Saturday, February 18, 2012

Vasari on Fra Angelico

Fra Giovanni was a simple man and most holy in his habits, and one day when Pope Nicholas V desired him to dine with him, he had scruples of conscience about eating meat without his prior's leave, not considering the Pope's authority. He would not follow the ways of the world, but lived purely and holily, and was a great friend of the poor. He painted constantly, and would never represent anything but the saints. He might have been rich, but did not care about it, saying that true riches are nothing else than being content with little. He might have governed many, and would not, saying it was less troublesome to obey, and one was less liable to err in obeying. It was in his power to hold dignities among the friars and elsewhere, but he did not esteem them, affirming that he sought no other dignity than to escape hell and attain to Paradise. He was most kind and sober, keeping himself free from all worldly ties, often saying that he who practised art had need of quiet and to be able to live without cares, and that he who represents the things of Christ should always live with Christ. He was never seen in anger by the friars, which is a great thing, and seems to me almost impossible to believe; and he had a way of admonishing his friends with smiles. To those who sought his works he would answer, that they must content the prior, and then he would not fail. To sum up, this father, who can never be enough praised, was in all his works and words most humble and modest, and in his paintings facile and devout; and the saints whom he painted have more the air and likeness of saints than those of any one else. It was his habit never to retouch or alter any of his paintings, but to leave them as they came the first time, believing, as he said, that such was the will of God. Some say he would never take up his pencil until he had first made supplication, and he never made a crucifix but he was bathed in tears.

From Giorgio Vasari's Lives of the Artists

Il Beato Angelico

Today is the feast day of Guido di Pietro, more commonly known as Fra Giovanni da Fiesole, even more commonly known as Fra Angelico.

Fra Angelico 073

(Fra Angelico, The Deposition of Christ, in the Museo di San Marco)

Friday, February 17, 2012

On Boudway on Religious Liberty

Matthew Boudway somewhat flubs his discussion of the recent contraception mandate accommodation controversy by overreaching:

Most critics of the HHS contraception mandate have said the controversy is about religious liberty, not contraception. Some of the same critics have said that the question is not whether Catholics could comply with the mandate in good conscience if they had to, but whether the government ought to force them to comply with it in the first place. But these two claims are logically incompatible with each other....

But if the argument is about religious liberty, then critics must persuade those who aren’t opposed to contraception or the coverage mandate that requiring Catholic employers to provide such coverage—or facilitate it in any way—would force them to violate the teachings of their religious community. If it can be shown, therefore, that such requirements would not force Catholics to violate their church’s teachings, then no one can oppose the mandate on the grounds of religious liberty.
Whatever one may say about the mandate, the accommodation, or Catholic views of the matter, this argument is a rather bad argument for the simple reason that the two claims are not logically incompatible with each other. The two claims mentioned, again are:

(1) The controversy is about religious liberty, not about contraception.
(2) The controversy is about whether the government ought to force Catholics to comply with the mandate, not about whether they could comply with the mandate in good conscience if they had to.

The contrastive clauses in each case simply deny an intentional object of the controversy; whereas the main clauses identify an intentional object. For these to be logically incompatible, the following claim would have to be self-contradictory:

(3) The controversy is about religious liberty and whether the government ought to force Catholics to comply with the mandate.

And obviously this is not self-contradictory.

Of course, what Boudway is trying to do is combine the first positive clause with the other negative clause:

(4) The controversy is about religious liberty, not about whether they could comply with the mandate in good conscience if they had to.

And he wants to say that this is logically contradictory. It is clearly not, though. If the government passed a law forbidding attendance at Mass on weekdays, Catholics could comply with this in good conscience, but it would be nonsense to say that this has nothing to do with religious liberty. For that matter, since the precepts of the Church only bind to the extent that it is genuinely feasible to obey them, if the government forbade attendance at Mass entirely, Catholics could comply with this in good conscience if they had to, although they would also have a duty not to comply if they could manage that. And, indeed, many other religions are far more generous about what falls within this classification than Catholicism. With full sanction of Quran and hadith, for instance, Muslims could in good conscience comply with an extraordinary amount if they had to -- but that doesn't mean that they would not fight any external attempt to restrict their religious practices only to those things unequivocally commanded and forbidden by the Quran. And if they did fight it, as far as religious liberty rights go they would be entirely right to do so.

The claims Boudway considers could only be logically incompatible if nothing were a matter of religious liberty except what your religion provably demanded that you do (or not do). But this is a leap at best. Thus Boudway's conclusion,

But if one is going to claim that the mandate violates the religious liberty of Catholics, one really does have to demonstrate that the material cooperation with contraception it requires is illicit according to the church’s own teaching.
 Simply is not supported by his argument -- and is, in fact, obviously wrong. Showing that it is illict according to the Church's own teaching is merely the simplest and easiest way to show that enforcing it endangers religious liberty. Religious liberty questions are simply not as cut and dry as Boudway wants to suggest; they are complicated and difficult to negotiate, which is why liberal societies have often espoused the principle, if not always the practice, of not predetermining what can and cannot be a matter of religious liberty.

Kant on Semblance and Error

From the nature of error, whose concept, as we noted, contains besides falsity the semblance of truth as an essential characteristic, the following important rule results for our cognition:

In order to avoid error -- and absolutely unavoidable is no error although it may be relatively so in cases where, even at the risk of erring, it is unavoidable for us to judge -- in order, then, to avoid error, one must try to discover and explain its source, semblance. This has been done by very few philosophers. They have sought to refute the errors themselves without indicating the semblance from which they have sprung. This disclosure and solution of semblance, however, is a far greater service to truth than the direct refutation of the errors themselves, by which one cannot block their source and prevent the same semblance, because one does not know it, from leading again to errors in other cases....

By explaining semblance one moreover accords a kind of equity to the erring person. For no one will admit that he has erred without some semblance of truth which might have deceived perhaps even a more perspicacious person; for here the subjective reasons count.
Immanuel Kant, Logic, Hartman & Schwarz, trs. Dover (New York: 1974) 59-60. The rule has a good Aristotelian provenance, and is salutary advice on all occasions.

Thursday, February 16, 2012

A Poem Draft


The thoughts of mind in swiftness rise to peak
upon a sandy shore where gilding sun
makes bright the line of strand, a flowing thread
that wafts across the beach; they then return
and flee away in fright or timid awe,
their own audacious height unmanning them.
And on return they wonder if their rush
had led them into folly; abstract shore
eludes again the waning flow and wave
and senses rule -- until the turn of tide.

Wednesday, February 15, 2012

Some Thoughts on Teaching Logic to Children

Logic is something that (1) everyone recognizes is valuable and (2) is obviously undertaught in most modern approaches to education; most of what people learn is fragmentary, incidental bits and pieces appended to various mathematical subjects. So I thought I would put up some very tentative thoughts on how this might be remedied. As I see it, the teaching of logic could be very roughly divided into three basic parts: pre-logic, basic early logic, and advanced early logic. In reality, though, the sorts of things one does in the 'pre-logic' stage should be done throughout, and, depending on how one decides to structure things basic and advanced early logic might overlap.


As I always tell my Intro students, logic is something we always do and, at least until you get into very, very advanced or specialized logical topics (all certainly more advanced than children are likely to get into), practically anything you learn in logic is something you already do, without realizing it, at least sometimes. Just as M. Jourdain discovered that he had always spoken in prose, so we discover that we have always thought in logic. The only thing we do when we learn logic is slow everything down, break it apart, see how it works, put it back together, as well as develop the habits to do these things -- and do them better -- on the fly.. But it helps if you already think more-or-less logically in the first place. And that is mostly just a matter of practice. So the thing you want, even before teaching children logic, is to have them do lots of logical thinking in the form of reasoning games, puzzles, and books. There are many, many options here. Looking back at what I remember of my childhood, long ago in the ancient world, there were quite a few things that were suitable in this way -- I liked Encyclopedia Brown, and Haledjian in Two Minute Mysteries by the same author, and I was enthusiastic, and I mean enthusiastic, about the game Clue, which, of course, is a reasoning game, and enjoyed Sleuth, which was a very, very simple DOS game version (I still have a copy, and occasional play it in the way people play Minesweeper). Although I rarely had the means to do scientific experiments, I also really liked books of scientific experiments -- much more, in fact, than books on scientific topics. In any case, there are many different ways to do this, and probably rigid regimentation of any sort at this level is a bad idea -- no matter what a child's interests are, it provides an occasion in some way to get started on thinking problems through logically, and this is something that really needs to be tailored to a child's interests.

Basic Early Logic

The pre-logic stage is mostly about sharpening natural skills. We actually get into the study of logic proper when we start looking at the structure of reasoning. Jumping immediately into this is probably not advisable. Rather, things at the basic early logic should share features with the things done at the pre-logic stage, only with a closer look at why the reasoning works. I suspect diagrams are generally ideal here. Two in particular seem especially worth mentioning.

(1) Venn diagrams. I think Venn diagrams are often used in rather sloppy ways, but the great advantage of them is that they are everywhere. It's easy to find logic games (such as the logic zoo) using Venn diagrams, and it's very easy to make up new versions of logic games for Venn diagrams. Most people get some Venn diagrams in their schooling, somewhere; but most people don't get much of them. I regularly have students who don't recognize them at all. They probably had them at some point, but not enough to stick. Little bits and pieces are not good when teaching or learning logic; you really need to practice and practice.

(2) Literal diagrams. Literal diagrams, on the other hand, are almost never seen; which is unfortunate, I think, because they end up being a powerful way to teach people to identify what's relevant, break apart logical arguments, and put together premises to get conclusions. And Lewis Carroll invented them to teach logic to children. (The intent is right with the author's name: when he writes for children he uses his pen name, Lewis Carroll, rather than his real name, Charles Dodgson.) The simplest presentation of how to use such diagrams is Carroll's The Game of Logic, although it's only with the Symbolic Logic that we get the full scope of what you can do with them (although, in fact, the full range of use presented in that book is simply not necessary). Literal diagrams are logically equivalent to Venn diagrams -- anything you do with one you can in theory do with the other -- but given the way literal diagrams are spatially organized they are more convenient and practical for handling anything beyond very simple problems. With literal diagrams one learns how to identify logically important information in a proposition and to use this analysis to draw conclusions, without anything getting too abstract. And since Carroll actually taught girls logic with this, it is entirely suitable for this stage. In addition, Carroll's problem sets -- hundreds and hundreds of problems, all Lewis Carroll-style -- are brilliant, as one might expect given that logic textbooks ever since have been stealing from them.

Probably around this stage, too, we should include true-false puzzles. Louis Sachar's Sidways Arithmetic from Wayside School has a handful of excellent ones, along with a number of other kinds of logic puzzle. (This is an excellent book all around, and I actually have it still on my shelf somewhere but (1) it is really more interesting as a book if children have read the Wayside School series already -- I actually started with this book, but I was weird in every way; (2) the difficulty of the puzzles varies wildly throughout the book. There's also a sequel, but I haven't read it.) But even without such books one can get the sense of what such problems are from problem 4 here. This could be linked to the literal diagrams by way of propositional versions of literal diagrams, but there are almost no resources for doing this.

Advanced Early Logic

With advanced early logic -- which I suspect would tend to begin to be suitable for children around 12ish in most cases, although this is something that I also suspect would vary considerably -- we actual get to applying formal systems, with emphasis very much on practice rather than theory. In a sense this is how Lewis Carroll arranged his logical teaching, although his own system (taught after literal diagrams), the subscript notation, is, I think, far more complicated to apply than anyone would really want. With literal diagrams students would already have been exposed to a perfectly good formal system, but it's deliberately set up to do a lot of the actual work for you -- you mostly just have to identify the logical parts of a proposition correctly, and the rules of the 'Game of Logic' completely handle the rest. In this stage we need to start making things more explicit, and this means actual logic. There are two tracks here that are important.

(1) Syllogisms. I first came into contact with syllogisms as a teenager on finding Teach Yourself Logic in the library. (Incidentally, I'm somewhat astounded to see that it was written by A. A. Luce; at the time, of course, I would not have known Luce from Adam, but Luce was in his day a pretty significant philosopher.) I loved that book, but, again, I was weird in every way. But Martin Cothran actually has a nice book for this, Traditional Logic I (he also has a DVD and answer key that goes with it, but neither of these are actually necessary); I've made use of parts of it for online logic modules for my Intro course, and any teenager could handle everything in this book without much difficulty, especially if the pace were leisurely and it were supplemented with additional practice. In any case, something like this is what I have in mind; it's very traditional -- traditional rules of syllogism, traditional mnemonics, etc. -- but I think this approach is probably the best approach at this stage. There are lots of other resources on this, although they may require digging -- almost any older 'traditional' or 'Aristotelian' logic manual will lay things out pretty well. Lots of things won't be explained, and there will be a fair amount of memorization, but at this level we're dealing with systems that are easier to use than to give rigorous explanations for.

(2) Boolean logic. If the main thing were to prepare for a philosophy course, one would get started immediately on truth tables in propositional logic and the like. But, honestly, this component of logic at this stage should be geared more toward prepping students for computer science, which will be more useful for more people. (A more computer science approach allows one easily to transition to the preferred approaches of mathematics and philosophy, whereas starting with a philosophical approach can make it hard to transition in the mathematical direction, and the mathematical approach requires much more background if one starts with it.) Truth tables should be in there, of course, but I think as a secondary matter. Really this component should be more a matter of Boolean reasoning, broadly speaking, than formal propositional logic in the sense people are taught it in philosophy departments. And that gives us where to start: basic Boolean-style algebra, the sort of thing you do with search engines. If they've had Venn diagrams, they've basically done this already -- Venn invented the diagrams as representations of algebraic logic along the lines invented by Boole. What you would be doing is making it more explicit and more algebraic, with AND, OR, and NOT as the key operators. There are lots of resources on this, too, combining Venn diagrams with explicit use of Boolean operators.

Expanding out from this, when students are comfortable with the basics of Boolean operators in a Venn diagram setting, they can easily be moved to Karnaugh maps, which should, in any case, be taught more than they are. As with literal diagrams, anything you can do with Venn diagrams you can do with Karnaugh maps, and, as with literal diagrams, Karnaugh maps are laid out for handling much more complicated problems than Venn diagrams are. Literal diagrams were designed specifically for syllogisms and Karnaugh maps were designed specifically for Boolean logic, but anything that one can do with one, one can do with the other, and anyone who has had lots of practice with literal diagrams can handle Karnaugh maps. From Karnaugh maps you can jump off in many directions but logic gates in circuits plus basic truth tables are the obvious way to go. There are quite a few resources here, too, although a lot of them go from truth tables to Karnaugh maps, whereas my suggestion here is that it should be the reverse. There's no need to rush too far or too fast here; just getting the basics of how Karnaugh maps work with respect to truth tables and logic gates is enough.

And that's it. Just getting the basics this far actually puts you (one way or another) a couple of weeks into the content of a college-level introductory logic course, whether it's taught by the mathematics department, the computer science department, or the philosophy department. And what is more, there is nothing in any of this, even at the most advanced stage, that goes beyond what any high school student with algebra under his or her belt can manage. Some of it tends to get taught already on a small scale, like the Venn diagrams. Some of it one never finds, like literal diagrams, or usually only finds at the college level, like Karnaugh maps, but it is all manageable. The main thing would just be to have lots of practice with each approach. It's actually not very much at all, and while it all requires practice, none of it is very difficult; but it's far more than students are typically taught -- even if you had for some reason to cut out literal diagrams or Karnaugh maps entirely, it would still be more than most students learn by the end of high school.

A Parable about Reasoning

Once upon a time (note the mythical cast) there was a man who thought he was dead. His concerned wife and friends sent him to the friendly neighborhood psychiatirst. The psychiatrist determined to cure him by convincing him of one fact that contradicted his belief that he was dead. The fact the psychiatrist settled on was the simple truth that dead men do not bleed, and he put the patient to work reading medical texts, observing autopsies, etc. After weeks of effort, the patient finally said, "All right, all right! You've convinced me. Dead men do not bleed." Whereupon the psychiatrist stuck him in the arm with a needle, and the blood flowed. The man looked with a contorted, ashen face and cried, "Good Lord! Dead men bleed after all!"
[John Warwick Montgomery, "Wagering on the Death of God," The Suicide of Christian Theology, Trinity Press (Newburgh IN: 1996) p. 122.

Tuesday, February 14, 2012

The Fourteenth of February

It's the feast of Saints Cyril and Methodius, so we all celebrate it as usual by celebrating one of the St. Valentines, we don't know for sure which one. (Of course, it's the feast of St. Valentine in Extraordinary Form and the feats of Ss. Cyril and Methodius in Ordinary Form.) Notable Valentine's Day posts (I'll put up others if I find them interesting):

Kelly Wilson makes a Valentine's poem out of all the dedications to Beatrice in A Series of Unfortunate Events.

Ben Kling has a bunch of Valentine cards, including several with notable philosophers. (ht)

Maureen discusses some of the historical and legendary background to the holiday.

Night Will Catch Her Breath Up

Arab Love-Song
by Francis Thompson

The hunch├Ęd camels of the night
Trouble the bright
And silver waters of the moon.
The Maiden of the Morn will soon
Through Heaven stray and sing,
Star gathering.

Now while the dark about our loves is strewn,
Light of my dark, blood of my heart, O come!
And night will catch her breath up, and be dumb.

Leave thy father, leave thy mother
And thy brother;
Leave the black tents of thy tribe apart!
Am I not thy father and thy brother,
And thy mother?
And thou -- what needest with thy tribe's black tents
Who hast the red pavilion of my heart?

I often think that appreciation of Francis Thompson divides the philistine from the nonphilistine when it comes to poetry. Although he is not the greatest of poets, his technical mastery is considerable and broad in scope. Even his weak poems have technical excellences. Thus inability to appreciate Thompson is in a way an inability to appreciate the poetic techniques out of which poems are made in the first place.

Brief Note

I will be shutting down my email address starting today. This affects almost nobody, since I mostly just used it as a back-up and for some listserv subscriptions; but just in case anyone has it in their address books, it will no longer be functional.

Sunday, February 12, 2012

Imperial Kitchen

For we have now come to a stage of human culture in which we have compartments of knowledge but not knowledge itself; specialization but no integration; specialists but no philosophers of human wisdom. This over-specialization of knowledge is not very different from the over-specialization in a Chinese Imperial kitchen. Once during the collapse of a dynasty, a rich Chinese official was able to secure as his cook a maid who had escaped from the palace kitchen. Proud of her, he issued invitations for his friends to come and taste a dinner prepared by one he thought an Imperial cook. As the day was approaching, he asked the maid to prepare a royal dinner. The maid replied that she couldn't prepare a dinner.

"What did you do, then?" asked the official.

"Oh, I helped make the patties for the dinner," she replied.

"Well, then, go ahead and make some nice patties for my guests."

To his consternation the maid announced: "Oh, no, I can't make patties. I specialized in chopping up the onions for the stuffing of the patties of the Imperial dinner."

Some such condition obtains today in the field of human knowledge and academic scholarship.
Lin Yutang, The Importance of Living, Reynal & Hitchcock (New York: 1938) p. 414.