Saturday, August 04, 2007

Notable Linkables

* Karen Marie Knapp died in her sleep on August 1; blogging at From the Anchor Hold, she was a staple of the blogosphere. She first posted May 30, 2002; her last was July 20, 2007. Her archives are well worth browsing. God bless her; and may she remember us in her prayers.

* Common-place has an article on the only still-intact residence of Benjamin Franklin: the house he lived in on Craven Street when he was in London representing the Pennsylvania Assembly. It stands near Charing Cross Station, and has recently been renovated (its status as intact had recently become a bit precarious).

* Under Hill by Gene Wolfe is a fun little short story. (ht: CC)

* Mr. H has pictures from the first Jesuit emblem-book.

* Those interested in the Reformed view of justification should take Rebecca's quiz; it's a quick tour of the Westminster Confession on the subject. She gives and discusses the answers at length here, here, here, and here.

* Mike Wallace's 1959 interview with Ayn Rand: Part I, Part II, Part III. (Ht: MP)

* An interesting mistranslation: The "Aggressive House Spider", also known as the Hobo spider, is actually fairly nonaggressive. So why the name? It appears to be a misunderstandng of the Latin name, Tegenaria agrestis. A large number of spiders of the Tegenaria genus (the mat weavers) are common and well-known house spiders, so the genus is often treated as a genus of house spiders. But the Hobo spider is not a true house spider; it's an outdoor spider. That is, in fact, where the Latin name comes from: agrestis means 'rural' or 'pertaining to the fields'; in Western Europe, its indigenous habitat, it sticks to fields far from human habitation. (In the Northwest U.S., where it was transplanted, it has tended to encroach on human territory much more often, although this may be changing due to increasing competition from other spider species.) But someone at some point misunderstood 'agrestis' to mean 'aggressive', and so we have a spider that's agrestis (and thus not a house spider) called 'the Aggressive House Spider'. You can find information on hobo spiders here.

* Early Christian Writings has an E-Catena; an excellent resource for understanding how the Church Fathers read the New Testament.

* Some delightful logic books online: Lewis Carroll's The Game of Logic.
Alfred James Swinburne's Picture Logic.
Martin Gardner's Logic Machines and Diagrams
D. P. Chase's A First Logic Book
Richard Whately's Easy Lessons on Reasoning

For a more advanced inquirer, John Venn's Symbolic Logic is a good discussion of Boolean logic, while his The Logic of Chance is still one of the best accounts of probability in frequentist terms. De Morgan's Syllabus of a Proposed System of Logic is worth reading, as is his Formal Logic. Boole's The Mathematical Analysis of Logic also has much food for thought.

Friday, August 03, 2007

Rowling and Pullman

Horace Jeffery Hodges looks at Christian echoes in the Harry Potter books. (See here as well.) I had missed the "great silver cross". One of the key points of the cemetery, though, I take it, is that Voldemort tries to lay up his treasures on earth (the Horcruxes), where, of course, thief can steal, in order to destroy death; but those who oppose him treasure friendship which (as we see in the William Penn quote at the front of the book) is immortality before "that which is omnipresent" and therefore makes possible the triumph of love over death.

I think Hodges is right, incidentally, about Rowling vs. Pullman. Pullman is very clearly the better stylist; Rowling is at best inconsistent. But Rowling has far and away the better craft: Pullman is at least as inconsistent in his craft as Rowling is in her style. There's nothing wrong with that, since both are good to have, and few manage to be consistently excellent in both, particularly over several books. There's no question that Pullman is a skilled writer worth reading. But I think in the end it means that Rowling almost always hits her marks whereas Pullman hits nothing. Rita Skeeter is finely crafted to be a commentary on journalism, to take one small example of which the books have many; but nothing in Pullman's story is like this. Pullman's Magisterium is nothing like a Church, being utterly insane, and therefore cannot pull off the intended commentary on churches in general as things that "control, destroy, obliterate every good feeling"; we learn nothing about good or evil from Lyra and Will, and certainly not from the death of God, which makes no narrative sense. Part of that is due to the fact that Pullman has little more than a basic sense of narrative himself; it's why he subscribes to Blake's notion that the imaginative sympathy in Paradise Lost is with Satan, despite the fact that virtually everything in the poem is constructed so as to show that Satan is a liar and the Father of lies, who cannot even talk to himself without obviously lying, and sometimes contradicting himself, in an attempt to make himself seem bigger and more important than he is. Part of it is perhaps that Pullman can't outmaneuver Milton, for all he makes a valiant attempt. In Paradise Lost, Satan, too, is chiefly a literary stylist; it is God who has the skill of a storyteller. When Milton is the major influence, a story from the Devil's point of view will inevitably be stronger on style than storycraft. God, being Almighty, can let the tale unfold, unworried about the outcome, but for Satan to be the victor in a battle against God, the story has to be rigged, and Pullman manifestly does rig it.

But in Pullman we get a very rich style, Miltonic and at least more-or-less consistent, full of rich description and beauty. Rowling's not bad at it, but her style is far simpler and considerably less consistent. Similarly, Pullman's not horrible at storytelling -- we do get genuinely interesting bits of storyline -- but he's not nearly as consistent at it, or as frankly clever with it, as Rowling is. Rowling may seem simplistic to the superficial reader, but she can be beautifully subtle. As an example, most readers come away thinking Harry destroyed two Horcruxes. But he didn't; he only destroyed one Horcrux himself. Someone else destroyed the other one that most people attribute to him -- and it's the only person who really could have, the most narratively appropriate person possible, so that, setting aside the Horcrux destroyed by accident (but, notably, by the ones most closely associated with the room in which it was done) each Horcrux was destroyed by one of the six people in the whole world that the whole preceding storyline had shown to be the most dangerous to Voldemort. And the fact that she recognized the suitability of one of those six, and that that one had to be that one, was not just a good sense of narrative, but a sheer masterstroke of storycraft. Pullman has some beautiful subtle descriptions, but nothing remotely like that. People often make jokes about Pullman's plotting; no one could honestly do the same with Rowling.

Political Discourse and Quotation

Ralph Luker has a great post commenting on some recent commentary on a speech by Obama:

Great rhetoric works best when it is not innovative, but summons us to the best that is already latent in our public memory.

One might also add to the examples Ralph gives Lincoln's Second Inaugural -- which clearly quotes Mt. 18:7 and Ps. 19:9 and alludes to Gen. 3:19 (the particular form the allusion takes shows that Lincoln is actually alluding to a previous speech in which he alluded to Gen. 3:19) and Mt. 7:1. The 'charity towards all' part is certainly derived from elsewhere, although it's sufficiently widespread at the time that a particular source might not be discoverable (but its use here is very probably influenced by 1 Peter 4:8-9; note the point about charity covering a multitude of sins). The mention of the soldier's widow and orphan taps into a long tradition of prophetic and ministerial discourse about caring for the widows and the fatherless (cf. Zech 7:10, James 1:27) that would have been recognized. Nonpartisan, to whom Ralph is responding, makes clear in the comments that Scriptural quotations are being set aside for the purpose of that argument, which focuses on quotation from the speech of other politicians; that, no doubt, is why Kennedy's "Ask Not" speech made it onto the list, since Kennedy very explicitly quotes Isaiah 58:6 and Romans 12:12. So Ralph's point needn't be seen as problematic for Nonpartisan.

But the point is important, I think, and there is an additional speech explicitly mentioned by Nonpartisan that fits it very well. Washington's Farewell Address may have no direct quotes, but it has some very clear allusions. The most obvious is the claim that virtue or morality is a necessary spring of popular government; the formulation of the maxim in terms of the 'springs of government is due to Montesquieu (The Spirit of the Laws, Book III), and since Montesuieu is widely read, it is a common claim. We find Robespierre, for instance, using very similar words just two years before (although he confines the maxim to times of peace; in times of revolution, he says, you need virtue and terror, which is a somewhat different twist). It's not a direct quotation of Montesequieu; but it's very, very close to being one.

It makes me wonder, though, if the problem is not originality or quotation of people who are effectively equals or even inferiors, as Nonpartisan suggests, but the fact that we have no political theorists worth quoting. You can build a government on Montesquieu; in the eighteenth century you could hardly do better. Even now, the primary difficulty with quoting him is just that he's over two hundred years old and no longer read by everyone interested in politics. Due to the fact that it has ongoing relevance due to reinterpretation, preaching, and the like, you can do much the same with the Bible; you have to select with good sense and good art, but you can tap into some powerful political thought by quoting the Bible. (MLK, Jr. is an excellent example of this; his task in this was made easier in part by the Social Gospel and political theological work with which he was very familiar and in part by the widespread use of the pulpit as a point from which society and sometimes government might be thoroughly critiqued.) But, honestly, what do we twenty-first century Americans have to build on? The Bible still has some residual force, perhaps; but setting that aside (and it is clear that, for a number of reasons, it would only take you so far these days, anyway) we really don't have any discourse you can build a government on. That takes both philosophy and poetry, and our talk about government has had precious little of either for a long time. And that's what's missing, I think.

Thursday, August 02, 2007

Three Poem Re-Drafts


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

The Dragons

The dragons are restless today;
they stir up hurricane and whirlwind,
puff forests to ash,
melt stone to rivers.

It must be mating day;
they sing with low trumpet-calls,
gather together and quarrel,
do aerial combat
and other things.

Once a century they come together
to multiply,
a fruitful congregation;
but with all these steel-clad knights
who rescue stupid damsels
(the kind who never learned how
to avoid the fiery dragons)--
they'll soon be extinct.

Then no one will know what it's like
to live in a world with dragons.
Imaginations will fail,
for a dragon is a sublimity
men and women cannot imagine.


A cathedral hewn of a single stone
holds a golden cross and an ancient throne
where the glory sat above the cherubim
in the holiest holy.

The Ge'ez prayers of an ancient rite
softly rise into velvet night
as Ezana's children pray by the wall
of the holiest holy.

I dreamed of Adsum where angels rest
on every tabot and stars are guest
at revels of hope and undying light
near the holiest holy.

Maryam Ts'iyon walks a path alone
through the cherubim beneath the throne
of the Highest High with His glorious gift,
the holiest of holies.


A tiny taste of what I've been listening to lately....

* Johnny Cash: Ghost Riders in the Sky (originally performed by Stan Jones)

* The Who: Behind Blue Eyes

* Show of Hands: Roots

* Ella Fitzgerald: Summertime

* Charles Trénet: La mer

* Clannad: Theme from "Harry's Game"

* Sarah Brightman: Scarborough Fair

* Queen: I Want It All

* Nick Cave & The Bad Seeds: Red Right Hand

* Leonard Cohen: Dance Me to the End of Love

* The Clash: I Fought the Law (originally performed by Sonny Curtis and the Crickets)

* America: Inspector Mills

* Mocedades: Eres Tu

* Ides of March: Vehicle

* Wailin' Jennys: The Parting Glass

Wednesday, August 01, 2007

Supposition Theory

From Chapter X of Michael Flynn's Eifelheim:

I was teaching still at the Albert-Louis, and Tom sent me an e-mail asking me the manorial records for Oberhochwald to find. These were supposed to be in our University collection. I replied, Was that a personal supposition, a material supposition, or a simple supposition? And Tom responded <LOL?> because he did not understand the joke. He supplied a list of key words and a request to search our manuscripts and incunabula for references pertaining to Oberhochwald, which I suppose was fit punishment for my attempt at medieval humor. Supposition theory is not much funny, especially as we don't really know what they meant by it all.

I don't think it's quite correct to say that "we don't really know what they meant by it all" (it's not like the theory of supposition is as obscure to us as, say, the theory of obligationes), but there is indeed some dispute about it. The standard view is that supposition theory is a theory of reference. That this is the standard view is in great measure due to Peter Geach. Gyula Klima has done some interesting work showing that one can actually get pretty far with the standard view; this paper (PDF) gives some idea of it. Catarina Dutilh Novaes, however, has written some interesting and excellent papers arguing that the standard view is somewhat off, and that supposition theory should be seen as an apparatus for the semantic analysis of sentences, a means by which one might uncover ambiguities and clarify them. This one (PDF) is a good place to start in order to get the gist of her argument.

'It's Against My Religion.'

Orac notes this story about parents increasingly claiming religious exemption to prevent their children from being vaccinated. He then says,

The pernicious effect of religion here is more than just on the children of parents who follow specific religions that may find vaccines objectionable (which, by the way are few in number). In this case, religion gives cover to parents who just don't want to vaccinate because of pseudoscientific fear-mongering or "philosophy." Undue respect for religious beliefs that clash with the scientifically proven ability of vaccines to prevent disease safely enables these parents to easily bypass vaccination laws. With an increasing number of states providing more and more religious and "philosophical" exemptions to vaccines, I fear that it will only be a matter of time before diseases once thought vanquished return in a big way on these shores.

Now, Orac is a doctor -- a surgical oncologist, if I remember correctly -- so it is not the least surprising that he gets worked up about this, and quite rightly, too. But I don't think this is quite the right way to put it. In part this is because 'giving cover to liars' is not a pernicious effect of anything; quacks appeal to science as a cover for their cons; it does not follow that quackery is a pernicious effect of science. As Orac notes, in twenty states in the U.S. you don't even need a medical or religious reason to get an exemption; a 'philosophical one' will do. This is not a case of philosophy having a pernicious effect of giving cover to antivaccination; it is a case of a law written so that a 'philosophical exemption' just becomes an exemption anyone can get without having to do anything to prove that they really have a serious philosophical reason for not vaccinating their children. The primary problem in these religious cases is clearly that there is no system of accountability in place to guarantee that religious exemptions serve the function of protecting religious freedom. As Orac notes, very few religious groups actually have an anti-vaccination stance; it has been noted in a number of surveys that most religious groups tend to be favorable toward vaccination, with Church of Christ Scientist being the major exception. Moreover, it is incorrect to say that the religious beliefs "clash" with the scientifically proven abilities of vaccines; unless the religious beliefs are that the vaccines don't work, which is also going to be rare, rather than (say) some view about what is required for the integrity of the body, there is no clash. Medical science is an instrumental discipline, not a normative one; it can't "clash" with a norm, however bad for health that norm may be. What is at stake here is a clash between personal moral opinion -- a community opinion in the rare genuine case of religious exemption, like that of the Christian Scientists -- and the general political and moral interest in a healthy populace.

Tuesday, July 31, 2007

The Little Girl with the Little Curl

On today, the Feast of Ignatius of Loyola, Jimmy Akin says,

Though it may be somewhat impolitic to say so, I've often remarked that Jesuits are like the "little girl with the little curl, right in the middle of her forhead." When they're good, they're very, very good, and when they're bad, their horrid.

And so it's always been, I suppose. They've also had a knack for getting into trouble, even when not being horrid.

The current Society of Jesus is, and is not, the Society of Jesus originally founded by the former Spanish soldier who wanted to build a spiritual army for the Church. The original Society, founded in 1541, was suppressed in 1773, the outcome of a long series of political intrigues. A rather serious set of events involving, among other things, commerce rights and the War of Paraguay, led to the Society being made illegal in Portugal in 1759. Jesuit power in Martinique combined with the dispute with the Jansenists combined with the French need to raise funds to compensate for what they were losing to the English navy led to their being made illegal in France in 1764. A faction of anti-clericalists in Spain managed to get them made illegal in Spanish dominions in 1767. In 1769 Clement XIV was made Pope, and found himself immediately hounded to put an end to the Jesuits once and for all. He gave in so far as to order the Suppression of the Society in all Catholic nations. And that, it seemed, was that.

But the Jesuits turned out not so easy to suppress. Much of the detail of putting the Suppression into effect was left to local bishops; in many places they were still allowed to teach as long as they did so under the authority of a secular priest rather than a Jesuit superior. And in Russia the Jesuits even kept most of their structure, since they were backed by the Imperial Court, who had the promulgation of the brief ordering the Suppression delayed. And in the meantime odd things were happening. The primary instigators in the Suppression had always been the Bourbon courts; but some of them were facing hard times due to little things like the French Revolution. During the time of Pius VI, Rome refused to issue anything official, and upheld the suppression, but the Pope often gave verbal assent to Jesuit undertakings, such as the aggregation of the English Jesuits to the Russian Jesuits in 1803. The US's first Jesuit college, Georgetown, became Jesuit during the Suppression, by association in 1805 with the Society in Russia. In addition, some former Jesuits joined together to form smaller societies that were Jesuit in all but name. The Society was officially restored on August 7, 1814; in effect, it extended the state of the Jesuits in Russia into the rest of the world. (The Russians threw the Jesuits out in 1820. Jesuits have often mused on the curious state of affairs whereby Russia, always hostile to the Jesuits, just shortly before they were suppressed become sufficiently open to them to preserve the Society intact there, and stayed open enough for this just long enough to see the Society restored everywhere else.) Things did not run smoothly for the Jesuits after that; the entire nineteenth century was on-again, off-again as they flourished, were exiled, returned, were persecuted by law, rebounded, and, in short, suffered every twist of fortune imaginable.

It was a Jesuit, I think, who once said that Jesuits are only not in trouble when they are taking a rest from being Jesuits.

Monday, July 30, 2007

Wilberforce on True Practical Christianity

True practical Christianity (never let it be forgotten) consists in devoting the heart and life to God ; in being supremely and habitually governed by a desire to know, and a disposition to fulfil his will, and in endeavouring under the influence of these motives to " live to his glory." Where these essential requisites are wanting, however amiable the character may be, however creditable and respectable among men ; yet, as it possesses not the grand distinguishing essence, it must not be complimented with the name of Christianity. This however, when the external decorums of Religion are not violated, must commonly be a matter between God and a man's own conscience; and we ought never to forget, how strongly we are enjoined to be candid and liberal in judging of the motives of others, while we are strict in scrutinizing, and severe in questioning, our own. And this strict scrutiny is no where more necessary, because there is no where more room for the operation of self-deceit.

William Wilberforce, A Practical View of the Prevailing Religious System of Professed Christians : in the higher & middle classes in the country, contrasted with real Christianity. T. Cadell (London: 1829) 214-215.

William Wilberforce Day

Today the Church of England remembers William Wilberforce. The Collect, which sums him up nicely:

Let your continual mercy, O Lord, kindle in your Church the never-failing gift of love, that, following the example of your servant William Wilberforce, we may have grace to defend the poor, and maintain the cause of those who have no helper; for the sake of him who gave his life for us, your Son our Savior Jesus Christ, who lives and reigns with you and the Holy Spirit, one God, now and for ever. Amen.

The Gospel, which also sums him up nicely:

Jesus said, "When the Son of Man comes in his glory, and all the angels with him, then he will sit on the throne of his glory. All the nations will be gathered before him, and he will separate people one from another as a shepherd separates the sheep from the goats, and he will put the sheep at his right hand and the goats at the left. Then the king will say to those at his right hand, `Come, you that are blessed by my Father, inherit the kingdom prepared for you from the foundation of the world; for I was hungry and you gave me food, I was thirsty and you gave me something to drink, I was a stranger and you welcomed me, I was naked and you gave me clothing, I was sick and you took care of me, I was in prison and you visited me.' Then the righteous will answer him, `Lord, when was it that we saw you hungry and gave you food, or thirsty and gave you something to drink? And when was it that we saw you a stranger and welcomed you, or naked and gave you clothing? And when was it that we saw you sick or in prison and visited you?' And the king will answer them, `Truly I tell you, just as you did it to one of the least of these who are members of my family, you did it to me.' "

Consider celebrating the day by giving to an abolitionist fund, devoted to ending modern-day slavery (of which there is a great deal), like The Amazing Change Fund or International Justice Mission. You can also earn money for IJM by using GoodSearch for your search engine for a while and making it your charity. This is a way to raise funds for them (about a penny a search) without even having to dig into your wallet.

Another way to remember the great social reformer is to re-read his famous 1789 Abolition Speech

Notes Toward a Formal Typology of Argument III

In Part I I laid out, in a rough way, the rationale behind my notation for this typology. In Part II I identified the key intra-hierarchy relation of attenuation and noted how it structures the four hierarchies I had particularly identified: R1, R2, ~R1, ~R2. I left off noting that R1 and R2 on the one hand and ~R1 and ~R2 on the other are parallel, and that R1 and ~R1 on the one hand and R2 and ~R2 on the other are reciprocal. This leads us to the key inter-hierarchy relation of preclusion.

Like attenuation, preclusion can be seen as an a fortiori relation; but it is, unlike attenuation, a relation of opposition. The use of one argument often precludes, if we wish not to be self-defeating in our reasoning, another. Suppose you have a given bit of evidence, e.g., my seeing that the sky is blue. And I conclude from this that, given this, the sky must be blue. That is an argument of the type a : Ra(XLT). If a is a good reason for (XLT), however, that precludes its being a good reason for opposing conclusions, e.g., that it is necessary that it is not true that the sky is blue. This is what I mean by preclusion; and I think it's fairly clear that it's an important relation between types of arguments, one that is important for argumentation in general. Unlike attenuation, preclusion is symmetrical; every argument-type precludes every type that precludes it.

Preclusion shows a number of interesting patterns.

(1) Preclusion between R1 and R2. Whether a given type of argument in R1 precludes a given type of argument in R2 (or vice versa) depends crucially on how strong the conclusion is.

Every argument-type precludes its modal- & stance-reversed counterpart in the opposing hierarchy and every type stronger than it. Thus, RL(XT) precludes RM(X~T) because they have opposing modalities and stances; and since preclusion of the more attenuated conclusion is a fortiori preclusion of the less attenuated conclusion, RL(XT) precludes every argument-type in R2 stronger than RM(X~T). Since RM(X~T) is the attenuation of every other argument-type in R2, RL(XT) precludes every type in R2. R(X~F) has as its reverse counterpart R(XF); it precludes R(XF) and every type of which R(XF) is the attenuation.

(2) Preclusion between ~R1 and ~R2. There is no preclusion between ~R1 and ~R2. It's easy to see why; since the ~R hierarchies are types of arguments that remove relevance by indicating that the base is not a good reason for the conclusion, if the base is entirely irrelevant to the claim, then all the types of ~R arguments can be made with regard to it. So no argument-type in the ~R1 hierarchy precludes any argument-type in the ~R2 hierarchy, and vice versa.

(3) Preclusion between R1 and ~R1. RL(XT) certainly precludes the whole ~R1 hierarchy; RL(XT) precludes ~RL(XT) for obvious reasons, and what precludes the weaker a fortiori precludes the stronger. This pattern is repeated. Every R1 argument-type has a reciprocal in ~R1 that it precludes; since the hierarchies themselves are reciprocal, and what precludes the weaker precludes the stronger, every argument-type in R1 precludes its reciprocal in R2 and every type stronger than it; and, of course, vice versa.

(4) Preclusion between R2 and ~R2. Preclusion between R2 and ~R2 follows the same pattern as preclusion between R1 and ~R1.

If you think about it, we have some sort of at least vague intuitive feel for both attenuation and preclusion; this is why a fortiori reasoning is possible, since these are clearly the two primary foundations for it. And it is in seeing the interaction between attenuation and preclusion in the typology that we begin to see how useful such a typology has the potential for being.

It has recently become fashionable to talk about defeaters, which are usually taken to fall into two groups, namely, rebutting defeaters and undercutting defeaters. It's immediately clear that preclusion and defeat are somehow related. Preclusion itself can't be defeat, because preclusion obtains between types of arguments, and defeat between particular tokens of a type. But preclusion is that which makes defeat possible. There is some dispute about how precisely we should distinguish between rebutting defeaters and undercutting defeaters; but the usual way of doing so at least roughly is to say that rebutting defeaters give one a reason for thinking the original conclusion argued for is false; whereas undercutting defeaters give one a reason for thinking the premises for the conclusion do not actually yield it (at least in that given case). But given our typology we can give a simple account of both that is more rigorous than this. R-hierarchy (whether one-base or multiple base) argument-types are rebutting defeaters for those opposing R-hierarchy argument-types they preclude. And I think it can be argued fairly easily, although I will not do so here because it involves going beyond the one-base case I've been considering, that ~RR-hierarchy argument-types (that is, types that are not one-base) are undercutting defeaters for R-hierarchy argument-types (i.e., lower-level arguments) they preclude, and so forth. Self-defeat is also easily characterized; it occurs in one-base cases when, given the nature of the base, the argument does not rule out the tokens of precluding argument-types. A more rigorous account of preclusion than I've here provided would yield a more rigorous account of defeaters. And note several essential points shown by the typology:

(1) Because the attenuation relations group the argument-types into separate hierarchies, we can see the reason why people could make the rebutting/undercutting distinction in the first place, since they are, in fact, rather different in structure.
(2) However, the typology shows that there are forms of preclusion, the tokens of whose argument-types do not exhibit either rebutting defeat or undercutting defeat, namely, R preclusions of ~R arguments. Undercutting defeaters are always ~RR to R (or ~RRR to RR and R, etc.); rebutting defeaters R to R; so the oppositions of R to ~R and ~R to R, as well as oppositions to undercutting defeaters, do not fall under either the category of rebutting defeater or undercutting defeater. But they certainly are important for ruling out arguments.
(3) Moreover, it shows that while the distinction latches onto something, it also glosses over an immense amount of structure. There are many different kinds of rebutting defeaters, and what they can defeat is both precisely characterizable and very different in each case. Likewise with undercutting defeaters -- indeed, there appear to be infinitely many possible types of undercutting defeaters, each with their own place in the structure, although, no doubt, most of them are not practically interesting and, perhaps, they might under futher investigation fall into groups.

That's all I'll suggest on this point right now; it's sketchy, but I think it shows some of the promise of the typology for understanding the workings of arguments. In the next post I want to add a further level of sophistication to it, and probably will close in the post after that with some examples and, perhaps, other applications.

Continue to Part IV

Sunday, July 29, 2007

Notes Toward a Formal Typology of Argument II

This post presupposes that the reader has already read the first part:

Part I

In my previous post, I laid down the R1, R2, ~R1, and ~R2 hierarchies without much comment. Each of these hierarchies are arguments that might be made given a single base. I will here use the R1 hierarchy to begin looking at the patterns of relations among arguments exhibited in these groupings. The R1 hierarchy, you will recall, is:


The reason for the hierarchy being structured as it is, is simply that the higher you go in the table, the stronger the argument, or, to be more exact, the stronger the claim made by the argument. Thus, a : RaL(XT) is the strongest in the schedule, and a : RaM(X~F) is the weakest. As we go from top to bottom the conclusions become attenuated; types of argument on the same line (e.g., a : RaL(X~F) and a : Ra(XLT)) are not attenuated with respect to each other. Thus the most important, and most interesting relation among these different types of argument, when we consider only a single hierarchy, is attenuation. When we make explicit the attenuation relations among these arguments, we get the following (sorry for the crudeness of this and all other graphics; they were thrown together as drafts):

The way to think of attenuation is to think of it as an a fortiori relation. If we have a good argument of type a : Ra(XL~F), then a fortiori an argument of type a : Ra(X~F) is a good argument. In other words, if some evidence is good reason to think that the sky is necessarily not false, a fortiori that evidence is good reason to that the sky is not false. The relation is transitive. If a is a good reason to conclude that it is a necessary truth that the whole cake is greater than any of its slices, a fortiori it is a good reason to conclude that this claim's being not false is a possible truth.

I mentioned before that some people might not like the idea of taking truth and false as contraries. What happens if you only allow two values, where T is taken as equivalent to ~F and F is taken as equivalent to ~T? You get the same basic hierarchy, but it collapses into a single line, since every argument-type on the left collapses into the argument-type immediately above it on the right.

When we recognize this it turns out to be easy enough to identify the attenuation relations for the other hierarchies. This is R2:

This is ~R1:

And this is ~R2:

Sharp eyes will recognize that R1 and R2, and ~R1 and ~R2, are parallel, whereas R1 and ~R1, and R2 and ~R2, are reciprocal. This brings us to the most important inter-hierarchy relation, preclusion. We'll discuss that in the next post on this subject.

Continue to Part III.

Church Establishments

Jason Kuznicki asks:

Suppose we created an official state church. Would this help increase religious faith and/or the intensity of belief? Or would the government botch the job of proselytizing, as it does so many others, causing people generally to lose their religious beliefs?

There are many different ways to have an official state church. In other words, there are many different ways one can make an official state church, and we should not assume that they will have the same results. In some establishments, the church is regarded as an independent entity officially recognized by the government for certain purposes. In other establishments, the church is regarded as a government agency or department. In all establishments the implications of recognition are limited, i.e., the recognition does not imply that the State can do anything it pleases to support the church, nor that the State is committed to do anything it can to support the church; but what those limitations are can vary considerably. In one establishment, recognition may mean nothing other than that it receives tax money; in another, it may mean that the church has some limited legislative and judicial jurisdiction recognized as authoritative by the state. Some churches are made state churches to the exclusion of any others; sometimes several churches can be made official. And so forth. So I'm inclined to think the question is unanswerable without determining what kind of establishment is in question, and what the character of the church established is. Gallican Catholicism had relations to the state that were radically different from those had by the Catholic Church in late eighteenth-century Quebec; neither could possibly be confused with the modern Chinese Patriotic Catholic Association; and none of the three are all that much like the Church of England in their relations to the government. And these are all cases where the internal structure and politics of the church is at least vaguely analogous; if we consider other possible forms of establishment, such as one would get by making, say, a Baptist Convention a state church, the relations would have to be yet more different. And it is these relations that would have whatever effect is to be had on the role of religion in that society. So the type of church, and the type of establishment, are both important for answering this question.

Notes Toward a Formal Typology of Argument I

This is an idea I had Monday, and which I have been working out here and there over the past week; it's a bit complicated, so it will take more than one post to lay it out. When it's done, however, I'd be interested in any feedback anyone might have.

In an argument we give reasons in order that we may draw a conclusion about what stance we should take with regard to a claim that might be made. In constructing a typology of argument, then, it is worthwhile to begin by positing four basic features to be used in your classification, which I shall call the bases, the argument-making operation, the conclusible, and the stance. The argument-making operation, which I will represent by R, I will take as primitive; to apply R is to do whatever is done to turn materials for an argument into an actual argument, and it is not of interest here what that involves. An argument has bases, starting points; these are the materials, the things that can be given as reasons for a conclusion. It is also not of interest here what those things may be, whether propositions, or sensory observations, or anything else. It has a conclusible, which is a candidate for being a conclusion; and it has a stance with regard to that conclusible. It is the combination of the conclusible and the stance which is the conclusion. For instance, my conclusion may involve taking the conclusible, "The sky is green" to be false. One important point with regard to the stance is what values we allow for it. I will allow four, T, F, ~T, and ~F; that is, I will be taking T and F as contraries. A conclusible may be neither true nor false. Some would prefer not to do this, and instead to take T and F as contradictory. This does not make a major difference to anything that follows if F is taken as equivalent to ~T and T as equivalent to ~F, then everything remains the same except that the patterns become simpler.

Given this, we can represent an argument along the following lines:

a : Ra(XT)

where a is the base, X the conclusible, and T indicates that it is taken as true.

We then get the following types of argument:

a : Ra(XT)
a : Ra(XF)
a : Ra(X~T)
a : Ra(X~F)

It is clear that this is not a very sophisticated typology on its own, and is certainly not exhaustive, representing only cases where something, call it a, is given as a reason for regarding X as true, false, not true, and not false respectively. To do justice to the range of possible arguments, we should introduce a further set of sophistications. The first is ~R. I use the negation sign because ~Ra represents an argument in which a is put forward as a nonreason for the conclusion. It's important to recognize, however, that ~R is as much an argument-making operation as R; the difference is that R indicates arguments where a is made to be relevant to the conclusion, and ~R indicates those where this link is severed. ~R-style arguments are one way in which we argue against R-style arguments.

We further need to recognize that we argue not merely for the basic stances already noted but for modal versions of them as well. That is, we don't merely fuss about whether arguments are true or false, or not, but also about the necessity and possibility of these. I will use L for the strong modality (necessity) and M for the weak modality (possibility). It is important, however, to distinguish two very different applications of modality in this regard, which can be represented by the difference between the two following types of argument:

a : RaL(XT)
a : Ra(XLT)

The first of these represents a case where the conclusion is that X is a necessary truth. The second represents a case where the conclusion is that X is necessarily true. Despite the verbal similarity the two are not the same. For if we take X itself as a (i.e., as the base), this trivial argument can legitimately be made for any X:

(XT) : R(XT)(XLT)

It is, in fact, the case, that, when X is taken as given, X is necessarily true. This is hypothetical necessity. If we take it as given that Socrates is sitting, it follows necessarily that Socrates is sitting. It does not follow, however, that "Socrates is sitting" is a necessary truth, because it is possible for Socrates not to be sitting.

I will also stipulate that R can take an argument within its scope. That is, you can have arguments like this:

a, b : Ra(Rb(XT)T)

Which represents the case where it is concluded, on the basis of a, that b is a truly a reason for concluding (XT). There are some complications with this. But in what follows I will mostly be focusing on the one-base case, in order to keep it simple and easier to understand, and only touch on these more complicated types of argument here and there.

Given these sophistications, we can begin constructing hierarchies of arguments. There are four notable ones. (In what follows, I will, to avoid clutter, abbreviate. For instance, a : Ra(XT) will simply be labeled, "R(XT)".) This is what I will call R1:


The following hierarchy I will call R2:


The following I will call ~R1:


And this is ~R2:


These forty types of one-base arguments are not exhaustive even of one-base arguments; as we will see later, there is at least one more sophistication that has to be introduced into the system. Nor are they unrelated. As we shall also see, there are interesting and, for the purposes of argument, important patterns of relations among them. We will begin discussing these patterns in the next post on this subject.

Continue to Part II.