Per Impossibile Reasoning and Counterfactuals

Previously when I've discussed the initially puzzling phenomenon of reasoning per impossibile, I've dealt with it in the following way:

When we reason per impossibile we posit some impossible thing. However, we never reason from the impossibility. The reason we posit the impossibility is that it's useful for abstracting from particular details....

In this sense we can see reasoning per impossibile as a form of idealization -- indeed, idealization taken to an extreme. We are not committing ourselves to the impossible idealization's being the way things are; rather, we are idealizing in order simply to clarify some particular point or other about the non-idealized (and therefore possible) case.

I still think this is right. If we say, "If, per impossibile, I existed by nature, I would always exist," we are not interested in what follows from the impossibility; we're interested in what follows from existing by nature. However, much more can be said about this, in particular with regard to counterfactuals in general. It's obvious, in fact, that reasoning per impossibile is reasoning that uses a certain type of counterfactual. The basic idea behind such reasoning is, "Were this impossible thing possible, such-and-such would be the case." Given this, however, we should be able to handle the puzzling nature of reasoning per impossibile directly, by recognizing a peculiar feature of certain counterfactuals.

As I've pointed out before a lot of counterfactual statements are really disguised factual statements. Brian Ellis puts this type of position very nicely in the case of causal conditionals:

The truths relating to causal conditionals are the underlying ones on which their assertability depends. That I am thirsty, for example, is a fact about me. It is also a fact that I like beer, and that there is nothing in the world that I would like better at the moment. Consequently, I would say, "If there were a beer in front of me I should drink it." It simply does not matter whether it is really possible for there to be a beer in front of me. And if this makes it vacuous, then it does not matter whether it is vacuous. By asserting the conditional, I tell you graphically what my desires are at the present time, and what you could do to satisfy them. It is better than saying "I am thirsty," because you might then offer me water, which is not what I want most. It is better than saying "I am thirsty, and I like beer," because this is compatible with my not wanting a beer at the moment.

[Brian Ellis, Scientific Essentialism. Cambridge UP (New York: 2001) 282.]

A mistake we often make is to assume that factual statements are always easier to deal with than counterfactual ones, as if they were more straightforward. But given how pervasive counterfactual thinking is, it seems plausible to say that this is not always the case. Sometimes it's easier to think through a matter counterfactually than to think it through factually, because thinking counterfactually allows you to highlight features directly that could only be highlighted factually in very complicated ways. This fits with some thoughts in cognitive research on the ways counterfactuals works; but in any case it seems a safe supposition to make until and unless we find clear evidence to the contrary.

It's clear that per impossibile counterfactuals would have to be this kind of counterfactual, because the counterfactual situation used is itself impossible. Take reasoning based on the following fictional epitaph from George MacDonald's David Elginbrod:

Here lies Martin Elginbrod.
Have mercy on my soul, Lord God,
as I would do, were I Lord God,
and you were Martin Elginbrod.

Now, however you slice the counterfactual situation -- that Martin Elginbrod and God were in each other's place -- it is impossible, particularly in the Scottish Christian context the epitaph assumes. It is not logically possible, it is not metaphysically possible, it is not physically possible, it is not epistemically possible. And yet we can make sense of it immediately, and take Martin's point without any trouble. We don't have to think through the impossible situation in order to see where Martin is going with this. The reason is that it's clearly not about a situation in which Martin and God are switched; it's about the actual situation, in which Martin is dead and needs mercy, and God can give it. If we were to try to be put "If Martin were God he'd be merciful to God, were God Martin" entirely into factual statements, we would have some difficulty because getting it right would be a bit complicated -- we'd have to go through facts about Martin's sense of mercy, how it works, etc., and we'd still fall short of the perlocutionary force of the statement, the petition for mercy. The per impossibile inference cuts through that to reach the point at once. And this, far from being unusual, is fairly typical of counterfactual reasoning generally.

Standardization

By some official oversight, which I am quite unable to explain, we are still allowed to write private letters if we put them in public pillar-boxes. The Postmaster-General does not write all our letters for us; even the local postman has as yet no such local powers. I cannot conceive how it is that reformers have failed to note the need for uniting, reorganizing, coordinating, codifying, and linking up all this complex, chaotic, and wasteful system, or lack of system. There must be vast amounts of overlapping, with some six young gentlemen writing letters to one young lady. There must be a terribly low educational standard, with all sorts of poor people allowed to put into a private letter any spelling or grammar they like. There must be a number of bad psychological habits being formed, by foolish people writing their sons in the Colonies or their mothers in the workhouse. And all this anarchy and deterioration could be stopped by the simple process of standardisation of all correspondence.

G. K. Chesterton, Government and the Rights of Man. The rest of the essay is very much worth reading.

Another Poem Draft

The Razor's Edge

I wandered, thinking well
through the sordid gates of hell
with subtle traipsing, made
to walk unknowing on a blade,
a razor's edge over chasm laid,
into which my glories fell,
as He bade.

Darkness all around me winging
was but the grace of heaven singing,
but the wedding party flinging
wine in dance, and like the sea,
wine-dark was the light in me.
And I with all my glories bringing
across a razor's edge did flee
above a dark and broiling sea
of fire; and it was me.

Meanders great and small in grace
brought me to the sacred place,
a grove of light, and there I burned
with flame inside and gravely yearned
to catch the fox that fled the chase,
which fox was me; and in that race,
I found a stream and turned
to see in the waters my own face.
What I learned
was a lesson hard and bitter-laced.

Across the razor's edge I fled,
across the shadows of the dead;
my success wandered among the shades,
a ghostly death of life that fades.
Each triumph bled
with flooding blood, flamed-iron red,
each glory a cut upon the blade,
each victory a fiction in my head.
I thought that I on lilies fed,
but I was to the darkness wed,
as He bade.

A moment before the dawn's bright flame
I caught an inkling of a name,
a hint of breath.
Each choice was made upon a wire
pending above the seething fire
that bore my face and death.
I played some old, forgotten game
with darkness and in desire
I saw my death; it was the same
in visage as my unwatched shame.
In the darkness softly stirred
a rustling like some morning bird
in leaves, a single word
like a lyre
that makes the air to sing;
exhausted, I beneath the wing
fell, protected by the Thing
that stirred but held me fast.
And in the darkness, still and fleeting,
no sound but grace and my heart beating,
light came at last.

Francis Thompson on the Kingdom of God

O world invisible, we view thee,
O world intangible, we touch thee,
O world unknowable, we know thee,
Inapprehensible, we clutch thee!

Does the fish soar to find the ocean,
The eagle plunge to find the air--
That we ask of the stars in motion
If they have rumor of thee there?

Not where the wheeling systems darken,
And our benumbed conceiving soars!--
The drift of pinions, would we hearken,
Beats at our own clay-shuttered doors.

The angels keep their ancient places--
Turn but a stone and start a wing!
'Tis ye, 'tis your estrangèd faces,
That miss the many-splendored thing.

But (when so sad thou canst not sadder)
Cry--and upon thy so sore loss
Shall shine the traffic of Jacob's ladder
Pitched betwixt Heaven and Charing Cross.

Yea, in the night, my Soul, my daughter,
Cry--clinging to Heaven by the hems;
And lo, Christ walking on the water,
Not of Genesareth, but Thames!

Ahadith and Written Traditions

Ophelia Benson has a puzzle. Reading the sentence, "Islamic tradition explicitly prohibits any depiction of Allah and the Prophet," she comments:

That doesn't make any sense. In fact it makes non-sense. How can 'tradition' 'explicitly' prohibit anything? It can't: that's why it's called tradition to distinguish it from law. Law can, obviously, explicitly prohibit things, but tradition can't, it can only implicitly prohibit them. Tradition isn't written down or codified; it's fuzzy; it's implicit; it has blurry edges. It's the very opposite of explicit.

But that's not exactly true. Tradition is just the handing down of doctrine or life-shaping principles; there's no reason to think we can't have written traditions. The most obvious example would be the Jewish Talmud, but in fact Islam has its own good example of written tradition, namely, the ahadith. A hadith is a written tradition about the Prophet (something heard by the writer from someone who heard it from someone who was there, for instance -- this chain of transmission or tradition is called the isnad). While such traditions do not have the authority of the Qur'an, given that the Qur'an enjoins respect for the prophets, they have played a major role in shaping Islamic perspectives, and much of the diversity in Islam comes from the fact that not everyone accepts the same ahadith as authentic. (In fact, which ahadith a Muslim scholar accepts as authentic will tend to have an immense influence on which school of Islamic jurisprudence he prefers, and vice versa. Ahadith are a major part of the data from which Islamic law is derived.) Through the ahadith one gets a picture of the sunnah or way of life of the Prophet. And clearly a tradition in this sense can explicitly prohibit or require; e.g., a tradition that the Prophet forbade pictorial representations of a certain kind.

And, as it happens, the BBC is repeating itself here. In a Q&A in February, we find this sentence:

Islamic tradition or Hadith, the stories of the words and actions of Muhammad and his Companions, explicitly prohibits images of Allah, Muhammad and all the major prophets of the Christian and Jewish traditions.

In fact, although I haven't looked at all the relevant ahadith, it seems to me that the ones I've seen put forward allow for a little more interpretive room than this suggests, and, of course, they are in any case not found in every collection of ahadith, nor are they accepted by everyone; but it's clear that the intention is to take 'Islamic tradition' as a sort of paraphrase-translation of ahadith. Benson is right that it's a bit misleading -- but what makes it misleading is not that tradition can't explicitly prohibit anything (which is obviously false since you can have even an oral tradition that carries forward an explicit prohibition, as with a taboo or an explicitly taught social norm), but instead that it makes hadith sound more monolithic, and less disjointed and patchwork, than it is.

Evil as a Problem in Politics

I think Arendt’s work on totalitarianism is key to showing us that evil is an important problem in everyday politics and that it has the possibility to emerge at any time and in any place. I believe that many have experienced in Iran what Arendt describes in the Origins of Totalitarianism as “the anti-political principle.” It is the end of ethics in the political realm and the unlimited degradation of civic morality. In 1979 the abyss between men of civility and men of brutal deeds was filled in Iran with the ideologization of the public sphere. One saw the breakdown of the old system, followed by the failure of political liberalism and the formation of the ideologies of 1979. One can say that when common sense breaks down or becomes impossible, hopelessness and resignation set in; people lose the capacity for action and despair over their ability to influence things.

Ramin Jahanbegloo, in an interview with Danny Postel. He goes on to say later in the interview:

Life is not easy when you have to live morally in the face of untruth. Maybe intellectuals in Iran have learned to face a life of challenges because the challenge of truth is more crucial to their existence than it is to others....I think this internal dialogue with oneself — listening to one’s inner voice, as Gandhi used to say — but also having an acute sense of the world, could be a quest not only to understand the meaning of our world, but also a ceaseless and restless activity of questioning on the nature of the evil that one has to confront in political life.

In Iran we have grown accustomed to living with political evil but to not thinking about it. I think today more than at any other time our mode of thinking and our mode of judging in Iranian society have a crucial role in determining where Iran can go from here.

Links for Thought

* "The Curt Jester" points to a MadTV clip on Jesus and the Terminator.

* Two interesting things by way of farkleberries, which is to internet linkery as Chicago is to food, namely, a great place for finding it:

Star Wars in ASCIImation

The Case Against Sufjan Stevens, which is rather too vague to be taken entirely seriously as a bit of musical criticism, but does make the legitimate point that Stevens might be better off learning from local music traditions rather than simply concept-hunting.

* This article discusses the three types of stem cell sources that the Catholic Church supports using (adult organs, miscarried or even aborted fetuses, and pregnancy matter). The only source it opposes gathering stem cells from is human embryos, when doing so involves their destruction. The position is fairly common among opponents of embryonic stem cell research. While this position would never and perhaps will never satisfy advocates of embryonic stem cell research, it's worth reminding ourselves at times that this is not an argument about the legitimacy of stem cell research but about the use of a particular type of stem cell (embryonic) gathered from a particular source (viable embryos) to the extent that the means of gathering it is destructive of that source. (H/T: The Western Confucian)

* An interesting discussion of Calvin's attitude to the Medieval potentia absoluta / potentia ordinata distinction at "Societas Christiana".

Scientific Laws and Imagination

"But the facts of Nature are to be discovered only by observation and experiment." True. But how does the man of science come to think of his experiments? Does observation reach to the non-present, the possible, the yet unconceived? Even if it showed you the experiments which ought to be made, will observation reveal to you the experiments which might be made? And who can tell of which kind is the one that carries in its bosom the secret of the law you seek? We yield you your facts. The laws we claim for the prophetic imagination. "He hath set the world in man's heart," not in his understanding. And the heart must open the door to the understanding. It is the far-seeing imagination which beholds what might be a form of things, and says to the intellect: "Try whether that may not be the form of these things;" which beholds or invents a harmonious relation of parts and operations, and sends the intellect to find out whether that be not the harmonious relation of them--that is, the law of the phenomenon it contemplates. Nay, the poetic relations themselves in the phenomenon may suggest to the imagination the law that rules its scientific life. Yea, more than this: we dare to claim for the true, childlike, humble imagination, such an inward oneness with the laws of the universe that it possesses in itself an insight into the very nature of things.

George MacDonald, The Imagination: Its Function and Its Culture

Book Meme

From verbum ipsum:

1. One book that changed your life: Bertrand Russell's A History of Western Philosophy

2. One book that you’ve read more than once: George Eliot's Romola.

3. One book you’d want on a desert island: 10 Wooden Boats You Can Build

4. One book that made you laugh: P. G. Wodehouse's Big Money

5. One book that made you cry: Where the Red Fern Grows by Wilson Rawls

6. One book that you wish had been written: Thomas Aquinas's commentary on the Timaeus (there's some reason to think that at one point he set out to revolutionize the teaching of philosophy by writing commentaries on all the works of Aristotle and all the major Platonic works; but the only Platonic commentary he actually wrote was on the Book of Causes.)

7. One book that you wish had never been written: The Protocols of the Elders of Zion

8. One book you’re currently reading: Flannery O'Connor: The Complete Short Stories

9. One book you’ve been meaning to read: Charles Dickens's The Pickwick Papers. I've been meaning to read this one since I first read Louisa May Alcott's Little Women ages ago.

10. Now tag five people: I don't tag people for memes, but if you want to take it, run with it.

Is Law a Natural Kind for Aquinas?

One of the chief reasons, I think, why natural law theory is not particularly popular in philosophy of law today is that it doesn't put much emphasis on lawyers. It doesn't, for that matter, put much emphasis on courts. This is because it is about law -- legislative functionality -- and not about what courts do with it, which is where a lot of the genuinely interesting work in philosophy of law finds itself. Of course, natural law theory doesn't preclude discussing what courts do with law -- in part, because courts can have their own sort of legislative functionality -- but it just doesn't focus much on it. It's like the old joke: fundamentally, law is not for lawyers but for reasonable people. Lawyers are just the necessary evils.

Another reason natural law theory is not popular, though, is almost certainly its metaphysical associations. So I've been reading with some interest William Brewbaker's "Thomas Aquinas and the Metaphysics of Law" (at SSRN). I'm very sympathetic to the argument, and think the overall argument (that whether or not you accept the metaphysics, it raises important questions you can't really afford to ignore) is more or less right. But I think the argument goes off the rails here and there in the details.

One of the claims Brewbaker makes that I think is clearly wrong is that Aquinas thinks that law is a natural kind. Brewbaker rightly notes that Aquinas does talk about law's essence; but it is clear, I think, that the 'essence' here is just what you can define. The mere use of the term does not imply anything about whether the essence belongs to a natural or an artificial kind, or whether it forms a natural genus or not. And there is, in fact, good reason for thinking that law is not a natural kind for Aquinas. To be a genuine natural kind, 'law' would have to be univocal across the various species of law (eternal, natural, positive). However, Aquinas is very clear that the species of law are related to each other by participation -- positive law is a participation, or 'parceling out', of natural law, natural law is a participation of eternal law. Now participation can allow for univocity only when the participating is just an instance of the participated. It's clear, however, that Aquinas doesn't think positive law is just an instance of natural law. Positive law adds determinations that are not in natural law, because it factors in questions of utility and enforceability. So positive law is related to natural law by participation, but not as a species participates its genus. This is only confirmed by the fact that Aquinas locates the unity of law in order to a common good -- again, the relation is analogical rather than univocal. Brewbaker reads this as an equivocation on Aquinas's part, but it seems to me to be more plausibly a case in which one of Brewbaker's interpretive assumptions is wrong. Thus law does not appear to be a natural kind. This is not to say there isn't anything natural about it (there are lots of things in Aquinas's metaphysics that are natural but not natural kinds -- transcendentia, for instance), but it is one thing to be natural and another thing to be a natural kind.

And attributing to Aquinas the claim that law is a natural kind leads Brewbaker to say some odd things. For instance, he asks the following questions on p. 28:

Humans, horses, trees, rocks, and their essential characteristics exist in their own right apart from human will. The same is true of eternal law and natural law. Positive law (human law, in Thomas’ terminology), on the other hand, is a human creation. Can a cultural artifact like human law be part of a natural kind? Or might it be part of law’s essence to exist apart from human will? Put another way, is human production of law consistent with human law’s status as law?

But this is only a puzzle if we assume that human law is part of a natural kind rather than (as Aquinas says it is) something devised by reason for purposes of justice and utility.

Another odd thing Brewbaker says in this connection is that "Thomas has no trouble with the idea of natural kinds because he believes God purposefully created the world." But while it's true that Thomas has no trouble with the sort of things that we call 'natural kinds', the reason for it isn't that 'he believes God purposefully created the world'. Suppose that Brewbaker is right, and Aquinas thinks of law as a natural kind. It still doesn't follow that 'God purposefully created the world' renders 'law is a natural kind' unproblematic, because law's being a natural kind would not be explained by God's purposefully creating the world. One of the kinds of law is eternal law itself, the divine reason insofar as it is ordered to practice. And this cannot be explained by creation. (The fact that one of the kinds of law is divine reason, however, is yet another reason to doubt that law forms a natural kind rather than being something that can be attributed analogously to different kinds of things.)

Now, it must be said that Brewbaker recognizes that 'law' is applied analogically rather than univocally; but he doesn't seem to see that this problematizes his claim that Aquinas attributes natural-kindship to law. Surely a condition for being a natural kind is being categorical; things that aren't categorical -- like 'good' or 'true' -- aren't natural kinds. But the sort of analogy that we find in the case of law shows very clearly that 'law' isn't categorical for Aquinas. So he isn't committed to the view that law is a natural kind.

Nussbaum on MacKinnon

MacKinnon sometimes comes quite close to saying that the modern state is a sexist relic that has had its day. Surely, however, the state is the largest unit we know of so far that is decently accountable to people's voices, and thus it is bound to be of critical importance for women seeking to make their voices heard. I think there is also a moral argument for the state: It is a unit that expresses the human choice to live together under laws of one's own choosing. Once again, it is the largest unit we yet know that expresses this fundamental human aspiration.

From Marthan Nussbaum's excellent review of Catherine MacKinnon's book (also by all accounts excellent) Are Women Human?. Highly recommended.

Linkabilia

* The SEP has a great article on the Lvov-Warsaw School of Logic, focusing on Łukasiewicz and Tarski, with a few others (including Stanisław Leśniewski, a founder of analytic mereology, although most mereology in the English-speaking world is closer to the Goodman-Leonard 'calculus of individuals').

* What's your 4400 ability? The questions aren't always the same when you go through it, so go through it more than once. I seem to waver between "Big-Hearted Healer" and "Mind-Control Master".

* Annette Ejsing has posted the introduction to her recent book, Theology of Anticipation: A Constructive Study of C. S. Peirce "Theology and Ethics from Liquidoxology".

* The program for the Hume Society meeting in Koblenz (August 7-10) is up. As is standard, members of the Hume Society can download the papers. You know what I'll be reading the next two weeks.

* At "God, Faith, and a Pen" Hesham Hassaballa reflects on stereotypes against Muslims in Getting to Know One Another.

Santiago

You can hear sung the first verse of the "Annua Gaudia," a hymn traditionally associated with today (the Feast of St. James the Greater), here.

Traditionally the day is celebrated in England by eating oysters; in France by eating scallops. Spanish Catholics celebrate by going crazy, because Santiago is their patron saint.

Take a virtual tour of Santiago de Campostela here.

Polish Notation

The new Philosophers' Carnival is up at "the boundaries of language." One of the posts is a post at LogBlog on the rules for dot notation (such as one finds in, e.g., the Principia Mathematica). A commenter (the same person who is rising great little posts here and here on the term logic of Englebretsen and Sommers; I am not inclined to say that Englebretsen, in particular, is not quite so arbitrary as the posts suggest, but part of the problem is that most of the work is scattered work-in-progress sort of stuff, and still needs clarification at times. For instance, the subscript notation is actually just a matter of convenience. It's clear from Englebretsen's summarized presentation in Bare Facts and Naked Truths, for instance, that their chief purpose is to help us keep the terms straight. They don't affect the syntax -- except to the extent that the meaning of the terms does. For instance, +C₁₂ would differ from +C₂₁ solely in that one is active voice, 1 C's 2, and the other is passive voice, 1 is C'd by 2. In that sense, they can be arbitrary, as long as you are consistent in using them; they are supposed to be due to the meaning of the term, and don't contribute anything to the form of the sentence except a way to avoid equivocation in handling things like voice.) -- A commenter, I say, in case you have forgotten the beginning of this sentence, which is easy enough to do given the massive parenthetical comment plunked down into the middle of it like a sore thumb -- A commenter, I say, suggested that it was less confusing than Polish notation. It is, of course, true that Polish notation is confusing; but it is also lovely. So I thought I'd say something about Polish notation, since I haven't at all. Since, as I insist once more, Polish notation is lovely, this is a serious omission.

Polish notation is a prefix notation for invented by the great Łukasiewicz in order to simplify propositional logic (it was expanded from there and later standardized). That is, it stacks all the operators on the prefix side. To see how this works, we need to introduce the standard operators. They are the same as you would get in any sort of propositional logic course, just in different notation:

Nx is (¬x)
Kxy is (x ∧ y)
Axy is (x ∨ y)
Cxy is (x → y)
Exy is (x ↔ y)
Dxy is (x | y), i.e., the Sheffer stroke
Mx is (◊x)
Lx is (x)
∑x is (∃x)
∏x is (∀x)

The real difference you have to see in action. For instance, take the following sentence:

(p → q) ↔ (¬q → ¬p)

In Polish notation we get rid of those ugly crutches, the parenthesis:

ECpqCNqNp

If you wanted to, of course, you could break it up:

E(C[pq] C[NqNp])

But then we've brought back those ugly parentheses. Without the parentheses, you just reason it out. E has to have two variables. Cpq has to be all together, because it's an implication; CNqNp has to go together, because it's an implication. Not only does it eliminate the need for parentheses, it allows you to see the order of operations in a clear and straightforward way. Of course, it can get confusing, because we don't teach people to pay attention to the order of operations, in part because the notation we're all taught is useful precisely in the fact that you can ignore the order of operations, because it's usually already organized according to order of operation. Let's take another:

CKAprKCpNqCrsANqs

Of course, this looks like gobbledygook at first. But that's because if we are beginners trying to read it, we want to read it forwards, when we really (as beginners) should read it backwards. So, starting from the right, we take the first chunk falling under the scope of an operator that takes more than one element (in this case, ANqs). So we have (not-q or s). Then we do the same for next (Crs) to get (r implies s). Then on to the next (CpNq) to get (p implies not-q). The next operator is K; it takes two elements, and so it takes the previous two chunks we found (KCpNqCrs). From it we get ((p implies not-q) and (r implies s)). The next chunk (Apr) gets us (p or r). The next operator, K, takes two elements again, namely, KAprKCpNqCrs; from it we get, ((p or r) and ((p implies not-q) and (r implies s))). The next operator is C; its scope is the whole thing, so we use it to put all our chunks together, and get the result (in Peano-Russell notation, and assuming I haven't made some stupid mistake somewhere):

((p ∨ r) ∧ ((p → ¬q) ∧ (r → s))) → (¬q ∨ s)

Which is not really any less confusing than the Polish original. Unless you're used to Peano-Russell notation, keeping track of all the groupings is not any simpler when they are put this way than when they are put the other way. The one and only advantage Peano-Russell notation has over Polish notation is that all the operators look clearly different.^* In Polish notation, of course, they are all letters of the alphabet, so you have to get used to how they work, and that takes more doing than in Peano-Russell. After a while you get used to things: taking the whole sentence in, you see that the first C has to be relating KAprKCpNqCrs to ANqs, and the first K has to be relating Apr to KCpNqCrs, and the second K has to be relating CpNq to Crs. But it takes a bit of practice. When I took an undergraduate logic course, I was often a bit bored, and had come across Polish notation; so I spent time translating all the Peano-Russell sentences into Polish sentences and back again. I still do it occasionally when I'm bored and have a logic text handy. But I find even now that I always have to reason the first few through before I start seeing the relations among the elements. (Also, sometimes I forget which is K and which is C, so whenever I start using Polish notation I have to begin by warning myself sternly not confuse conjunction and implication merely because conjunction starts with C, which is the operator for implication.) But it's all quite lovely and economical. And I wish, actually, that undergraduate logic courses taught it first. Logically it works just like P-R notation; but it forces beginners to think through what goes with what. And everyone who starts with Polish can easily pick up P-R, because they can easily see that it involves the same logical pattern of operators, whereas almost nobody who starts with P-R ever gets the hang of Polish, because they don't learn to see the logical pattern of operators, just the groupings. That's why people trained in Peano-Russell have difficulty reading Polish notation, despite the fact that the two are merely different notations portraying exactly the same logical operations: they aren't seeing the logical operations at all.<sup>**

*</sup> Well, strictly speaking I suppose you could also say that anyone who has taken algebra is used to organizing sentences this way; but I'm inclined to think this less important than it is usually thought. We're used to working with fractions, too; but we rarely use fractional notations, and find them confusing when we do. And so on with other mathematics-based notations.
^** And there are other advantages, too. For instance, I think truth tables and truth trees can be made much, much more perspicacious for undergrads by using Polish notation. In part this is because you can write Polish notation horizontally, vertically, or in stepwise fashion, as you deem fit. So you can use the diagrammatic arrangement most convenient for what you are doing.

The Popularization of Kabbalah

I saw wise men, men of understanding and piety, engaging in long discourse, who have written great and terrible things in their books and epistles. And once something is written it cannot be concealed any more, for often it will get lost or the author will die and the letters will pass into the hands of scoffers and idiots, and the name of God is profaned.

[Isaac the Blind to Nahmanides and Jonah Gerondi, quoted in Harvey J. Hames, The Art of Conversion: Christianity and Kabbalah in the Thirteenth Century. Brill (Boston: 2000) p. 51.]

So seriously did the great Kabbalist take this issue that he refused to write down anything about his views in a letter even to a Halakhic authority as great as Nahmanides, when Nahmanides had asked him to clarify a point. Instead, he sent one of his disciples to clarify in person. True Kabbalah, for Isaac, is not something that can be learned from books; it is passed as a living tradition from ear to ear and in no other way. He would be horrified at the popularizations of Kabbalah we have to deal with today.

However, this was as serious an issue in the thirteenth century as it is today, and perhaps more so, because the very future of Judaism was at stake. The source of trouble -- it is the source of most of the intellectual and religious troubles in the thirteenth century -- was the flood of Aristotle (and Aristotelian commentators) being injected into Christian Europe at the time. The Christians were not the only ones who had to deal with it. After all, one of the great figures who became prevalent in Europe at this time (through his written works) was Rabbi Moses himself, the great Maimonides, who had used Aristotelian philosophy to clarify theological matters. This led to the introduction of a trend in certain parts of Jewry to 'philosophization' of Jewish thought and life. These people are often called the 'Maimonidean' party, and the controversy they sparked is often called the 'Maimonidean' controversy. The label is very misleading; any comparison of Maimonides with (say) the very Aristotelian Gersonides will show very clearly that Maimonides was not so clearly in the philosophizing camp. Further, the big worry about the 'Maimonideans' was that they were replacing Jewish tradition with Greek tradition, and Nahmanides, a great and well-respected opponent of the philosophizers, recognized that Maimonides was actually an ally against the philosophizers, rather than a philosophizer himself. Nahmanides was surely right; but his was a minority view at the time, and Maimonides himself came up for considerable criticism.

A battle, even an intellectual and cultural battle, needs opposition. Who was opposing the philosophizing camp? The Kabbalists; which is not surprising, since the sort of Jewish reform they were advocating was in some ways diametrically opposed to the sort of reform advocated by the philosophizers. The battle wasn't, properly speaking, between innovators and traditionalists -- it was pretty clear on both sides that both groups were innovating, because they were both advocating reform, and with reform there necessarily comes innovation to deal with new situations. The real heart of the dispute was over which side was the genuine bearer of the living tradition. Who was carrying forward the torch of authentic Judaism? Who was the divergent branch? Which innovations developed the tradition rather than deviating from it? The Kabbalists' innovation was the use of Kabbalah not merely as an esoteric tradition among rabbis, but as a way of adding additional cohesion and richness to Jewish thought and life. The philosophizer's innovation was the use of Greek reasoning in a similar way. Both claimed, as a rule, to be presenting the truly Jewish path.

The controversy came very near to tearing Judaism apart. Nahmanides lamented at one point that instead of having one Torah, they had split it into two Torahs. While he was very definitely in the Kabbalist camp, he nonetheless firmly insisted that both groups treat each other respect (he vehmently defended Maimonides on a number of occasions, despite his many disagreements with him), and held that there was room, under Halakhah, for both of them. In part because Jews on both sides took Halakhah seriously, and in part because Nahmanides was the foremost Halakhic scholar of his times, it was Nahmanides's approach that (generally) won out; because of him, Jewish thought made room for both Kabbalah and philosophy as important contributions to Jewish life.

But in the meantime, people like Isaac the Blind, who were definitely in the Kabbalist camp, but very much of the old school, were profoundly worried at the changes afoot. Much of the infusion of Kabbalah into the broader Jewish consciousness is due to the dispute between the Kabbalists and the philosophizers. In order to attack, refute, and respond to the philosophizing camp, the Kabbalists were forced to make the esoteric doctrines of Kabbalah more and more exoteric. Hence Isaac's worry about the men of understanding writing "great and terrible things" -- things that should be reserved for oral tradition, and not committed to writing.

The paradox of Kabbalah as we know it dates from that time. For on the one hand, it has spread out and out, so that Kabbalistic ideas have become more and more common (and not just among Jews). On the other, Kabbalah is esoteric; it is discourse on mysteries, a discourse that cannot be carried on a written page, but only in the careful and wise guidance of someone who knows them at first hand. A Kabbalah that is common knowledge is not the true Kabbalah.

A Little Bit of Duhem

Chad Orzet has a great post on quantum mechanics and common sense. The position he takes is very Duhemian. That's perhaps not surprising; Duhem was a physicist himself (a thermodynamicist) who had thought long and hard about the relation between physics and common sense. Duhem's position on the subject can roughly be summarized in the following way:

(1) The practice of science, like all rational practice, is governed by common sense. This is the procedural point Orzet makes so well.

(2) Phyics is radically underdetermined by common-sense principles. Common sense is always consistent with lots of different possible physical theories because it is (generally) quite vague. But it's precisely because they're vague that common-sense principles can be obvious, right, and stable. Physical theory adds much-needed distinctness, but its precision comes at the price of being much less obvious, right, or stable.

(3) Bit by bit through the ages scientific practice adds to the depository of common sense. As scientific conclusions become more and more obviously right, however, they are assimilated to common sense. Even our common sense physics -- which is chiefly good for approximations in our general size-vicinity at practicable speeds -- is not read off of the world in any obvious way, but is the result of quite literally centuries of slow adaptation. (Arguably a reason why physics now seems so non-common-sensical, is that it has changed so quickly. Because common sense only includes things that have reached the point of clarity and obviousness to virtually all educated, rational persons, physics suddenly shot ahead of the slow pace at which common sense develops.) Common sense is in great measure a depository of science that has over the long years succeeded in becoming luminously clear, or, at least, that has succeeded in approaching such luminous clarity. What is more, on Duhem's view this is one of the twin goals of physics: the whole point of making a physical theory is (1) so it can be useful in the short term (for calculation, making new theories, etc.); and (2) so that, when your theory has in the long term begun to approach a state of perfection, it begins to be clearer and clearer how the theory relates the phenomena to the foundational principles of common sense. (This is also, according to Duhem, why we should be a bit suspicious of people claiming that a scientific conclusion is simply common sense; because more often than not, if they are right, it is because science has informed common sense rather than re-discovering something already there.)

(4) Common sense requires no justification. The principles of common sense are things that have become obvious. They are the very heart of what we call 'true and certain' -- the things that are foundationally, paradigmatically so. We aren't always right about what follows from these principles (in fact, we are often wrong), but the principles themselves are impeccable. Because of this, no skepticism can seriously defeat them. Duhem likes to quote and paraphrase Pascal on this: We have an impotence to prove that is invincible to any dogmatism and an idea of truth that is invincible to any skepticism. Common sense is the 'idea of truth' invincible to any skepticism, even though we cannot justify it in terms of anything more fundamental than itself. Common sense is what makes sense of things; a complete divorce between it and physics could never be possible, because such a divorce would mean that the 'physics' would be simply unintelligible, in every respect, to every rational person.

Some other things I've written on Duhem: Duhem's Realism; German Science; Teaching Physics by History.