Clausewitz on Hypothetical Exercises

Carl von Clausewitz, Two Letters on Strategy, page 51:

Since it is impossible to generate all essential facts in a hypothetical exercise, it is evident that the more detailed our account, the more illusory it becomes. We may make any number of tacit assumptions, and develop an analysis that in the end might not be relevant to one case in a hundred. Reasoning of this kind may still be useful to train our judgment, of course. But it is clear that such an analysis can never be satisfactorily refuted by equally arbitrary arguments. If we are contentious we won't be able to reach an agreement; if we honestly seek a solution we will eventually fall into a disagreeable state of perplexity, in which we might almost despair of the validity of any theory whatever.

Clausewitz, of course, is thinking of hypothetical exercises in military strategy (he had been asked by a friend to give his analysis of two such hypothetical scenarios); but it might be applied, mutatis mutandis, to other analytical uses of hypothetical scenarios, such as many so-called 'thought experiments' in philosophy.

Richard on Grue and Shepherd on Non-Difference

Richard discusses what is, in effect, the difference between natural and artificial classification, noting that, for instance, 'green' makes a better candidate for natural classification than 'grue'. I was reminded of a passage in Lady Mary:

All mathematical demonstration is built upon the notion; that where quantities, or diagrams, resemble each other, the relations which are true, with respect to ONE of each kind will be true with respect to all others of a like kind; ONLY because there is nothing else to make a difference among them. So, if in all past time, such secret powers could be shown necessarily connected with such sensible qualities; yet in future it could not thence be proved to continue so, unless supported by the axioms;--that LIKE Causes must EXHIBIT like Effects, and that DIFFERENCES CANNOT ARISE of themselves.

[Shepherd, An Essay Upon the Relation of Cause and Effect, pp. 77-78. All the weird emphasizing is Shepherd's own.]

Thus one can extrapolate what Shepherd would say about cases like grue, and it would be fairly similar to the argument Richard suggests:

One way to bring this out is to think about projectability, or what properties you can reason inductively from. All the emeralds I've seen so far have been green, so I expect the first emerald I see after 2020 will also be green. That seems a perfectly reasonable induction. On the other hand: "All emeralds I've seen so far have been grue, so I expect the first emerald I see after 2020 will also be grue" is clearly not good reasoning. This is because green is a more natural property than grue. It is an objectively better way to categorize reality.

Boole and Babbage

An interesting comment by Mary Everest Boole, George Boole's wife, on the relation between the ideas of Boole and of Babbage.


The Preparation of the Child for Science By Mary Everest Boole

Mary Everest Boole (1832-1916) is interesting in her own right. She assisted Boole in the editing of his works (e.g., The Laws of Thought, before their marriage). Since women were unable at the time to teach degree courses or receive degrees, she was unable to teach, as she wanted; she became a librarian for a while at Queens College, and eventually moved into the teaching of children, where, she found, she excelled. Late in life she began to publish a series of important and influential books to teach children the basics of mathematics and science; these books included a number of innovative approaches, some of which can still be found in classrooms today. (Just one example: she invented curve stitching in order to help children learn geometry.)

Links for Thinking

* A computer analysis of the Shakespeare authorship question. (ht)

* Clayton recently had a paper for a conference simultaneously rejected and accepted. Fortunately, as you might expect, it was really accepted.

* Sudy at "A Womyn's Ecdysis" has an interesting argument that feminists should favor the concept 'kyriarchy' over the concept 'patriarchy' in analysis of oppression.

* A meme for teachers went around a while ago, the 'Passion Quilt'. If you haven't browsed some of the entries for it, you should. There are metaphorical entries, literal entries, some quite clever, many quite thought-provoking.

* Mark Chu-Carroll has been doing some posts on zero-sum games:
Zero Sum Games
Simple Games, Utility Functions, and Saddle Points
Iterated Zero-Sum Games

* The Proceedings of the Old Bailey is a treasure-trove of information about crime and punishment in England, 1674-1913. (ht) They've recently added the Ordinary's Accounts, which are especially interesting.

* Turkel's book, The Programming Historian, online. This looks like a great resource for scholarly online work; I'll be perusing it. (ht: EMN, with additional resources)

* (Speaking of historians, I'm looking for good resources -- especially books, but other resources will do -- on archive theory, if anyone has any recommendations.)

* Illuminating Lives, by Beth Randall (a series of biographical sketches of "various people whose lives illuminate some aspect of the religious quest")

* The Gifford Lectures Online. I've linked to it before, but it was still in a pretty primitive state at the time. It has come along nicely. Almost 120 years of arguably the most prestigious philosophical lectureship in the world, much of which is online, searchable, and almost all of which is well worth browsing.

UPDATES:

* Stern & Jones, The Coherence of Natural Inalienable Rights (PDF)

Three New Poem Drafts and a Re-Draft

The last word of the last line of the third, by the way, is deliberate: to tale, i.e., to tally. The Gubbio reference is to the wolf in the famous legend about Francis of Assisi.

Thorn in the Side

Lest I take the lesser road,
spur me in my side;
lest I arrogate myself,
puncture all my pride;
let no willow rod be spared
to spoil this wayward child,
yea, though it be a bitter pill
to drive a man half-wild,
lest I wander, ever lost
in lands of lie and fear,
or trap myself in mirror-glass,
that maze of death and tears!

Devilish

How devilish the devil is,
how filled with devil's wiles!
Let out the trump of virtue,
the devil only smiles.
Each hand manipulates the world,
each word is laced with guile:
How devilish the devil is,
how filled with devil's wiles!

Extension

The wideness of God's mercy, like the all-extending sky,
sublimely outextends any mercy in my eye,
overrules this little world like heaven's endless vault,
and beyond each mountain's snow-crown looms and overexalts.
And the boundless blue above, by sweeping light reminds
that I am not the one who judges all, and rules, and binds;
that from Heaven I cannot bar whatsoever folk I please;
that, yea, the slimy worm, and such slithering snakes as these
may play in God's own land with peace and even grace;
that that murderer, the lion, may with the lamb share place;
that the wolf that once mauled calf may, like Gubbio's distress,
snuggle there with calves and by those calves be blessed;
that though it be by fire, with smoke upon their tails,
saved may be the wicked, by a grace no man can tale.

The Narcissist

So fair is his existence,
no eye resists;
a third of heaven would turn traitor
and give up bliss
for but the lying promise
of his kiss.

The Devil is a lovely creature --
and he knows it.
All creation and his smile
show it.

His beauty is so great,
his style so nice;
his smile sparkles so,
like starlit ice,
that God might die to make him --
if that's the price.

Yes, the Devil is a lovely creature --
too bad he knows it,
and would to God he had the grace
not to show it.

Disjunctive Syllogism and Material Conditionals

I have always been puzzled by the fact that philosophers working with paraconsistent logic have always had a thing against disjunctive syllogism. Since someone dealing with paraconsistent logic wants a logic that does not allow contradiction explosion (if a contradiction is true, everything is true), the ostensible reason is that DS requires explosion:

(1) p & ~ p
(2) p
(3) p v q
(4) ~p
(5) q

(2) and (4) come from (1) by conjunction elimination; (3) from (2) by the disjunction rule called addition (also commonly called disjunction introduction); and (5) from (3) & (4) by DS. But this is not an adequate reason; you can also block the argument by rejecting addition, and there's a fairly obvious reason for it. Contradiction explosion occurs because any arbitrary proposition can be introduced; but DS does not introduce any propositions. Addition, however, does. Addition, in fact, is already explosive, in a mild sense: given addition, any proposition can be introduced into any argument. And we find that outside philosophy (e.g., computer science) it seems fairly common to explore paraconsistency by rejecting addition. So is there any other reason for picking on DS?

Graham Priest (An Introduction to Non-Classical Logic 1.10.4-5) gives the following sort of argument. The following principle seems reasonably plausible:

(*) 'If A then B' is true if there is some true statement C such that from C and A together we can deduce B.

But we can reason in the following way:

[Mat]
Assumed:
(1) ~A v B
Assumed:
(2) A
By Disjunctive Syllogism, from (1) and (2):
(3) B

Then by (*) we get 'If A then B'.

OK, so why is that supposed to be an issue? The above argument is apparently supposed to be an argument that 'If A then B' is a material conditional. But this is a problematic conclusion; and DS is certainly responsible if anything is.

I find the argument intriguing; I'm no fan of the material conditional interpretation, so I would consider an argument that DS requires that interpretation to be a strike against it. But this argument doesn't show that 'If A then B' is a material conditional; it simply shows that whenever you can assume both A and (~A v B) you can conclude 'If A then B' (if you assume DS). But this is not particularly interesting, because it is not distinctive to the material conditional interpretation. If the material conditional interpretation is true, you can conclude 'If A then B' from (~A v B), without having to combine (~A v B) with A; and the argument doesn't show that you can do this. All it does is show that on the material conditional interpretation DS and modus ponens are redundant: you can do with DS anything you can do with MP.

We can see the problem more clearly when we realize that there are other statements that can be plugged into (*)'s C. Consider this one:

Assumed:
(1) Necessarily (If A then B)
Assumed:
(2) A
From 1, by T axiom (i.e., in modal system M):
(3) If A then B
From (2) and (3):
(4) B

And by (*) we can conclude 'If A then B'. So by parallel reasoning, 'If A then B' must be the modal 'Necessarily (If A then B)'; and, being modal, this is definitely not a material conditional. But you can run the first argument in modal system M, too. So if the above argument were acceptable, it would imply that for M 'If A then B' is both a material conditional and not a material conditional; and this is a problem for the material conditional interpretation. This confirms the point above about the gist of the original argument.

So I'd say there's nothing problematic about [Mat], even for one who rejects the material conditional interpretation. This was so obvious to me on reading it that I really wonder if I'm missing something subtle and clever.

Petition, re UF's Philosophy Ph.D. Cut

Apparently the University of Florida is cutting its Ph.D. in Philosophy. It has had some discussion in the blogosphere. Honestly, I think it's a good thing; the philosophy market can't handle the Ph.D.'s being produced as things are. (For similar reasons, I think the recent increase in philosophy majors is bad for the profession, not because it's bad to have more philosophy majors, but because we are kidding ourselves or lying to our students if we are suggesting that things are set up so that they are likely to gain anything more from the philosophy major, relative to other degrees, than the personal philosophical growth they might get from it if their program is well taught. If the increase consisted of all double majors, that would be different.) Better that it be simply cut at a university that is being forced into massive budget cuts than to limp and decline as crunch after crunch comes along under an administration that isn't going to make it a priority. But I seem to be very much in the minority on these issues (unsurprisingly). For thoughtful contrary arguments see Leiter Reports, Praeter Necessitatum, and the Florida Student Philosophy Blog. There is an online petition, put together by Sabrina Jamil, to protest; I won't be signing it, of course, but if you feel strongly about the issue, it is something to consider. (If you do sign the petition, be sure to follow Leiter's advice and put some indicator of who you are, e.g., "assistant professor in philosophy at Ivory Tower University," "graduate student in philosophy at Hudson College," or whatever, so that there's more than just the name.)

UPDATE: Sabrina Jamil left a comment that I'll put here, so it doesn't get eaten by Haloscan down the road.

A dissenting opinion is always valuable, and I think you make some excellent points, but it seems that the problem you target (issues with the job market) are the result of a larger attitude that treats philosophy as unimportant. At institutions where philosophy is valued, in fact, the potential for jobs is ample, but budgetary constraints prevent them from becoming actual jobs. For instance, at Miami Dade College (where I currently work), there are very few full-time lines in philosophy -- one to two per campus, over eight campuses -- but the college overall easily offers 3 or 4 times the number of courses that can be taught by full-time faculty. The remainder courses are taught by adjuncts. If the budget allowed for it, presumably the College would open up more full-time positions, and hire more Ph.D. faculty, rather than M.A. faculty such as myself. The issue here is no different than it is for any other discipline within the "humanities" umbrella -- the discipline itself is undervalued by institutions of higher learning, so the budget for those disciplines is constrained. A better approach to the problem of job flow is to encourage growth in the discipline that will push institutions to open more full-time positions. (This is effectively how the position I hold now was created.)

Nussbaum on Shakespeare and Philosophy

Martha Nussbaum has a fascinating review of a number of works on Shakespeare and philosophy (ht):

Philosophers often try to write about Shakespeare. Most of the time they are ill-equipped to do so. There is something irresistibly tempting in the depth and the complexity of the plays, and it lures people who respond to that complexity with abstract thought, even if for the most part they are utterly unprepared, emotionally or stylistically, to write about literary experience. Such philosophers see profound thought in Shakespeare, not wrongly. But armed with their standard analytic equipment, they frequently produce accounts that are laughably reductive, contributing little or nothing to philosophy or to the understanding of Shakespeare.

To make any contribution worth caring about, a philosopher's study of Shakespeare should do three things. First and most centrally, it should really do philosophy, and not just allude to familiar philosophical ideas and positions. It should pursue tough questions and come up with something interesting and subtle--rather than just connecting Shakespeare to this or that idea from Philosophy 101. A philosopher reading Shakespeare should wonder, and ponder, in a genuinely philosophical way. Second, it should illuminate the world of the plays, attending closely enough to language and to texture that the interpretation changes the way we see the work, rather than just uses the work as grist for some argumentative mill. And finally, such a study should offer some account of why philosophical thinking needs to turn to Shakespeare's plays, or to works like them. Why must the philosopher care about these plays? Do they supply to thought something that a straightforward piece of philosophical prose cannot supply, and if so, what?

The review is Nussbaum at her best; well worth reading.

Masculine Sensibility

While the traditional masculine ideals of 'independence, moderation, courage and self-command' remained central, from the late seventeenth century, increasing emphasis was placed on civility, as the ideal of 'the polite man of the eighteenth century replaced the martial hero of earlier periods'. And with the emergence of the 'culture of sensibility' in the middle of the eighteenth century, sensibility came to be viewed as both a touchstone of true civility and gentlemanliness and a corrective to artificial politeness and over-refinement. Nor was there any inherent contradiction between sensibility and manliness, as Adam Smith maintained: 'Our sensibility to the feelings of others, so far from being inconsistent with the manhood of self-command, is the very principle upon which that manhood is founded', as 'the man who feels the most for the joys and sorrows of others, is best fitted for acquiring the most complete control of his own joys and sorrows'.

Andrea McKenzie, Tyburn's Martyrs. Continuum (New York: 2007) p. 213. Quite a good book, by the way.

A Rough Jotting on Ecumenical Theology

One of the difficulties in talking across ecclesial and denominational lines is that the same words often don't mean quite the same things. For instance, when a Baptist talks about 'women's ordination', he means the notion that women may be called or consecrated to pastoral ministry and preaching, and that this call or consecration may be recognized as part of the worship of the congregation. This is not at all what a Catholic would mean when talking about women's ordination. Indeed, for a Catholic 'women's ordination' in a Baptist sense has long been a settled issue: in the Catholic tradition women can be called to pastoral ministry and preaching, and their ministry and preaching can be recognized as part of the worship of the congregation. There is a long history of this, in fact; the most obvious examples are abbesses. One finds that even among Catholics who are very conservative on the question the issue is clear enough; for instance, very traditionalist Catholics will deny that an abbess can preach but when pressed will affirm that an abbess can exhort. There are not-wholly-unreasonable reasons for this -- the point is to make very clear that the abbess has no sacramental function, and so where a word, like 'preaching', is often associated with the sacramental function of bishops, traditionalists tend not to use it outside of that sacramental function. But sacramental function aside, there is no functional difference between the pastoral role at least some abbesses can legitimately yield and that of any other pastor of the Church; and insofar as preaching involves, e.g., giving pastoral exhortation in public, abbesses can be said to have some authority to preach (e.g., in chapter). So any controversy over women's ordination among Baptists has no real parallel among Catholics; at most there there is room to dispute how far an abbess's authority as spiritual mother can extend, in matters like preaching and correction, before it invades the sacramental precincts reserved to prelates. When Catholics talk about 'women's ordination', they are not talking about whether women can be called to pastoral ministry, understood as the sort of functions exercised by a Baptist minister (which, consistent with the actual practice of the Catholic Church through the ages can only be given an affirmative answer; and, indeed, there is no doubt that an abbess in Catholic tradition is understood to have much greater spiritual authority over her 'congregation' than a Baptist pastor over his), but whether they can be called to the sacramental ministry associated with the sacrament of holy orders (which is answered firmly in the negative). And it is noteworthy that no less an authority than Thomas Aquinas holds that this latter is the one and only form of authority a Catholic woman cannot exercise: every other form of temporal and spiritual authority (even, he says, spiritual authority greater than that of a bishop, where God has intervened with a special gift) is open to her if God calls her to it; and even this one is only denied her to signify a divine point until glory, which transcends every such gift of grace we may receive in this lifetime. Thus a Baptist and a Catholic talking this matter over have to be careful to understand what the other person really means.

Similar impediments to straightforward discussion are everywhere. A Catholic, for instance, must think that the Zwinglian is wrong about the Catholic Eucharist; but since the Catholic doesn't think the Zwinglian Lord's Supper is sacramental, the Catholic can't immediately rule out the possibility that the Zwinglian is right with regard to that. Indeed, the question with which the Catholic is faced is whether the Zwinglian is right or is (so to speak) selling himself short. Thus in every case of discussion across ecclesial or denominational lines, care should be taken to know how the person across that line is using the term, and good judgment should be used in comparing it to usage on this side of the line.

Augusta Ada, Countess Lovelace, on Mathematical Machines

Those who view mathematical science, not merely as a vast body of abstract and immutable truths, whose intrinsic beauty, symmetry and logical completeness, when regarded in their connexion together as a whole, entitle them to a prominent place in the interest of all profound and logical minds, but as possessing a yet deeper interest for the human race, when it is remembered that this science constitutes the language through which alone we can adequately express the great facts of the natural world, and those unceasing changes of mutual relationship which, visibly or invisibly, consciously or unconsciously to our immediate physical perceptions, are interminably going on in the agencies of the creation we live amidst: those who thus think on mathematical truth as the instrument through which the weak mind of man can most effectually read his Creator's works, will regard with especial interest all that can tend to facilitate the translation of its principles into explicit practical forms.

This is from one of the great early classics of computer science, Ada Lovelace's translation of Menabrea's 1842 "Sketch of the Analytical Engine Invented by Charles Babbage," complete with her notes, in which she brilliantly lays out a vision of a mathematical science of operations, thus earning herself a place in history as the founder of computer programming. Babbage and others had programmed machines before, of course, including early models and parts of Babbage's engines, but Lovelace was the first to recognize that such programming was more than just adjustment of a machine to get results, that it was a mathematical approach in its own right.

UPDATE

Here's the passage from Babbage's Passages from the Life of a Philosopher in which he notes Lady Lovelace's work:


Passages from the Life of a Philosopher By Charles Babbage