at the contexts in which the non-indexical statement is true, the indexical statement has to be true in all of them. This general point can be made more precise with model theory, and it can be generalized to all of the other cases, and, what is more, the point is true in multiple different modal logical systems (Russell looks at S4, B, and S5 in particular), with only minor incidental modifications appropriate to the difference in logical systems.

Of course, it's always possible that there are other logical systems, particularly nonstandard modal logical systems, that plausibly represent some sort of modality we actually use, which will not allow the barrier principle; and deontic reasoning is the form of modal reasoning that has always been hardet to fit with standard moral logical systems. (I also do not think Russell's account of normativity is a very good account of what people generally mean by normativity, even in using the descriptive-normative version of Hume's Law. But it's in the general ballpark.) It's worth remembering that a barrier with exceptions is in fact less a barrier than a gateway, and all of logical reasoning is described by such gateways. As noted above, what Russell actually shows is that all of the above principles are false; despite the title of the paper, what the paper shows is that Hume's Law is wrong. We knew this from the counterexamples -- at least, everyone who wasn't stubbornly holding on to Hume's Law knew it from the counterexamples. Nonetheless, she establishes a general account of how this relates to other principles, and how one can in each case actually make the kind of inference that is forbidden in a way that explains why people would err in thinking that it could not be made.

Apparently Russell is working on a book on Barriers to Entailment; I will definitely have to read it when it comes out.

Sunday, October 24, 2021

Occult Circe of the Hours of Sleep

The Potion of Dreams
by Clark Ashton Smith

What occult Circe of the hours of sleep
Mixeth the Cup of Dreams with potent art?
How doth the sorceress cunningly impart
To it such wondrous virtues, and where steep
That powerful potion? Opium poppies' brew
Nor hasheesh from far India's mystic land
Have not such properties, nor can command
Visions of more fantastic form and hue. 

Pleasure and pain in mingling mystical
Are in that cup. There past and present meet,
With pageantry of earthly sights and sounds.
Abysses bottomless, heights that appall
With plainlands infinite about their feet,
And seas horizonless, lie in its bounds.

Saturday, October 23, 2021

Heaven's Delicious Breath

 Sonnet -- October
by William Cullen Bryant

Ay, thou art welcome, heaven's delicious breath!
When woods begin to wear the crimson leaf,
And suns grow meek, and the meek suns grow brief,
And the year smiles as it draws near its death.
Wind of the sunny south! oh, still delay
In the gay woods and in the golden air,
Like to a good old age released from care,
Journeying, in long serenity, away.
In such a bright, late quiet, would that I
Might wear out life like thee, 'mid bowers and brooks,
And dearer yet, the sunshine of kind looks,
And music of kind voices ever nigh;
And when my last sand twinkled in the glass,
Pass silently from men, as thou dost pass.

Thursday, October 21, 2021

The Four Cardinal Virtues and Aristotle's Definition of Virtue

 I've always been really taken with Thomas Aquinas's account of the four cardinal virtues, which I think is actually quite brilliant, but the way he develops it, I think, obscures a bit what he is doing. In effect, Aquinas is having to deal with a peculiar set of problems. First, there are vast numbers of lists of virtues, constructed on all sorts of different principles, and, for that matter, there is necessarily a huge number of virtues to be expected. So we need some kind of way to keep track of them. We need reference-point virtues so that we can stay oriented in Virtue Country. Second, you might expect a very strong Aristotelian like Aquinas to favor Aristotle's own preferred set of reference-point virtues, but there's a practical problem. Aristotle's preferred set makes sense, but it's not particularly obvious or straightforward. Essentially, Aristotle picked out the virtues that were most important for life in a Greek city-state. This means that for a lot of other contexts, the selection has an odd flavor, including as it does things like magnanimity (originally linked to how one relates to social status in a Greek city-state), magnificence (originally linked to Greek taxation practices), eutrapelia (the virtue of playfulness and witty banter, originally linked to Greek customs of relaxation). The problem is not the virtues themselves -- they're all good candidates, they all have some importance somewhere, and St. Thomas certainly takes them all to be virtues, although occasionally with modification -- but while it's a great reference-point list for Greek city-states, picking out some of these virtues as the primary reference points is arguably something you'd only do for a Greek city-state. Third, the list of phronesis, dikaiosyne, andreia, and sophrosyne, or, to use the Latin, prudentia, iustitia, fortitudo, temperantia, is both much easier to use and far more widespread, due to the fact that it was favored by Platonists, Stoics, and (also important for St. Thomas) is specifically referred to in the Biblical book, the Wisdom of Solomon.

So what St. Thomas really needs is an Aristotelian reason to favor the more common list. If you are an Aristotelian and you had that, you wouldn't have to change much in Aristotle's ethics to adapt it to the common list. While Aristotle does not treat the four cardinal virtues as a list as particularly important, all four of the cardinal virtues are in Aristotle's list of virtues; what is more, all four of them are virtues which he discusses extensively. This isn't surprising; he was a student of Plato, who uses the list occasionally, and lived in Ancient Greek, where it was apparently a fairly common list, since Plato doesn't seem to have invented it. So this is what we want to find out: Is there a specifically Aristotelian reason why we might take the four cardinal virtues as our primary reference-point list for virtues? And St. Thomas solves this problem, conclusively, and indeed in such a way that it explains why the list of the four cardinal virtues is so extremely popular and practically useful.  As I said, the way he sets it up in some ways obscures the brilliance of what he is doing, so what follows is a re-organizing of it to bring it out.

There is no more Aristotelian place to start than with Aristotle's definition of virtue. Aristotle tells us that a virtue is:

(1) a kind of second nature (hexis/habitus)
(2) concerned with choice
(3) consisting in a mean relative to us
(4) as determined by reason in the way a prudent person would determine it.

So, to fit this definition, a virtue is going to have to have certain qualities. You have something as a kind of second nature when you can easily and consistently perform the relevant actions in a wide variety of circumstances. So what is second nature is durable, enduring, consistent. From this we learn that a virtue needs to be STABLE. Virtues are concerned with choices, and choice is the structuring principle of deliberate human action, so from this we learn that virtues need to be concerned with action or ACTIVE. A mean is literally a middle between extremes, but Aristotle is clear that it's a matter of balancing requirements so as to avoid what is too much or too little, and thus not necessarily exactly in the middle. So from this we know that every virtue must in some way find a harmonious balance, that is, every virtue must be MODERATE. And, of course, the last portion of the definition tells us directly that every virtue must in some way be RATIONAL.

Thus every virtue, without exception, needs to be stable, active, moderate, and rational; moral life is to live according to a character that harmoniously blends these four qualities. But specific virtues concern different aspects of life and have different content. Honesty is very different from chastity or patience, despite the fact that each of these is in some way stable, in some way active, in some way moderate, and in some way rational. And when you look at specific virtues, it becomes clear that, while they all have these qualities, they do not all equally display these qualities. Compare modesty and patience. Both have all four qualities because both are virtues. But it's much more obvious that patience involves stability than that modesty does. Modesty, the virtue concerned with how you present yourself in public, is much more adaptable to different details in different situations; its stability is more abstract. If you are trying to be patient, you end up having to focus on remaining stable a lot; if you are trying to be modest, on the other hand, you will focus much more on finding a good balance. Patience involves balance or moderation, but it's not so obviously a balancing act as modesty is. This generally the case. All virtues have all four qualities, but different virtues will more clearly manifest one of the qualities than the others.

The implication is that virtues fall into four different families, depending on which of the four qualities they more obviously express. Some virtues more obviously involve rationality, others action, others stability, others moderation. Every virtue is related to every other virtue, but the natural grouping of virtues is by these families. So what we want for our reference-point list -- for the North, South, East, and West of our map of Virtue Country* -- is to pick out the virtue from each family that is most usable as a reference point. In practice, this means we need to pick out virtues that both (1) directly deal with very pervasive or common features of human life and (2) cover the most important cases in which a given quality of virtue needs to be manifested.

So let's start with the RATIONALITY FAMILY, the family of virtues that very obviously have to do with thinking and reasoning and being reasonable. It's the easiest, because the central virtue of the family falls directly into our lap from Aristotle's definition: PRUDENCE. And this makes sense. A lot of the virtues in this family obviously concern things that make it easier to make good decisions -- caution or carefulness, for instance, or reasonable estimation (good guessing), or teachableness (docility). But prudence is the virtue of actually making good decisions -- prudence pays attention to the circumstances and makes a decision appropriate to them -- and there's nothing else that is more properly characterized as pervasive and important for living as a human being than making decisions. All virtues in the Rationality family will be prudence-like in some ways, because prudence is, of all the virtues in the Rationality family, the one most commonly and completely expressive of the rationality of good character.

Now let's turn to the ACTIVITY FAMILY of virtue, the family that is most obviously expressive of the active nature of virtue. Every virtue is active, but the arena of human life in which we are obviously going to most clearly see moral action is the social arena -- an arena in which we face constant demands to act toward other people, with other people, and on behalf of other people. All of society is coordination of action. So while the Activity family of virtue is not exclusively social in its expression, every member of the family has a very obvious social side. So we need a virtue in this society-building family that concerns action-situations that are extremely common and also very important. There are several candidates (human social life is a vast field, so it covers a lot of very important things). But an extremely good candidate is the virtue that has as its particular province the preserving of goodness in human action. There are many ways in which I can act that would benefit me but only at a cost to you, and many ways in which you can act for your own benefit but only by leaving me worse off. If these actions are all we have, society collapses entirely into a struggle to exploit and coerce -- if you don't exploit others, you will lose everything for their benefit. In good social interactions, however, all parties should benefit, at least to the extent we can guarantee this by deliberate action. My benefit and your benefit do not have to be the same, but we need to come away with them being in some way even. The virtue that guarantees this is JUSTICE. Justice renders what is due so that we benefit evenly. There are lots of other virtues in the family, but we can easily understand them better by relating them to justice. For instance, some of the virtues of the family -- filial piety, religious devotion, gratitude -- handle situations where it's impossible to give an appropriate return to make things even (you will never be even with your parents or God, and those who give you gifts often do so in situations in which trying to make it even would be inappropriate); others, like everyday respect or honesty, deal with a different kind of equality or evennness, or else help make it easier to act justly.

The STABILITY FAMILY handles matters that most obviously require consistency, an ability not to be pushed around by circumstances. Thus, while they don't only deal with difficulties, they do obviously handle difficulties. So to find the best reference-point virtue, we need to consider a difficulty that is extremely common and has a huge amount of power to affect our choices. And there is one difficulty all human beings face, without exception, in one way or another, that affects our choices like nothing else: our own mortality. Death, and things that could kill us, and things that could people we care about -- these are universal and have an immense power to influence our choices. There are times when we face difficulties that we would regard as more difficult to face even than death -- but those are rare. There are difficulties that are as universal as death -- but none more devastating. So the central virtue of the Stability family, the virtue that most perfectly expresses moral strength and endurance, is FORTITUDE, endurance even in the face of death. To face even death and not be broken by it -- this is a test of the stability of your character, and one that we all at some point have to face. Other virtues in the Stability family, like patience, are obviously important, and they obviously have a lot in common with fortitude, revolving around it like planets around a sun, or like stars around an even bigger star. But there is no question which virtue has the greatest gravity.

That leaves the family of virtues that most obviously show that virtue involves a balance, the MODERATION FAMILY. All situations require balancing a lot of different things, but the situations where we most often have to focus specifically on finding a balance are situations that involve powerful motivators -- things associated with strong pleasures. Nothing is more likely to result in toppling over than reaching for something very pleasant. So all members of the Moderation family, while not exclusively concerned with pleasurable situations, nonetheless have something or other to do with pleasure and the strong motivations that are tied up with it. When somebody finds a balance in the face of very tempting pleasures -- that's the situation in which you most obviously see how virtue can be and must be moderate. So what we need to do to find our reference-point virtue is find a kind of pleasure that affects our choices to a large extent and is extremely common. It doesn't take much to find it. You'll have difficulty finding pleasures that are more common than those tied directly to the needs of our biology and the most basic of these -- our individual survival needs of food and drink, the need of our species to reproduce -- involve immensely powerful motivations. Thus the reference-point virtue for the Moderation family is TEMPERANCE, the virtue of restricting the pursuit of physical pleasures in light of what is more important (or more human, as St. Thomas likes to put it). Other virtues in the family -- eutrapelia, modesty, studiousness, and so forth -- also deal with pleasures, and so are temperance-like, but they are either pleasures that are more rare or pleasures that are easier to restrict.

Thus we have our North, South, East, and West of Virtue Country: Prudence, Justice, Fortitude, Temperance. Just like every direction is related to every other direction but they are not all equally related to each other, so also every virtue is related to every other virtue but not equally. Just like we pick as reference-points the directions that are easier to use for orienting ourselves in our environment (North from the north star or magnetic north, East and West from the rising and setting of the sun, and so forth), so we pick as our reference-points the virtues that are easiest for orienting ourselves (because they concern things that are very common and have a significant effect on our lives). And from Aristotle's definition of virtue, as Aquinas shows, we can prove why these four are such useful candidates for reference-points. We could pick any directions we wanted to be cardinal compass points, but we usually pick North, South, East, and West, for extremely good reasons. And likewise, since all virtues are related to all virtues in some way, you can start with any set of virtues and use them to help you understand every other virtue. But there are reasons why Prudence, Justice, Fortitude, and Temperance make a list that people keep coming back to, that people repeatedly find to be easy to use and valuable, and if you are an Aristotelian, Aristotle's definition of virtue explains that.


* The adjective 'cardinal' in the name 'cardinal virtues' is derived from the Latin word for a hinge, so it's common to say (and St. Thomas does) that they are in a sense the 'hinge virtues'. But St. Ambrose, who actually came up with the name 'cardinal virtues', almost certainly intended to draw a parallel with a figurative use of the term, to indicate the cardinal directions of the compass, and doesn't seem to have had the literal sense of the term in mind at all.

Wednesday, October 20, 2021

Two Poem Drafts and a Poem Re-Draft

 Wave Song

I, worried, watched and wondered at the washing of the wave;
the sands were ever-changing where the children splashed and walked.
The sea itself was singing in a music without words 
and I undid my burdens and my shoes that I might wade.

The whales through waters wander on their weightless wilder-way.
They sing their songs of freedom and on tyrants do not wait.
And how can creatures flourish unenslaved by endless wants?
They sing in ancient choir far beneath the shifting waves.

The whooshing wind on waters whips the wavelets wide awake;
I find myself at peace, although I scarce can figure why
amidst the host of elements in ever-rushing war;
but I am singing softly with the wisdom of the waves.

The Greatest City

Shadows soar to breathless heights.
Down below, the city lights
brightly shine, with just a hint
of twinkle in their starry glint.
Worlds around each shining star
are spinning. On each road a car
is moving fares from place to place
slowly through deep outer space
and endless void of cosmic night
broken only by stars' light.

Texas Hymn 

The birds woke me at the sunrise hour
when grass was dewy and all was pale
beneath the light of a high white star;
it sang the message that all was well.
And I in the breeze (it trickled down
the blades of grass then quickly wound
around my legs to tickle my feet) --
I knew the light, and it was sweet. 

The thirsty drink from flowing spring
and come to life, made quick by source;
thus I, when I hear mornings sing
in bird, or wind in winding course,
then know, as rolling sun will rise,
a Spirit lives, God's very breath,
who lightens sky and human eyes
and raises sinning souls from death.

Tuesday, October 19, 2021

Like a Cheerful Traveller

Cheerfulness Taught by Reason
by Elizabeth Barrett Browning 

I think we are too ready with complaint
In this fair world of God's. Had we no hope
Indeed beyond the zenith and the slope
Of yon gray blank of sky, we might grow faint
To muse upon eternity's constraint
Round our aspirant souls; but since the scope
Must widen early, is it well to droop,
For a few days consumed in loss and taint?
O pusillanimous Heart, be comforted
And, like a cheerful traveller, take the road
Singing beside the hedge. What if the bread
Be bitter in thine inn, and thou unshod
To meet the flints? At least it may be said
'Because the way is short, I thank thee, God.'