Saturday, January 19, 2008

Ecumenism Is a Conversation for Saints

People who know my view of the Council of Florence and the Filioque are sometimes surprised to find that I also very much like St. Mark of Ephesus, who, of course, was a vehement opponent of both. But it has always seemed to me that the problems people have with St. Mark are really with the people who try to use him as a club to hit people with. It is not pleasant to be hit with a club, and it stirs up feelings of dislike; but, really, it is not the club's fault. We should not judge saints by their followers. I learned this over a space of several years with St. Gregory Palamas. As I've said before, I'm a Palamite; and, what is more, I am a Palamite despite all of Palamas's defenders. The 'despite' is not an exaggeration. If it were a matter of paying attention to their arguments, the Orthodox defenders of Palamas would long ago have convinced me that the distinction between essence and energies is incoherent, confused, unbiblical, unconciliar, and leads to an astounding amount of malice in its defenders. Fortunately, I took the trouble to start reading as much of Palamas himself as I could -- not easy, because despite their considerable heat, surprisingly few of the polemicists who use St. Gregory as a club take much trouble to make him more accessible to the people they are attacking. And it was St. Gregory who convinced me, because St. Gregory articulates and defends the doctrine properly. Perhaps this is because he actually experienced it personally rather than (as many of his followers) merely talking as if he had. He began with God in Christ, not abstractly but personally, both in prayer and in participation in the tradition of the Church; the doctrine of energies came out of that. This contrasts sharply, it seems to me, with many of the defenders of the doctrine today, who begin with opposition, as if the point of the doctrine were to tell you why Catholics (or Protestants, as the case may be) are idiots and heretics. This is unfortunate; even the best-intentioned defenders are sometimes only borderline competent to say anything about the subject at all, since, unlike St. Gregory, they are more apt to garble than to clarify.

Similarly, the thing that I find likable -- admirable is perhaps a better word -- about St. Mark Eugenikos is that, for all his polemic, he did polemic the right way. It is sometimes necessary to remind Orthodox polemicists that saints aren't made saints because they did one thing only; what made St. Mark a saint was not that he attacked the Latins but that he was a holy man even in attacking the Latins. He, too, began with God, not with opposition; he, too, was more interested in Christ than in beating Catholics over the head. I don't think he was right in every claim; indeed, I think he made a fair number of mistakes. I don't think he's a perfect model for handling the situation. But it was a new sort of situation; mistakes are human, even for saints, and we don't look to a particular saint for inerrancy and flawless exemplarity. But he began in the right place, and his prayer was deep; these were the essential things, from which everything else followed, and everyone could do much worse than to imitate him in these most important things. I also think that St. Mark -- not the people who use his words as a chess piece -- is a reason Catholics need to have a certain sort of sympathy with prayerful, charitable Orthodox who look West and feel inclined to voice the objections he voiced. There are plenty, and although they are not usually the loudest voices, they are far and away the important ones. These Orthodox who really do follow in the footsteps of Eugenikos, those who begin with God and Christ and find the Filioque, at least as often expressed, worrisome, should lead all who accept the Filioque to take more thought on such matters, and to examine themselves more thoroughly for impediments to charity, and to take care that all that they may say on the matter begins with God and Christ as well.

And that brings me to the view expressed in the title of this post. I'm inclined to think the divisions of the Church are rifts beyond all human healing; reunion comes not by human argument and scheming but by moral miracle, if at all. Neither you, nor I, nor anyone else can contribute anything to it except insofar as we may be instruments of it. The pen does not write for the writer, the scalpel does not have the wisdom of the surgeon, the staff does not possess deep insight into the ways of the shepherd. Our task is not to invent the solution to the problem. It is not to force the other side to listen. It is not invincibly to refute them. Our task is what it is in every other part of our lives, to walk the path of Christ in the manner of Christ, prayerfully and through His grace, doing good to those around us as is befitting of children of the Father, teaching not with clever words but with the power of the Spirit. Our task is to begin in the right place. And it is only if we do this that there is any sure hope at all in this regard; the only certainty for hope is in the Lord. Reunion will come not because we have designed it, not because we have been smarter than our opponents, not because we have brought it about; it will only come about, when and if it comes about, as a living outgrowth of the Spirit-inspired conversation of the saints through the ages.

Friday, January 18, 2008

A Bit of Flour

Tomorrow commemorates, among others, St. Makarios the Great, Lamp of the Desert:

Once the holy Makarios went to keep an ill hermit company. Casting an eye around the ill man’s naked cell, he saw that there was nowhere even a scrap of food.

“What would you like to eat, brother?” asked the Saint.

The ill monk hesitated to answer. What was he supposed to ask for, since there was nothing in that wilderness? Finally, since the Saint was waiting for him to answer, he said that he had the desire for a little soup made with flour. But where was flour to be found?

The holy Makarios, so as to comfort his sick brother, went fifty miles on foot to Alexandria to find flour.

Thursday, January 17, 2008

St. Anthony and the Silver Dish

For the feast of St. Anthony the Great:

And yet again the enemy seeing his zeal and wishing to hinder it, cast in his way what seemed to be a great silver dish. But Antony, seeing the guile of the Evil One, stood, and having looked on the dish, he put the devil in it to shame, saying, 'Whence comes a dish in the desert? This road is not well-worn, nor is there here a trace of any wayfarer; it could not have fallen without being missed on account of its size; and he who had lost it having turned back, to seek it, would have found it, for it is a desert place. This is some wile of the devil. O thou Evil One, not with this shall you hinder my purpose; let it go with you to destruction.' And when Antony had said this it vanished like smoke from the face of fire.

From St. Athanasius's Life of Anthony, one of the great spiritual classics. This is one of several interesting stories the work; it makes one wonder, what are our silver dishes in the desert?

Book Recommendations, Anyone?

I've recently come into a nice gift certificate (a Christmas present that went astray and finally made it to me); does anyone have any must-reads that they've recently discovered and want to recommend? I have very, very broad tastes in reading, so recommendations from just about any genre are welcome.

Rambling on Subalternation and Existential Import

It's not uncommon in logic textbooks to find long and belabored (or short and simplistic) complaints about the traditional operation of subalternation (the inference from "Y is predicated of all X" to "Y is predicated of some X") because it violates existential import. I've noted before that this is a bit silly, first (as many people have noted) because it confuses particular propositions with existential propositions -- it is, in fact, a matter open to controversy whether particular propositions are existential, and we should not assume that the modern assumption that they are is right, just on the logic textbook's ipse dixit; and second, because most of these logic textbooks go on later to teach universal instantiation as the most natural thing in the world. But universal instantiation and subalternation are so closely analogous as logical operations that they have one and only one logically significant difference: subalternation concludes to an indefinite particular (some), while universal instantiation concludes to a definite one (a particular). Thus, from (x)(Fx) you can infer Fa for some a that's an x; and from "All things are F" you can infer Some things are F. Indeed, strictly speaking, although it's not the usual way of doing it, there seems no reason whatsoever why you couldn't have a subalternation that does the same thing as universal instantiation, concluding "A certain thing is F" from "All things are F", and it would take considerable ingenuity (which I've never found anyone taking) to explain why they aren't both giving us a result we could identify as "A certain thing, let's call it a, is F". Perhaps this is what Boethius has in mind with his quidams. I don't know. I certainly wouldn't wager on it; but I still think it gives me reason to complain about how cavalier most logic textbooks are about this. If you're worried by it in subalternation you'd better have some excellent reasons for not worrying about it with UI; and these reasons are never anywhere in sight.

But setting that aside, we can see more clearly what's involved in subalternation, and what you have to assume for it to work, by putting it in terms of Sommers's Term Functor Logic, which (to distinguish it from all other possible term functor logics) I call SETL.

"All S is P" in SETL is:


The first sign indicates quantity (universal), the second quality (affirmative). "Some S is P" is:


To get from -S+P to +S+P you need to make an assumption. That assumption is:


Some S is S. Thus you have:


Which simplified is:


Which gives you:

+P+S or +S+P, as you please.

All that's pretty basic. What it shows is that all you need in order to allow subalternation is the assumption that some S is S. The real question, then, is whether "Some S is S" requires the further assumption that an S exists. That's the one and only question to be asking about subalternation.

Tuesday, January 15, 2008

Superata Tellus

Five translations and the original:

Why slack off and turn your backs? When you overcome the earth, the stars will be yours.

Why do ye sluggards turn your backs? When the earth is overcome, the stars are yours.

Why do you lazy ones expose your backs?
The earth surpassed, the stars are bestowed.

Shoulder now your burden,
Now without delay, for the earth, once conquered,
Gives you the fixed stars.

Why so sluggishly expose your backs unguarded?
Once earth is overcome, the stars are yours for the taking.

cur inertes
terga nudatis? superata tellus
sidera donat.

The first is Richard Green (the Library of Liberal Arts edition); the second is Beck; the third is Cooper; the fourth is Relihan (the Hackett edition); the fifth is P.G. Walsh (the Oxford World's Classics edition). The lines are the closing lines of Book 4 m7 of Boethius's Consolation of Philosophy, my very favorite lines in a work full of favorite lines. But the poems are tricky, and never quite get translated well. My rough attempt at 'Englishing' these lines would be:

Why, sluggards,
do you unburden your backs? Earth transcended
gives the stars.

'Unburden' is not a strictly literal translation; but the idea here -- making the back bare or exposing it -- gets its meaning in context from the labor of Hercules where he bears the heavens on his shoulders and for it (and his other labors, which have already been enumerated in the poem) receives the reward of a place among the stars of heaven. I think Relihan has the right idea with his "Shoulder now your burden"; he's hampered in being closer to the Latin because he's trying to convey the rhythm of the Latin in English. He does it decently enough, and I think we need translations that do it, but I don't always like the results, since while the syllables are about the same, English uses little words and Latin long ones, making the English translations always wordy in an attempt to keep up with the Latin. But from what I've read of his translation, he has an excellent ear for the meanings. Beck's and Walsh's would be perhaps be more natural in another context (I'm not a Latin scholar, by any means, but it was the first to occur to me); the Latin does sound a bit like asking why the sluggards 'turn tail' (terga vertere), but I can't make any sense of that in the context.

Monday, January 14, 2008

A Poem Draft


Such splendor is but sign,
living image of a gesture;
each color and each line
speaks the word of holy lecture.
God's glory in the heights
is come to humble home
and Mary is the light
that guides the one who roams;
this virgin hope displays
the faith of chosen nation,
Mary who points the way
to our Great Salvation!

A girl with simple charms,
in whom it all did start,
holds God within her arms
and points to Heaven's Heart.

Deviant Propositional Logics and Existential Import

Previously I had noted a version of propositional logic in which implication becomes like conjunction; and Tom noted in the comments that in context this seemed analogous to taking A propositions to have existential import. I think this is right, and it started me thinking about the propositional analogues for different assumptions about existential import. As I've noted before, it's somewhat obscure to me what's going on in 'existential import', and what I'm writing here is merely some rough notes; but here is my thought about it.

Let's take four of the many assumptions you could make about existential import.

(1) Under the first assumption, which I will call ALL, all the main types of categorical proposition have existential import: A, E, I, O.

(2) Under the second assumption, which I will call NONE, none of the main types have existential import.

(3) Under the third, which I will call SOME, only particular propositions have existential import: I, O.

(4) Under the fourth, which I will call AFFIRM, only affirmative propositions have existential import: A, I.

So what properties would the analogous propositional logics have?

The first issue is that implications in propositional logic are essentially the same as A propositions. Now, whatever existential import may be, an A proposition with existential import is such it is legitimate to conclude from All S is P to There is some S. Propositionally, this is means concluding p from p → q. Both ALL and AFFIRM allow this inference. Thus for both of them, implication collapses into conjunction, or, to be more precise, p → q is only possible where (p & q) is also true.

The second issue is that disjunctions are essentially E propositions. Thus, a principle that allows E propositions to have existential import is one in which, from a disjunction, you can conclude the falsehood of either of its disjuncts. Thus (p v q) is No nonp is nonq, which allows the conclusion There is some nonp, which is ~p. Among the above four, only ALL allows this inference.

The third issue is that conjunctions are essentially particular propositions. Thus any assumption that denies existential import for these propositions makes conjunction elimination impossible. NONE, then, makes it impossible to conclude from (p & q) to p or to q. AFFIRM gives existential import to I propositions but not to O propositions. I'm not wholly sure what this means for its propositional analogue, but I think it means that it allows conjunction elimination but only if neither conjunct is negated. Thus, we can conclude from (p & q) to p, but not from (p & ~q) to p.

Thus we have:

ALL: Implication is only allowed when antecedent and consequent are both true; disjunction is only allowed when both disjuncts are false (i.e., every disjunction is false). But conjunction elimination is allowed.

NONE: Conjunction elimination is forbidden, but disjunction and implication seem to act normally.

SOME: I think this may be the assumption for standard propositional logic. It is certainly the only one of the four that gives the right answers on the above issues: conjunction elimination is allowed, from (p → q) you can't infer p, and disjunctions aren't always false.

AFFIRM: Implication collapses to conjunction, and conjunction elimination is impossible if one of the two conjuncts involves negation. However, you can have conjunction elimination if neither of the two conjuncts involves negation.

This is all very rough and vague; I'm sure that much more could be said about these four. And, of course, there are other schemes of existential import. It might be worth noting that SOME is the usual modern assumption for existential import; NONE is the assumption for Free Logic; AFFIRM is the assumption for which Lewis Carroll argued; Venn thinks that Jevons hints at ALL, and thinks it is implied by the traditional approach to immediate inferences and the square of opposition, but I think he himself accepts SOME, and this is what Keynes attributes to him. John Neville Keynes, who gives us perhaps the most thorough study of existential import, attributes ALL to Mill (at least for real propositions); he doesn't attribute NONE to anyone, but considers it. Keynes rules in favor of SOME.

Keynes also considers a view, which he attributes to De Morgan and Jevons, in which every categorical proposition imports existence for its subject, its predicate, and their contradictories (so that All S is P implies the existence of S, nonS, P, and nonP); that would yield a very odd propositional analogue indeed, since in such an analogue every proposition implies a contradiction. (I'm not sure it would have contradiction explosion, though. At first glance it seems that explosion would be limited by the fact that you can only conclude the terms and their negations. I'll have to think about this a bit more.)

Sunday, January 13, 2008

Thoughts on Witherspoon

Jonathan Rowe makes what I think is a surprisingly common mistake with regard to John Witherspoon, quoting approvingly the following claim of Noll, et al.:

Witherspoon did not derive his politics from the Bible. He did not think the Christian God had a specific role to play in public life, where the rule of nature prevailed. And he did not worry about assuming an Enlightenment perspective on political matters.

This, however, is directly contrary to what Witherspoon himself tells us. In his sermon on the extent of visible religion, for instance, Witherspoon is very insistent that "the Christian God" has a "specific role to play in public life", since he holds the fairly common Christian view that religious practice includes all of one's moral life. (The phrase 'the Christian God' is telling since it seems to assume -- which Witherspoon certainly would not -- that you can take Christianity, or orthodox Christianity, as Rowe calls it, and isolate it into a few purely dogmatic beliefs, like that of the Trinity, separate from everything else.) Witherspoon argues that it is essential for Christians to show that no one can discharge his duty any public or social duty whatsoever so well as those who "are renewed in the spirit of their minds," because they, "having the love of God shed abroad in their hearts, must of consequence love their brethren also." Thus for Witherspoon any fulfillment of the duties of public life (he explicitly includes those pertaining to magistrates and rulers) must be, for the Christian, an expression of Christian life and love of God. Yes, the Christian God, if you want to use that odd pleonasm. He considers this essential because, as he says, reason and argument "is but an uninformed picture for the living man"; for people to be guided in what they must do, they need not merely speculative reasoning about the good, but, much more importantly, the sensible representation of the good as found in the life of the righteous. That he does get at least some of his politics from Scripture is seen by his footnote on the magistracy in his treatise criticizing stage-plays and the famous sermon on the dominion of providence over the passions of men.

Thus there really is no evidence that Witherspoon "attempted to synthesize Christianity with Enlightenment rationalism" as is suggested in the post; this comes, I think, from confusing what would have been standard education with "Enlightenment rationalism," however we are to understand that. After all, Witherspoon was Scottish; the Enlightenment he knew didn't need to be synthesized with Christianity, because it was a largely Christian movement. With the exception of a small circle around Hume, it was all Presbyterian: Hutcheson, Reid, Campbell, Beattie, etc. It is true that Witherspoon stands alone as a member of the Evangelical party of the Church of Scotland; the other major names were all members of the Moderate party of the Church, and thus to that extent his theological opponents. But, of course, both camps shared the fundamentals of the faith (while other differences occasionally arose, they differed mostly on the role of the people in church, the Evangelicals being the more democratic), and also pride in what was arguably the most successful education system in the period. There was no need for synthesis; it was already there -- enough so that one can perhaps argue that too many people accepted the particular way they were synthesized a little too uncritically. But people like Hume had to go to great lengths to break down this synthesis, and in the more freethinking Founders we find simply a (slightly) more advanced stage of this process (aided, no doubt, by the influence of the more successful freethinking movements in France).

Infinitely Large Nonexistent Strawberries

From John Venn's Symbolic Logic (p. 339):

I once had some strawberry plants furnished me which the vendor admitted would not bear many berries. But he assured me that this did not matter, since they made up in their size what they lost in their number. (He gave me in fact the hyperbolic formula, xy=c2, to connect the number and magnitude.) When summer came no fruit whatever appeared. I saw that it would be no use to complain, because the man would urge that the size of the non-existent berry was infinite, which I could not see my way to disprove. I had forgotten to bar zero values of either variable.

This little parable serves to illustrate a point about the occasional surprises that lurk in taking a formula outside familiar limits (the particular surprises he is discussing at that moment are the paradoxes of material implication).