Saturday, October 07, 2006

Sommers-Englebretsen Term Logic, Part VIII

A quick wrap-up post. In previous posts I've covered some basics of SETL:

In Part I, I noted the basics of SETL, in a rough way.
In Part II and Part III, I discussed briefly some special cases and how SETL handles them.
In Part IV, I discussed some basics of argument using SETL.
Part V looked at some simple arguments for which SETL gives us a better sense of what's going on than ordinary predicate logic does.
In Part VI I looked briefly at Englebretsen's discussion of how to extend SETL to modality.
In Part VII I looked at Murphree's union of SETL with numerical syllogistic.

Here are a few on-line references for further reading. All of them except Purdy's review of An Invitation to Formal Reasoning are found at the Notre Dame Journal of Formal Logic at Project Euclid.

Englebretsen, George
A Note on Contrariety
Do We Need Relative Identity?
Preliminary Notes on a New Modal Syllogistic
Sommers on Empty Domains and Existence
The Square of Opposition

Murphree, Wallace
Numerical Term Logic

Purdy, William
On the Question, "Do We Need Identity?"
Review of Sommers & Englebretsen, An Invitation to Formal Reasoning

Sommers, Fred
Predication in the Logic of Terms
The World, the Facts, and Primary Logic

Friday, October 06, 2006

The Festival of Ingathering, the Season of Our Rejoicing

On the second day of the month, the heads of all the families, along with the priests and the Levites, gathered around Ezra the scribe to give attention to the words of the Law. They found written in the Law, which the LORD had commanded through Moses, that the Israelites were to live in booths during the feast of the seventh month and that they should proclaim this word and spread it throughout their towns and in Jerusalem: "Go out into the hill country and bring back branches from olive and wild olive trees, and from myrtles, palms and shade trees, to make booths"-as it is written.

So the people went out and brought back branches and built themselves booths on their own roofs, in their courtyards, in the courts of the house of God and in the square by the Water Gate and the one by the Gate of Ephraim. The whole company that had returned from exile built booths and lived in them. From the days of Joshua son of Nun until that day, the Israelites had not celebrated it like this. And their joy was very great.

Nehemiah 8:13-17

A Theory of Human History

I believe what really happens in history is this: the old man is always wrong; and the young people are always wrong about what is wrong with him. The practical form it takes is this: that, while the old man may stand by some stupid custom, the young man always attacks it with some theory that turns out to be equally stupid.

G. K. Chesterton, in the Illustrated London News, June 3, 1922.


I've seen this around a lot. I can't find much that's very official or very clear, so I might be missing something; but I think this can be said as first approximation:

(1) The rejection of limbo (to the extent it is one) is not, in fact, a very strong rejection. All that appears to have happened is that the Pope has approved of a commission's argument that children dying before the age of reason are granted the beatific vision.

(2) This, if it is what was really done, is not a rejection of limbo. It is a common misconception that limbo is for unbaptized children. In fact, limbo is just sheol, and I can pretty much guarantee you that the Pope has not claimed that there is no sheol, or anything equivalent to it.

In fact, limbo, generally, is a very easy doctrine to prove from Scripture. Sheol is mentioned over and over again in the Old Testament; it is translated as hades in the New Testament; and it is found in the doctrine of Christ's descent into hell -- i.e., into hades. What is difficult to say is who is in limbo, and why, and what's involved in being in limbo. Traditionally, limbo was considered a state reserved for two groups in particular -- the unbaptized righteous -- patriarchs like Samuel (1 Sam 28) and Abraham (Luke 16) who had prefigured Christ's coming; and the unbaptized innocent, like children. The usual understanding of it was that it was a state of natural happiness, without torment or penalty. Further, people can be redeemed from limbo, whereas they can't from hell in the strictest sense; Christ's descent into hell, in fact, is in part the claim that Christ redeemed the patriarchs from limbo and exalted them to a supernatural happiness.

Two big and controversial questions have been whether noble pagans are admitted into the state of limbo and whether unbaptized children who were not of God's chosen people could be redeemed from it. Dante suggested that there was a limbo of noble pagans; although, of course, this may have been as much a poetic as a theological move. The point that has really worried people, however, is whether unbaptized children in limbo can be redeemed from it. Part of this has just been confusion; people don't distinguish properly between hell as limbo and hell as second death, in part because of our tendency to polarize the afterlife rather artificially into Heaven (all Beatific Vision) and Hell (all torment and regret), without considering that hell (and its cognates) used to have a much broader meaning than they usually do today, covering all states of immortality that do not involve the supernatural grace of the Beatific Vision. The two are not even remotely the same; limbo is just what you get if you can't ever be happier than we can be in this life, and hell as second death is punishment in a positive sense. On the other hand, we have very little information about how far the redemption we know the patriarchs received extended. Much of the historical controversy over the limbo of children was due to the Calvinist tendency to point at it as yet another instance where the Catholics had shown human weakness and Pelagianized grace. (If I recall correctly, the Pelagians, in fact, were among the ones who early on used the term 'limbo'.) It is a sign of the times that the pendulum of controversy has swung entirely in the opposite direction, and limbo is treated as yet another case of Catholics delighting in the punishment of the innocent.

Of course, because people worried so much about the limbo of children, when people talk about the doctrine of limbo, they usually mean the doctrine that all unbaptized children after death are in a state of limbo, which is not quite the same thing. For, after all, the possibility of limbo as a general state is Catholic dogma; the Council of Florence, for instance, makes very clear that souls of those who depart in original sin receive the proportionate punishment (which includes at minimum lack of Beatific Vision); and the Council of Trent is very clear that the unbaptized are not free of original sin. What is not Catholic dogma is the view that unbaptized infants (or anyone else) are never redeemed from the state of limbo by any extraordinary work of Christ and God's grace; and the usual claim has always been that we simply lack information about such matters. So limbo in that sense -- in the sense of unbaptized infants being eternally unredeemed -- is what is really at issue here.

Such is the first approximation, anyway. I find it noteworthy that all the news announcements are in future tense up to October 5, when the Pope was 'expected' to do something about it -- the Pope had not taken action on it -- and then, nothing. It's also noteworthy that they've been saying he was just about to do it for well over a year now. So the real state of affairs seems to be this: there's no information yet, and we can't really say anything until the information actually comes up. And yet people keep saying things....

Tuesday, October 03, 2006

Links of Note

* History Carnival XL is up at "Old is the New New."

* Biblical Studies Carnival #10 is up at "Religions of the Ancient Mediterranean."

* Bob Marley's "Redemption Song" covered by Joe Strummer and the Mescaleros. Probably my favorite version of the song. Joe Strummer, of course, was one of the pioneers of punk, best known for his work with the Clash.

* A Non-Philosopher's Guide to Philosophical Terms (HT: EMN)

* The Little Professor has Pilgrim's Progress links.

* Those who found my recent post on morning and evening knowledge interesting would probably also like Msgr. John McCarthy's summary of Augustine's account of the first four days of creation. (Ht: In illo tempore)

* Probably the best place to look for those interested in the Pope's recent Regensburg speech is "Gypsy Scholar." At that weblog Horace Jeffery Hodges has pointed out what the Pope actually said in the original German, discussed Tariq Ramadan's comments on the speech, compared the Pope's line of thought with a line of thought found in Rémi Brague, discussed Lee Harris's comments on the speech, commented on Marie-Hélène Congourdeau's comments, compared the Pope's comments on Europe to things he has said elsewhere, pointed out that a part of the speech is a critique of Protestantism, and discussed Berwick's comments on the speech.

* There's an interesting discussion of national debt at "Asymmetrical Information."

Sunday, October 01, 2006

Two Poem Drafts

Prometheus on the Roadside

The thorn in my side grows longer,
its burning fury ever stronger,
aching without time's release,
aching for the ache to cease.

In some dark law my flesh is caught;
what I would do, I do not
from a pain and ache that do not cease,
the pain and ache for last release.

I delight in the glorious breath,
but my heart is seized by the rigors of death,
seized by a pain that will never cease,
an ache that yearns for the soul's release.

Mercy's my madness; it sets me right,
but I am chained by the dark of night
in a chain no time can ever release,
in an ache that longs, never to cease.

The thorn in my side grows longer;
death is but a dream;
time is but a stranger
in a river of what seems.


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 Geez prayers of an ancient rite
softly rise into velvet night
and 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
as the cherubim that make the throne
for the Highest High and His glorious gift,
the holiest of all holies.

And something that's not quite a poem draft, but just a lark:

The Blurb

The blurb for this poem is quite true;
it sort of gets inside of you
with its vision of life and a whiff of types
that fulfill the prophecies of the hype.

And yes, 'tis true, beneath the sun,
that the author is a new John Donne
or Milton; but to be truly fair,
only Dante can compare
to his biting wit and his turning line
and his perfect rhythm and his flawless rhyme.

Yes, the hype is every bit true;
and I have a poem to sell to you.

Hazy Bayesies

Due to Unwin's recent letter to the editor in response to a review of Dawkins's The God Delusion that mentioned Dawkins's criticism of Unwin's Bayesian argument for the existence of God (PZ Myers helpfully quotes the relevant selection from Dawkins here), the question of the status of Bayesian arguments of this sort has been raised. So I thought I'd say something about this.

Bayesian epistemology is a noxious weed that first entered the philosophical garden through philosophy of science. Struggling to develop an account of the scientific confirmation of theories that was both adequate and formal, people began adapting the work done on Bayes' Theorem in the probability calculus to the topic at hand. From there it has spread all over the place, with a number of variations. It's important to keep in mind that this sort of adaptation of mathematical Bayesianism is not the same as mathematical Bayesianism itself. The strengths and weaknesses of Bayesian statistics don't automatically translate into the strengths and weaknesses of every adaptation of it to a different field, because every adaptation makes use of assumptions that may or may not be good assumptions. Bayes' Theorem is quite cool on its own; there's no reason, of course, to think that every absurd use of it is the fault of the innocent little Theorem.

Philosophical Bayesianisms of all sorts may be roughly characterized as claiming the following things:

(1) There are degrees of belief.
(2) There are degrees of evidence.
(3) Degrees of belief and degrees of evidence are commensurable to the extent that they can both be characterized by a single probability calculus.
(4) The relation between degrees of belief and degrees of evidence must be consistent with the probability calculus in all epistemic agents who are acting rationally.
(5) Given an original degree of belief and the addition of new evidence, the rational agent (at least usually) transforms an original degree of belief to a new degree of belief by determining the probability of what is believed on the new evidence.

There are slight variations on these, but these are more or less the positions held by philosophical Bayesians, whether they are Bayesian about scientific confirmation, about decision theory, or whatever else. The idea is that this is supposed to be a model of rational belief change (or non-change). I happen to think that all five claims are false in the senses required for all five together to be a good model of rational belief change. I'm a Newmanian about assent, which means that I don't believe that belief has degrees -- although, naturally, there are other things (like feelings) that are closely related that do, and which allow us to talk about degrees of belief in a loose sense. And the arguments in favor of the claim that belief does have degrees are all very bad in any case. My position on evidence is similar. Even setting that aside, I think it's clear that we have no stable way to measure either (the most plausible candidate is wagering behavior, which won't do); so we can't establish any clear commensurability. I disagree with (4) again because I agree with Newman about assent; and, in fact, while initially plausible, it seems to require implausible ideas of rationality (e.g., the logical omniscience problem). Bayesians themselves generally recognize that (5) has to have a qualification (like "at least usually"); I just think the exceptions are much more common than Bayesians do.

But my interest in this post is not to give my own reasoning on why philosophical Bayesianism is false, but to protest a certain slipperiness with the use of Bayesian arguments. So let's set aside all my qualms and suppose that (1)-(5) are all true (presumably in some form slightly more precise than the vague one I've given). What then?

A common approach seems to be to treat it in this way. Suppose you want to consider the question, "Is there a black hole in such-and-such region of space?" You assess your initial estimate of the probability (degree of belief) that there is, identify the evidential factors you think relevant, and then establish a new probability for (degree of belief in) the claim that there is a black hole in such-and-such region of space given those factors. Up to this point all is well and good, at least if you accept a Bayesian epistemology.

However, a problem arises if this rational thought process is taken as an objective argument that there is a black hole in such-and-such region of space; because it's a horrible way to argue for anything (except, perhaps, for the claim that you are believing rationally in believing as you do, given your assessments). In essence, what we have in philosophical Bayesianism is a theory of rational belief change. Given an original set of beliefs, we have a set of rules for how they should change (or not change) due to new evidence coming in. But because this is an account of rational belief change, it works very poorly as a means of arguing. The Bayesian account covers every rational belief change (at least in probabilistic circumstances) for every combination of initial probabilities, evidences, and claims. By presenting a Bayesian argument you haven't presented a good argument that there is a black hole in such-and-such region of space; you have presented one of infinitely many rational justifications of belief changes that favor or don't favor the conclusion. No one else, even if they are Bayesian, will accept that particular line of reasoning unless they agree with your assessments of prior probability, of relevant evidences, and of the relations between the evidences and the claim. You've not given an argument; you've just given an example of how one might come to be persuaded without ceasing to be rational. This can be an interesting result, if you don't try to make it into something it is not. Unfortunately, there is a widespread tendency to make it into something it is not.

To put it another way. Assuming that Bayesian epistemology is true, and assuming that you are accurately portraying your own assessments of evidences and probabilities, all you have shown is that you are not irrational in believing (or disbelieving) the claim there is a black hole in such-and-such region of space, given those assessments. But this is a very weak result, much weaker than the conclusion that there really is a black hole in such-and-such region of space. The weaker result can only become the stronger result if you have good, solid arguments that everyone, or almost everyone, who is rational will assess things more or less as you have done. But this means that the actual work done in showing that there is a black hole in such-and-such region of space is done by different arguments, not the actual Bayesian argument you are running. The Bayesian argument is just a way to organize those arguments so that you can see their point. It itself does no serious work in the actual proof.

So it makes no sense to run 'Bayesian arguments' for a given conclusion, unless that conclusion is that you are rational to accept that conclusion on the assessments you've made, even if Bayesianism is true. It's fairly clear, however, that philosophers do this a horrid amount. And the result is always just silly, since anyone can point out that a different set of assessments leads to a different conclusion. The result is both that Bayesian epistemology looks much more stupid than it really is, and that the conclusion looks laughable in light of how apparently arbitrary you had to be to get the conclusion. This leads to the irritation of intelligent mathematicians and others who wonder what in the world you think you're doing, and is bad for the reputation of philosophy in general. I'm very much opposed to philosophical Bayesianism, but even I have to protest how silly this rush to argument makes philosophical Bayesianism (and philosophers generally) look. Even Bayesian epistemologists deserve better.

Links for Thought and Play

* Russell Arben Fox has a fascinating review of Linker's The Theocons at "In Medias Res".

* Rebecca has a good post on the theological discussion-stopper, "The God I worship wouldn't...."

* "Historia Ecclesiastica" has a post on 'Troublechurch' Browne, the sixteenth-century Separatist. It sheds some interesting light on the roots of Baptist views on individual liberty and separation of church and state.

* "Happy Catholic" posts Phyllis McGinley's rhyming summary of St. Jerome's life, The Thunderer.

* A bit about dialect:

Your Linguistic Profile:
60% General American English
20% Dixie
10% Yankee
5% Midwestern
0% Upper Midwestern


* Pure Creepiness: A Mary Worth storyline faithfully acted out. Mary Worth is not usually considered either a funny or a creepy comic strip, but that's because its pace is tortoise-slow. It is actually both.