Saturday, February 17, 2007

Hume's Philosophy of Mathematical Practice

Which I distinguish from Hume's philosophy of the mathematics studied by mathematicians. Hume does, in fact, say some interesting things about what mathematicians study. I've briefly discussed some of them -- for instance, Hume insists that geometry is necessarily imprecise, approximate, and inexact, and that geometers are fooling themselves if they think they work with any sort of precision. But perhaps more interesting than this is what Hume says about mathematical practice.

To discover what Hume says on this subject, we have to look at the subject of curiosity, which Hume sometimes glosses, a bit misleadingly, as love of truth. Curiosity is actually an extremely important concept for Hume. As a skeptic, he tends to think that there are no (stable) speculative or theoretical justifications for particular fields of enquiry, and, what is more, he is quite frank and straightforward about the horrors of 'philosophical melancholy' that this can induce if nothing compensates for it. So Hume's justification for intellectual endeavors is always rooted in what he considers to be stable driving passions -- most generally curiosity and vanity. This is the justification for philosophical investigation Hume gives in Treatise 1.4.7, a justification even skepticism cannot defeat (one which he calls "the first source" of his inquiries in Treatise 2.3.10. I've dramatized it a bit in a doggerel mnemonic or 'dogmonic' called The Shipwreck of David Hume. It makes for quite an adventure; but, as you can see if you compare it to the relevant section of the Treatise, I didn't have to take much poetic license to make it one.

But my interest here is to discuss what Hume's justification of mathematics by curiosity commits him to saying about mathematical practice. The relevant section of the Treatise is 2.3.10. His primary interest in this section is to argue that truth is not desired as such; rather, it is desired only insofar as it is "endow'd with certain qualities". I won't go through the arguments, although I have also discussed some of them elsewhere. Rather, I want to sum up what I think these 'qualities' are that make mathematics an object for curiosity.

(1) An occasion for exercising ingenuity. Hume calls this the "first and most considerable circumstance to render truth agreeable." It is enjoyable to exercise one's mind in a way that reflects well on one's skill. The point here is not merely that mathematics is difficult; even difficulty doesn't always exercise our "genius and capacity," as Hume calls it. What curiosity requires is not merely a difficulty but an intriguing challenge, something that requires us to "fix our attention or exert our genius."

(2) An occasion of importance. Even the potential for stimulating thought is not really adequate. It might be sufficient for a mild recreation, but it just doesn't capture the passion of an intellectual endeavor. What is necessary is that the problem or puzzle challenging us is in some way important. Hume has an interesting idea about how to understand this importance; he appeals to his account of sympathy. Imagine, he says, an engineer surveying a properly fortified city. He gets satisfaction and pleasure from seeing how well done the fortifications are. This is not, however, because he gets any immediate use from them. Rather, he gets the satisfaction because, being human, he sympathizes with those who benefit from them (and presumably with the satisfaction of the engineers who built the fortifications in order to benefit them). So by sympathy we can have a very broad sense of the utility of something indeed -- even things that don't immediately benefit us or anyone we know can still give us a sense of this broader utility, if we can have some notion that it might be of real value to someone somewhere.

(3) An occasion that admits of success. The project, after all, must not be completely futile. But Hume is very concerned to reject the claim that avoiding futility requires finding truth; which is not at all surprising, since curiosity is the primary justification of his philosophical work in the face of skepticism about whether the truth can be found in many important areas of research. To argue this, he treats study and research as analogous to pursuits like gambling and hunting. In such recreations, we actually have a dual sort of success. There's the immediate success -- in the case of gambling, winning, and in the case of hunting, catching the prey. But a person's passion for gambling simply can't be explained in terms of his desire to win; this desire may spark the passion, but the passion is for gambling itself. And so with hunting. The pursuit itself becomes its own form of success. For this to be possible we need the precondition of importance -- someone who loves hunting partridges is not going to get the same enjoyment out of hunting magpies, because he's not going to be able to value magpies at the same level; the first are fit for the table (and note that by Hume's understanding of importance, this can be operative even if the hunter himself doesn't eat partridge), whereas magpies are largely useless for things like that.

Thus the object of curiosity, the prospect that really enlivens our interest and justifies mathematical endeavors, is, according to Hume: the discovery of possibly viable solutions to puzzles that are, from the perspective of the community, important, and that are, from the perspective of the individual mind, stimulating. To the extent that a field like mathematics provides this, Hume thinks, it justifies the pursuit of truth in that field. And, of course, as a matter of empirical fact we find that mathematics can provide it in spades.

Curiosity, then, is the governing motive of mathematics, the one that shapes it into a pursuit and a passion. It is not, of course, the only motive; nor is it in every particular case the strongest motive. There is, for instance, vanity, the desire to make a name for oneself. And we should not pretend that academics are above such sordid desires; anyone who has ever had dealings with academics knows that they are often almost obsessed with the possibility of being well respected, and that this motivation in at least many cases overtops even curiosity as a driving force in their work. Academia is filled to the brim with vanity; on a Humean view, this is one of the reasons it works in the first place. But vanity, unlike curiosity, doesn't shape the endeavor itself, considered as a community effort; the goal of the community of mathematicians is, at least in principle, determined by curiosity. What vanity adds to this is merely a powerful incentive for meeting the curiosity-proposed standards of that community; it cannot shape the community because it presupposes it. Curiosity, however, really does shape the community, especially when joined with sympathy.

So that, more or less, is Hume's account of mathematical practice. It's rather general, of course, since Hume was not a mathematician and does not seem to have had much notion of mathematics itself; it's really an account of intellectual inquiry in general, in which he continually appeals to mathematics as a paradigm example. But it's interesting in its own right, I think. I started thinking about this topic again on reading one of David Corfield's posts at "The n-Category Café"; some of what he says there is similar to what Hume is trying to get at, although at least part of what Hume is saying is shaped by his attempt to build an apraxia objection to certain forms of skepticism. One of the things Hume is missing that would greatly strengthen his account is the notion mentioned in that post of a 'mathematical story'; a problem with his analysis is that if it's taken as sufficient, we just get a string of interesting puzzles. But, of course, part of what really drives our curiosity in any field is the sense of taking part in what is (so to speak) an epic adventure of the mind. Even if the 'adventure' is only minor, it still needs a bit of sweep to it, a background against which the individual problems can be placed. Hume's sympathy account of intellectual importance is interesting and carries, I think, a serious grain of truth; but on its own it is clearly not adequate. Hume is right that importance is a major necessary condition for serious, sustained intellectual inquiry; he is right that sympathy plays a role; but an adequate account has to appeal to more than this. It needs a telos, a goal or end, and this telos needs to be that not merely of the individual problem but of the field as a whole. Corfield has argued (PDF) that this is a matter of tradition-constituted inquiry. Hume, of course, doesn't think in such terms. He goes far enough that he thinks in terms of community -- an immensely important achievement to which most people discussing mathematical, scientific, and philosophical practice don't attain -- but never develops a sense of the history or narrative of the community as a community that is (so to speak) united together in common cause, of the discipline not merely as a recreation but as an adventure of progress in a form of civilization. Something like that is needed to give an adequate account of any major field of intellectual inquiry.

A Mixed Tape for My Readers

As quirky as you'd expect, given that it's from me to you.

Ben Folds Five, Philosophy

Alphaville, Forever Young

Sufjan Stevens, Chicago

Metallica, Nothing Else Matters

Capercaillie, Miracle of Being

Ellis Paul, God's Promise (by Woody Guthrie)

Duke Ellington and John Coltrane, In a Sentimental Mood

Raymond Levesque, Quand les hommes vivront d'amour

Freddie Mercury and Montserrat Caballé, Barcelona

Amy Grant, El Shaddai

Joe Strummer and the Mescaleros, Redemption Song (by Bob Marley)

Kansas, Dust in the Wind

Johnny Cash, God's Gonna Cut You Down

Leonard Cohen, First We Take Manhattan

Vincent of Lerins on Development of Doctrine

An extended passage, but it's worth quoting:

But some one will say, perhaps, Shall there, then, be no progress in Christ’s Church? Certainly; all possible progress. For what being is there, so envious of men, so full of hatred to God, who would seek to forbid it? Yet on condition that it be real progress, not alteration of the faith. For progress requires that the subject be enlarged n itself, alteration, that it be transformed into something else. The intelligence, then, the knowledge, the wisdom, as well of individuals as of all, as well of one man as of the whole Church, ought, in the course of ages and centuries, to increase and make much and vigorous progress; but yet only in its own kind; that is to say, in the same doctrine, in the same sense, and in the same meaning.

The growth of religion in the soul must be analogous to the growth of the body, which, though in process of years it is developed and attains its full size, yet remains still the same....This, then, is undoubtedly the true and legitimate rule of progress, this the established and most beautiful order of growth, that mature age ever develops in the man those parts and forms which the wisdom of the Creator had already framed beforehand in the infant. Whereas, if the human form were changed into some shape belonging to another kind, or at any rate, if the number of its limbs were increased or diminished, the result would be that the whole body would become either a wreck or a monster, or, at the least, would be impaired and enfeebled.

In like manner, it behoves Christian doctrine to follow the same laws of progress, so as to be consolidated by years, enlarged by time, refined by age, and yet, withal, to continue uncorrupt and unadulterate, complete and perfect in all the measurement of its parts, and, so to speak, in all its proper members and senses, admitting no change, no waste of its distinctive property, no variation in its limits....

Therefore, whatever has been sown by the fidelity of the Fathers in this husbandry of God’s Church, the same ought to be cultivated and taken care of by the industry of their children, the same ought to flourish and ripen, the same ought to advance and go forward to perfection. For it is right that those ancient doctrines of heavenly philosophy should, as time goes on, be cared for, smoothed, polished; but not that they should be changed, not that they should be maimed, not that they should be mutilated. They may receive proof, illustration, definiteness; but they must retain withal their completeness, their integrity, their characteristic properties.

Commonitorium Chapter XXIII. I will be discussing this at some point.

A Thought on the Filioque

It occurred to me recently that one complication in the dispute over the Filioque that is often overlooked is that the Latins think of the matter chiefly in terms of spiration. One might expound the view as follows. When you take the notion of spiration seriously, it becomes difficult to see how you can avoid saying that both the Father and the Son spirate, or that the Holy Spirit is spirated by both Father and Son alike. For we know that the Holy Spirit is not merely the Spirit of the Father, nor merely the Spirit of the Son; He is the Spirit of the Father and the Son both, and, moreover, He is the Spirit of the Son precisely because He is the Spirit of the Father. If we were to deny that the Holy Spirit is spirated by the Son, we would have effectively denied that He is really the Spirit of the Son; if we were to hold that He is spirated only by the Father, we would have effectively affirmed that He is really the Spirit only of the Father.

In this light we can make sense of virtually all Latin claims about the procession of the Spirit. First, that the Spirit proceeds from the Father and the Son: for He is spirated by Father and Son alike. Second, that the Spirit proceeds from the Father principally: for He is the Spirit of the Son because He is the Spirit of the Father, not vice versa. Third, that the Spirit proceeds from the Father and the Son as from one principle: for He is the Spirit of both wholly in virtue of the fact that He is breathed forth by the Father. Fourth, that the Spirit proceeds from the Father through the Son: for He is immediately the Spirit of the Father and also the Spirit of the Father by being the Spirit of the Son. Bonaventure, in fact, has lots of arguments very similar to these; and his sharpest criticism of the Greeks on this issue (to whom he generally tends to be sympathetic) is that they have an inadequate understanding of spiration.

So the Latin understanding of procession is dominated by this notion of spiration. And, indeed, the scholastic way of discussing the Filioque, although not common today, suggests this very strongly. For, if we might summarize it a little oversimply it is this: essentially, i.e., insofar as He subsists in the divine nature, He is God in His own right; personally, i.e., insofar as He receives the divine nature from the Father as Principle of the Godhead, He is from the Father alone; notionally, i.e., insofar as He is not the Son but the Spirit of both the Father and the Son, He is from the Father and the Son. The Father and the Son are one notional principle of the Spirit inasmuch as the Spirit must be marked by an idea that makes Him the Spirit of the Father and of the Son alike, and that not incidentally; thus He is spirated from both, but by a single spiration; which is why the Father and the Son are said to breath forth the Spirit inasmuch as they are the same God, for the Son has it from the Father that the Spirit is the Spirit of the Son.

This does not, I think, resolve the dispute; rather, it shows more clearly just how difficult the dispute is to pin down; thus, for instance, the argument never occurs in terms of spiration, although the Latin notion of spiration is clearly a significant reason why the Latins think the Filioque not only to be plausible but essential to the faith.

Friday, February 16, 2007

Three More Poem Drafts

Nightmare While Flying

All our city lights,
all our human might,
all our gardens, graces, greatness;
all our hair-thin roads,
all our troubles and our goads:
gold dust in the darkness.

All our hopes and deeds,
all our wants and needs,
all our worries, wonders, wars;
all the things we know,
blurred to a gold-green glow,
gold dust in the darkness.

All our palatial spaces,
all our care-worn faces,
all our crying, dying, rising;
all our engines and machines,
all our lanterns, wires, screens,
gold dust in the darkness.

All our goodness and our waste,
all our fashion and our taste,
all our vision, fission, fire,
our sinning hid by silence,
our safety and our violence,
gold dust in the darkness,
and despair:
all the progress of our nation
as the hope of desperation,
the collapsing of creation,
and a falling through the air.

What Great Poems Say

The sky is blue, the sun is bright,
the grass is green, the clouds are white,
the rose is red and touched with dew,
the sunrise starts the day anew,
in autumn splendor bright leaves fall,
death is sad and takes us all,
the love of friends is bright with glow,
great poems say what all hearts know.


In the silent distance I can hear
the tumult of the dogs a-glow
as they bound on clouds and bay;
a shaft shoots swiftly forth,
striking the fleeing beast.
It staggers, stumbles, falls.
The sun leaps up and in smooth stroke
slits the throat of darkness.


As I've pointed out before, one of the issues in philosophy of science that I think important that apparently no one else does is popularization as a form of general scientific pedagogy; and I've complained before that people seem to have a dangerously confused view of what popularization in general is and requires. H. Allen Orr, thankfully, gets it right (about a different sort of popularization):

Daniel Dennett's main complaint about my review is that I held Dawkins's book to too high a standard. The God Delusion was, he says, a popular work and, as such, one can't expect it to grapple seriously with religious thought. There are two things wrong with this objection. The first is that the mere fact that a book is intended for a broad audience doesn't mean its author can ignore the best thinking on a subject. Indeed it's precisely the task of the popularizer to take this best thinking and present it in a form that can be understood by intelligent laymen.

This is exactly right. Good popularization requires more rigor and careful reasoning than writing for those in the know -- precisely because it is writing for those who aren't in the know. When you popularize you need to work even harder to get it right than when you are writing in more scholarly mode because (1) you have to convey the ideas to people who aren't used to them; (2) you have to avoid shortcuts (metaphors, analogies, etc.) that are useful for experts who can distinguish the relevant from the irrelevant, or else use them much more critically and carefully than the experts themselves do; (3) you have to make it easy for people to distinguish understanding the subject from understanding (say) the point of the subject; and many, many more. There are so many constraints to good popularization that it's inevitably going to be harder than scholarly writing, where you can trust that your already informed audience will be able to take away the point without becoming confused by incidentals. This is true for all forms of popularization in any subject. The worst forms of popularization are those that 'dumb down' or oversimplify or give themselves a free pass for bad reasoning and sloppy thinking because it's for the consumption of the masses. The ideal forms are those that revolutionize common sense by finding a way for ordinary people to see immediately the point, value, and content of an important discovery or theory. It's too much to expect that every (or perhaps any) popularization will succeed in the latter way; but as there is an entire spectrum between the two extremes, it's not too much to demand that they succeed better than popularizations in the former group.

Vincentian Canon

Michael Liccione criticizes, rightly, a misuse of the Vincentian Canon. I left a comment, but as the topic fits very well with what I often talk about here (being a misinterpretation of an important theological text), I thought I'd also post it here:

What always strikes me about this sort of use of the VC is that St. Vincent didn't put it forward as a definition of the Church; he put it forward as a guideline for how we individuals can interpret Scripture in conformity with the Church -- namely, by taking into account the confession of the whole Church (everywhere), respecting the interpretations of our holy predecessors in the Church (always), and sticking as much as possible to those truths that have achieved a consensus among bishops and teachers of the Church (by all). So it's a very odd thing to use as an ecclesiological criterion a guideline for interpreting Scripture that already presupposes the Church as its reference point.

Notes and Links

I was away for the past several days; hence the lack of posting. More normal posting will return this weekend.

* By way of Fred Clark at "slacktivist" I found that Brad DeLong has an interesting series of posts on game theory (here, here, here, here).

* John Guilmartin's The Tactics of the Battle of Lepanto Clarified discusses the role of socioeconomic factors in employment tactics and weapons system design. He discusses the matter further in another essay on the battle.

* The movie Amazing Grace, about William Wilberforce is coming out on February 23 to celebrate the 200th anniversary of Britain's abolition of the slave trade by the Slave Trade Act. You can see the trailer here. Spread the word. Wilberforce was the great abolitionist and social reformer of his day. Through the Internet Archive, you can read Wilberforce's A Practical View of the Prevailing Religious Systems of Professed Christians, a thorough (and thoroughly Christian) criticism of the Christianity of the middle and upper classes in his day (and it still manages to be a hefty critique of purely nominal Christianity even for today; I highly recommend it); and a collection of his private papers, which mostly consists of letters to him, but also has some lovely letters from Wilberforce to his daughter Elizabeth and son Samuel.

* Speaking of which, Rebecca has posted a review of Piper's Amazing Grace in the Life of William Wilberforce. Those who want a more thorough biography can consult Robert Isaac Wilberforce's five-volume Life of William Wilberforce online.

* In the meantime, you should also visit The Amazing Change website. As it points out, the fight against slavery is far from finished; it's devoted to carryiing forward Wilberforce's fight by stirring up consciousness of this fact. It might also be a good thing to blog something about liberty on February 18, which in many places around the world is Amazing Grace Sunday, a day of celebration for past victories against the slave trade and of prayer for future victories.

* Sister Sara Butler's paper, Ordination: Reviewing the "Fundamental Reasons", is the place to go for understanding the Catholic reasoning in refusing to ordain women. Butler has for some time been one of the most important and influential female theologians in the Catholic Church.

* Tim Enloe at "Societas Christiana" has a good post on Protestant historiography.

* The newest History Carnival is at Aardvarchaeology.

* I find myself in good company in a post at "Laudator Temporis Acti".


* In my undergraduate days, I used to listen to this Alphaville song over and over again.

* In Colin Klein's An Imperative Theory of Pain (PDF) there's an interesting argument that pains should be thought of on the model of proscriptions.

* I read with interest Amanda Marcotte's apologia in Salon. It suffers from two faults: (1) She talks as if the dispute were about her. But it clearly wasn't; it was about Edwards, and his association with a person whom others regarded as a bigot, whether rightly or wrongly, whether reasonably or unreasonably. (2) She tries to play up the argument that the critics were sexist and misogynistic; which may have in many cases been true. The trouble is that it's not really much of an argument in context: whatever the motivations for making the criticisms that were made, the criticisms themselves were about anti-Catholic bias, not sex, and stand or fall on their own merits. In that context, the sexism defense seems simply to be yet another self-indulgent case (of which there are far, far too many in politics) of someone trying to avoid the consequences of their actions by shoving a noble cause in the path of the oncoming bullets. Fighting against sexism and defending Marcotte are two very different things, as are being sexist and criticizing her; and yet the two never come apart in her article. This is very disturbing, and not at all convincing. I'm not much of a fan of Marcotte, but I had hoped she would give a more rousing defense than she managed. Here, as elsewhere, McEwan has a more intelligent take, but she misses the first point as well; she wasn't the target, nor was Marcotte; she was the accidental occasion for making a point -- several points, probably -- and when people make points in politics, it is an activity that is often brutal, to say the least. (Both Marcotte and McEwan came out relatively unscathed compared to what sometimes happens.)

Sunday, February 11, 2007

Three Poem Drafts

All very rough.

Tristan and Iseult

A poison sweet like honey,
bitter to the soul, spreads swiftly,
fire-violent, through the veins,
bewitching mind and body
with wondrous wode and witching.
But potion becomes temptation,
witchery's made treachery,
sweet made acid; the bud withers,
the blossoms fail in blight.
What joy, O lovers, in joy that dies?
What glory in love that spoils?
Only rot remains, and grave ghosts.
Can hope be reclaimed, redrawn?
No. Bitter winds drive hard bargains,
black sails bring suicide.


I sat upon the wayside and thought
of long years and great ideas, and loves,
of hopes and hearts in darkness caught,
of the topics handled with kid gloves
by men who never think save on their meals,
by minds that know no truths but only feel,
who never have the maiden Wisdom sought.

Through all my many days of cloud --
the days are many, tho' the years be few --
of this I was most often proud,
that I knew and saw more than others do;
but minds are mirrors wavy and unwise,
prone to malice, and mischievous with lies.
When I saw the world, I saw it wasn't true.

Or perhaps it was, but in a different way;
for many are the threads that God can spin
upon the loom of life, and in the day
one pure white refracts through many men,
yet is not less a white for playing on the face
of crystal hearts before it turns to race
and dazzle mind and eye with plural ray.

A rabbit stole the sun; it, fearless, rose
and snatched a piece away, a shattered shard
that broke into the stars that nightly glow.
Perhaps a god inspired the lonely bard
who told that tale, that we might come to see
that rays of light refract through you and me
to be caught again by all the pure of heart.

For truth, they say, is simple, one, and whole;
it stays as it ever stays, unbroken and most pure;
when the titan for our sake the glory stole,
it shattered for only God could it endure
to adorn and dress; as flint on steel,
the sparks flew out to set our minds to reel,
incendiary visions lodged in earthen souls.

A Rumor's Rumor

A young man journeyed far
beneath both sun and star,
over mount and mead,
driven by a need,
aching with a passion,
that, like a sprouting seed,
pushed up and up, not to be denied;
he sought Truth; Truth did hide.

Many long and sleepless nights he sought,
walking, running, keeping watch,
nights and days, weeks and years,
through thorn and river, sweat and tears,
for a rumor's rumor, which had told
that Truth was lovely and dressed in gold.

At last on a cold grey mountain
he came upon a garden
within which sprang a fountain
so cold no man could taste;
and a woman old and hardened,
stringy-haired and broken smile,
by the prickly thorn and holly,
croaked a song and broke his haste.
Struck by a sudden patience,
he stopped to ask her name;
and the ugly hag and ancient,
from age to age the same,
told him she was Truth.

How hardly hopes are shattered!
Almost he departed,
but the he softly sighed.
"For years I have been seeking,
for Truth alone been aching;
shall my youthful pride
bring all to nought, as folly?"
And by the sprouting holly,
accepting his defeat,
he gave up all his journeys
to sit at an old hag's feet.

For years he sat and pondered
at her feet with thought and wonder,
and although Truth was ugly,
he grew old, and well, and wise,
his mind farther and farther reached.
Then the hag Truth came to him
on a twinkling twilight dim,
to say she had no more to teach.
"But all my lore must be repaid;
my pay is this: for all your days,
when people ask you of Truth's face,
do not say she is foul and old,
but that she is lovely, bright,
full of glory and of light,
clothed not in rags but gold."

Real Presences

I read with interest this post at "Historical Theology," entitled 'Trent's Eucharistic Inconsistency', but came away a bit puzzled. The author, Darren, attributes the following position to the Council:

In the document the council begins by addressing the controversial matter of real presence. Is the real body and blood of the Lord Jesus Christ present in the bread and the wine of the Eucharist? The Catholic position is an unqualified "Yes." Christ is "truly, really, and substantially contained under the species of those sensible things" — that is, under the bread and wine that still look, feel, smell, and taste like bread and wine. This presence is not at all contradicted by the fact that Christ remains bodily at the right hand of the Father (still a common argument made against Transubstantiation).

The basis for this is the divine attribute of omnipresence, which the council suggests that Jesus shares even in his incarnate, resurrected and glorified body.

What's puzzling is that this is usually considered not a Tridentine view but a Lutheran one, and one of the major efforts of Counter-Reformation thinkers (like Bellarmine), was to attack it. This Lutheran view was that Christ was really present in the eucharist by virtue of the fact that His humanity participated in the omnipresence of his divinity. It's called the ubiquity of Christ. The idea is that there is a 'communication of properties' in Christ in three ways:

(1) idiomatic: where we ascribe the properties of the nature to the person;
(2) apotelesmatic: where we ascribe the properites of the person to the nature;
(3) auchematic: where we ascribe the properties of one nature to the other.

The real presence of Christ by ubiquity would be an example of (3).

This view was strongly opposed by Calvinists and Catholics alike, who, whatever their differences, share a similar understanding of the Chalcedonian definition, and regard this doctrine of ubiquity as a clear violation of it. Further, it has been pointed out by this reasoning, Christ would be bodily present in every cabbage in your garden, and the uniqueness of the institution is lost. (There are versions of the Lutheran doctrine in which this is not the case; for instance, 'volipresential' views hold that Christ's humanity in virtue of its union with the divine has the power to be present as He wills -- a virtual rather than actual omnipresence.)

The Tridentine view is rather different:

For neither are these things mutually repugnant,-that our Saviour Himself always sitteth at the right hand of the Father in heaven, according to the natural mode of existing, and that, nevertheless, He be, in many other places, sacramentally present to us in his own substance, by a manner of existing, which, though we can scarcely express it in words, yet can we, by the understanding illuminated by faith, conceive, and we ought most firmly to believe, to be possible unto God.

That is, Christ is present not naturally (by virtue of his humanity) but sacramentally (by virtue of the power of God). This sacramental presence is a key part of what it is to be assimilated to the Body of Christ, which is sacramental union with Christ, whereby through His presence we partake of His life.

The Calvinist opposition to ubiquity was along broadly similar lines. Like the Catholics they insisted that

(1) at the heart of the institution of the eucharist is an inexhaustible mystery;
(2) the key to this mystery is our union with Christ.

Unlike the Catholics, however, the Calvinists held that the presence of Christ was better understood in terms of reconciliation than in terms of bodily presence. That is, the Catholic view is that Christ has a unique mode of presence, by which he is substantially present in the eucharist, uniting believers to Himself. The Calvinists held that Christ is not substantially present in the eucharist; rather, His presence is the very act of uniting believers to Himself. It's usually called spiritual presence.

This Calvinist viewpoint eventually began to lose ground in Reformed churches to a Zwinglian viewpoint, in which there is no real presence at all, only a symbolic one: the Lord's Supper symbolizes Christ's body and blood, and nothing more. This has been an ongoing struggle in Reformed circles, with the Zwinglians usually having the upper hand (an upper hand, however, that they seem to have been steadily losing in past decades).

The World's Last Night

Today is the Judgment Sunday in the Orthodox calendar, so I thought I'd put up something. John Donne's Holy Sonnet XIII:

What if this present were the world's last night?
Mark in my heart, O soul, where thou dost dwell,
The picture of Christ crucified, and tell
Whether His countenance can thee affright.
Tears in His eyes quench the amazing light;
Blood fills his frowns, which from His pierced head fell;
And can that tongue adjudge thee unto hell,
Which pray'd forgiveness for His foes' fierce spite?
No, no ; but as in my idolatry
I said to all my profane mistresses,
Beauty of pity, foulness only is
A sign of rigour ; so I say to thee,
To wicked spirits are horrid shapes assign'd;
This beauteous form assures a piteous mind.

And a bit more rousing and stern, from Michael Wigglesworth's Day of Doom:

Still was the night, Serene and Bright,
when all Men sleeping lay;
Calm was the season, and carnal reason
thought so 'twould last for ay.
Soul, take thine ease, let sorrow cease,
much good thou hast in store:
This was their Song, their Cups among,
the Evening before.

They put away the evil day,
And drown'd their care and fears,
Till drown'd were they, and swept away
by vengeance unawares:
So at the last, whilst Men sleep fast
in their security,
Surpriz'd they are in such a snare
as cometh suddenly.

I don't think Wigglesworth gets sufficient credit for his poetic choices in the poem, which has a rhythm and rhyme scheme that works very well to build the sense of inexorable doom, and has the flexibility needed for carrying a sense of both quiet suspense and sudden destruction (we see a bit of it in the quick transition of the second stanza, which does come suddenly). It would perhaps do better as a shorter poem, and a little more selective deviation from rhyme and meter, which is a little too steady; but I think people get too distracted by the content to recognize the considerable merits of its composition. Perhaps Wigglesworth would be pleased by that, though. In any case, the rest is worth reading. It's often criticized for its judgmental tone, but this comes, I think, from selective reading. Consider, for instance, this stanza:

Christ's Flock of Lambs there also stands,
whose Faith was weak, yet true;
All sound Believers (Gospel receivers)
whose Grace was small, but grew:
And them among an Infant throng
of Babes, for whom Christ dy'd;
Whom for his own, by wayes unknown
to men, he sanctify'd.

And this theme, that God's mercy is greater than we know, or even can know, is actually an important subtheme throughout the poem. After all, Wigglesworth is not writing a poem about the Last Judgment in order to incite people to despair, but in order to make them to reflect on their need for mercy. Reformation comes through recognizing the severity of the offense; and this requires recognizing the severity of a final judgment on it, if nothing is done for it.

Two Types of Barbarian

If the German calls the Russian barbarous he presumably means imperfectly civilised. There is a certain path along which Western nations have proceeded in recent times; and it is tenable that Russia has not proceeded so far as the others: that she has less of the special modern system in science, commerce, machinery, travel or political constitution. The Russ ploughs with an old plough; he wears a wild beard; he adores relics; his life is as rude and hard as that of a subject of Alfred the Great. Therefore he is, in the German sense, a barbarian....The Russians, having nothing but their faith, their fields, their great courage, and their self-governing communes, are quite cut off from what is called (in the fashionable street in Frankfort) The True, The Beautiful and The Good. There is a real sense in which one can call such backwardness barbaric; by comparison with the Kaiserstrasse; and in that sense it is true of Russia.

Now we, the French and English, do not mean this when we call the Prussians barbarians. If their cities soared higher than their flying ships, if their trains travelled faster than their bullets, we should still call them barbarians. We should know exactly what we meant by it; and we should know that it is true. For we do not mean anything that is an imperfect civilisation by accident. We mean something that is the enemy of civilisation by design. We mean something that is wilfully at war with the principles by which human society has been made possible hitherto. Of course it must be partly civilised even to destroy civilisation. Such ruin could not be wrought by the savages that are merely undeveloped or inert. You could not have even Huns without horses; or horses without horsemanship. You could not have even Danish pirates without ships, or ships without seamanship. This person, whom I may call the Positive Barbarian, must be rather more superficially up-to-date than what I may call the Negative Barbarian. Alaric was an officer in the Roman legions: but for all that he destroyed Rome. Nobody supposes that Eskimos could have done it at all neatly. But (in our meaning) barbarism is not a matter of methods but of aims. We say that these veneered vandals have the perfectly serious aim of destroying certain ideas which, as they think, the world has outgrown; without which, as we think, the world will die.

G. K. Chesterton, The Appetite of Tyranny (1915). I think one of the great benefits of philosophy is that it keeps reminding us of the danger of Positive Barbarism, which would still be a danger to be considered even if we advanced so far that we could raise the dead and sail amidst the stars.