Thursday, April 08, 2010

Earth Transcended

Someone came here searching for the phrase "Superata tellus sidera donut", which is a typo I found to be somewhat funny. That's certainly a baked good you won't find at Krispy Kreme or Tim Horton's. I talk about the actual phrase, from the last poem of Book IV of Boethius's Consolation of Philosophy, here.

I will be off in San Antonio tomorrow and Saturday as I attend the Metaphysics and Philosophy of Religion workshop at UTSA, so there will probably be no posts until Sunday.

Philosophy and the Humanities

Jason Stanley has an article at Inside Higher Ed called, "The Crisis of Philosophy," about the estrangement between philosophy and the other humanities. There's an interesting discussion of it at "Feminist Philosophers", where I left a comment; but I decided I wanted the comment over here as well.

I’m skeptical, I suppose, of the idea that philosophy as we now know it has ever been a natural fit to the humanities. Academic philosophy of the sort with which are familiar (whether analytic or not) came out of a reaction against the development of psychology departments; the psychologists were the people who held that mind should be studied experimentally, and philosophy departments, as stand-alone departments, grew up in response in places where it was assumed that this was not a suitable way to study the human mind. (This in fact, is the explanation for an otherwise curious feature of most philosophy from the early twentieth century to the present, namely that so much of it concerns epistemology, language, and philosophy of mind. Through most of the nineteenth century it had seemed that moral philosophy was absolutely and unassailably the dominant philosophical interest; even the debates in philosophy of science between Mill and Whewell were minor side-disputes in a larger skirmish over utilitarianism.) And since colleges began developing stand-alone philosophy departments, philosophy has gone its own way, usually interacting more with mathematics and psychology than with other disciplines in the humanities; it seems to me that at least a plausible case can be made that if philosophy has become estranged from the humanities, it has estranged itself by paying relatively little attention to topics of importance in other humanities disciplines. (One can sort-of imagine an alternate-dimension academic philosophy that would fit into the humanities well — it would be an academic philosophy where aesthetics, philosophy of history, and political philosophy are clearly the primary philosophical interests in the field, where Collingwood is read more widely than Russell and early modern classes focus on theories of taste rather than disputes over dualism and on Hume’s essays rather than the Treatise or the ECHU. That would be a very different academia.)

Wednesday, April 07, 2010

Gilman on the Problem of Evil

A Common Inference
by Charlotte Perkins Gilman

A night: mysterious, tender, quiet, deep;
Heavy with flowers; full of life asleep;
Thrilling with insect voices; thick with stars;
No cloud between the dewdrops and red Mars;
The small earth whirling softly on her way,
The moonbeams and the waterfalls at play;
A million million worlds that move in peace,
A million mighty laws that never cease;
And one small ant-heap, hidden by small weeds,
Rich with eggs, slaves, and store of millet seeds.
They sleep beneath the sod
And trust in God.

A day: all glorious, royal, blazing bright;
Heavy with flowers; full of life and light;
Great fields of corn and sunshine; courteous trees;
Snow-sainted mountains; earth-embracing seas;
Wide golden deserts; slender silver streams;
Clear rainbows where the tossing fountain gleams;
And everywhere, in happiness and peace,
A million forms of life that never cease;
And one small ant-heap, crushed by passing tread,
Hath scarce enough alive to mourn the dead!
They shriek beneath the sod,
"There is no God!"

Tuesday, April 06, 2010

Proving a Negative

I've noted before that much of what passes for principles of critical thinking is actually folklore -- some of it having some real foundation, much of it not. One of my bêtes noires in this regard has been the claim, "You can't prove a negative," which I've repeatedly found in recent times, so I thought I'd consolidate some of my comments on the subject into a single post.

It's difficult to say why this particular claim has such staying power; it has been around for at least two hundred years now, despite the fact that you can quite literally find philosophers and logicians in every generation who point out that it is false. It's also difficult to determine exactly where it came from; one possibility is that it first arose in the context of the British court system. Court systems, of course, typically have conventions defining various kinds of proof requirements for the purposes of protecting the innocent and bringing the guilty to justice, and relative to particular proof requirements it is indeed true that you might not be able to prove a negative. But this is not merely true of negatives; it's necessarily true of affirmatives, as well. And this, in fact, is quite general: you can only get the claim by creating an artificial asymmetry between negative and affirmative claims.

It's easy enough to think through. Even if we ratchet up the level of proof required to rigorous demonstration, there is a straightforward way to prove a negative: show that what's being negated and something known to be true imply a contradiction. In reality, we usually don't require the standard of proof to be anywhere near so strict, since we usually allow for defeasible proofs. If you want to prove that there is no ordinary cat on the desk in front of you, look and see whether there is a cat on the desk in front of you. It's barely possible that there's an invisible cat on the desk in front of you, either because of something to do with the cat (like the one in H. G. Wells's Invisible Man) or because of something to do with your eyes. If you want to prove that there is no invisible cat in front of you, feel around and check it out. If someone suggests that there is an invisible, intangible cat on the desk in front of you, you should be able to prove that an invisible, intangible cat implies a contradiction, unless the word 'cat' is being used in an odd way. And so forth.

It is curious that we tend to assume this sort of asymmetry between affirmations and negations.It has been pointed out before that affirmations and negations are convertible -- every affirmation can be stated in an negative way and every negation can be stated in an affirmative way. If you can prove an affirmative claim, you can prove infinitely many negative claims. This, of course, is a purely formal issue; one might think that it's just an artefact of the formal system, i.e., that the formal system fails to model real affirmations and negations on this point. There's some plausibility to that, but even setting aside the formal issue there are problems with the claim that you can't prove a negative. In particular, if you treated affirmations in the way negations are treated by the cliché, it seems you couldn't prove an affirmation, either. If you aren't accepting the testimony of your senses as proof that there is no cat on the desk, why would you accept the testimony of your senses as proof that there is a cat on the desk? If you can't prove that rain isn't caused by an unobservable cause, what is the basis for thinking you can prove that rain is caused by an observable one while using the same standard of proof?

I think one reason for the long life of the cliché is that it gets confused with considerations of irrelevance. Most of the cases that people propose as instances showing the difficulty of proving a negative are actually just cases showing the difficulty of proving something irrelevant to the topic at hand. Suppose someone says that rain clouds are guided by invisible leprechauns, and this is clearly something they believe rather than just made up for some reason. Unless the existence of the invisible leprechaun is suggested by specific relevant evidence (either pertaining to the causal processes of rain, or external to but associated with them), there is no way to link it to the phenomenon as relevant one way or another. And if you can't link it to the phenomenon as relevant, you can't (short of showing 'invisible leprechaun' self-contradictory) say what would prove or disprove its involvement in that domain at all. If you can't lay down any conditions of proof for a claim, under any standard of proof short of rigorous demonstration, you can't prove or disprove the claim except by rigorous demonstration. So the problem with proving that invisible leprechauns who guide the rain don't exist is not that the claim is negative; it's that we have no clear idea of how the two are supposed to be related.

It's also likely that the cliché gains some of its plausibility due to the problem of exhaustive division. How do you know that your inductive process covered all of the possibilities? You can't, unless you can show that it divided the field of possibilities completely. Depending on what kind of possibilities you are considering, however, this can sometimes be prohibitively difficult as a practical matter, because you have to show that it is a contradiction for there to be a possibility you did not cover. This is a high standard of proof we can't usually meet. Thus, it's very difficult to prove that there is nothing you've left out -- some hidden factor that you haven't recognized yet. However, even here we can still often show (and sometimes very easily) that a given candidate cannot be this hidden factor; so we can still prove negatives, although there are negatives that are prohibitively difficult to prove at this level of proof. This is also not exclusive to negatives, however; there are affirmative statements that are prohibitively difficult to prove at this level of proof, for exactly the same reason. (The problem of division is closely related to Wilkins's suggestion that it's a problem with lack of caution with regard to universes of discourse.)

We need some good serious study of critical thinking folklore; it's an area of folklore that is very common, but it's overlooked because when people think of folklore they think of savages with feathers and not of themselves. What are the origins of principles of folk-logic like these? What keeps them in currency? There is so much about this area that we just don't fully understand. And when you don't understand what underlies these principles, it's hard to say how to make them extinct when they need to be made so.

We Know the Way

Easter Tuesday
by Christina Rossetti

“Together with my dead body shall they arise.”

Shall my dead body arise? then amen and yea
On track of a home beyond the uttermost skies
Together with my dead body shall they.
We know the way: thank God Who hath showed us the way!
Jesus Christ our Way to beautiful Paradise,
Jesus Christ the Same for ever, the Same today.
Five Virgins replenish with oil their lamps, being wise,
Five Virgins awaiting the Bridegroom watch and pray:
And if I one day spring from my grave to the prize,
Together with my dead body shall they.

Monday, April 05, 2010

Out in the Rain

Easter Monday
by Christina Rossetti

Out in the rain a world is growing green,
On half the trees quick buds are seen
Where glued-up buds have been.
Out in the rain God's Acre stretches green,
Its harvest quick tho' still unseen:
For there the Life hath been.
If Christ hath died His brethren well may die,
Sing in the gate of death, lay by
This life without a sigh:
For Christ hath died and good it is to die;
To sleep whenso He lays us by,
Then wake without a sigh.
Yea, Christ hath died, yea, Christ is risen again:
Wherefore both life and death grow plain
To us who wax and wane;
For Christ Who rose shall die no more again:
Amen: till He makes all things plain
Let us wax on and wane.

Sunday, April 04, 2010

Blackford and Is/Ought

I hope at some point to say a few words about the recent discussions in the blogosphere of Sam Harris's TED talk on morality and science, since unlike most discussions inspired in some way by Sam Harris they were actually interesting. But I have been crazy-busy recently, and I'm not sure if I'll have enough time even in the coming week. But I did notice with a bit of interest that Russell Blackford in a side comment in a post on the is/ought distinction gives a fairly straightforward example of what I at one point called the Statement interpretation of the is/ought divide:

Hume pointed out that no number of propositions that use the copula "is" can ever logically entail a proposition with the copula "ought". Yet, he says, we often see philosophers slip into "ought" conclusions without ever explaining how they did it. That's a shrewd observation, and we should not throw it out in the name of being able to study morality more easily. It imposes a discipline on us, that if we start introducing "oughts" we must explain how we did it, and it can't simply be a logical entailment from a string of "is" statements.

But, as I noted before, the Statement interpretation is not at all tenable. Blackford is right that Hume said that authors of systems of morality shift from propositions with 'is' and 'is not' copulae to propositions with 'ought' and 'ought not' copulae without explaining their shift or even recognizing that it had happened. But it is trivially easy to find propositions with the copula 'is' that logically entail propositions with the copula 'ought' (if we assume for the sake of argument that 'ought' counts as a copula); for instance, "We ought to do good" is a true proposition entails We ought to do good. Disquotation is actually not even necessary, but it shows immediately the problem with putting Hume's point in terms of logical entailment. Hume's reason for his observation was not this but that moral rationalists of his time regarded obligations as necessary relations perceived by reason alone and Hume was arguing throughout the relevant section obligation cannot be a relation and cannot be perceived by reason alone.

Thou but Yesterday a Thorn

An Easter Carol
Christina Rossetti

Spring bursts to-day,
For Christ is risen and all the earth’s at play.

Flash forth, thou Sun,
The rain is over and gone, its work is done.

Winter is past,
Sweet Spring is come at last, is come at last.

Bud, Fig and Vine,
Bud, Olive, fat with fruit and oil and wine.

Break forth this morn
In roses, thou but yesterday a Thorn.

Uplift thy head,
O pure white Lily through the Winter dead.

Beside your dams
Leap and rejoice, you merry-making Lambs.

All Herds and Flocks
Rejoice, all Beasts of thickets and of rocks.

Sing, Creatures, sing,
Angels and Men and Birds and everything.

All notes of Doves
Fill all our world: this is the time of loves.

Ability and the Too-Heavy Stone

The paradox of the stone is usually phrased as the question, "Can God create a rock so heavy He cannot lift it?" More expansively we could summarize it as the following dilemma (the particular form of which I borrow from C. Wade Savage):

(1) Either God can create a stone which He cannot lift, or He cannot create a stone which He cannot lift.
(2) If God can create a stone which He cannot lift, He is not omnipotent (because He cannot lift it).
(3) If God cannot create a stone which He cannot lift, He is not omnipotent (because He cannot create it).
(4) Therefore, God is not omnipotent.

It doesn't need to be a stone, of course. The paradox is more of a trivial curiosity than anything very profound; it relies on a notion of omnipotence as 'being able to do anything' and this is not the notion of omnipotence that was in view when traditional doctrines of omnipotence were developed, but simply one rather late offshoot, so (4) has to be suitably restricted.. And it is also often noted that the apparent force lies in the problematic assumption that among the things you must be able to do if you are able to do anything are logical impossibilities, which are not usually included in the scope of 'anything'.

What is not often recognized, though, is that even on its own terms the paradox of the stone is not actually a paradox, because there are no logical problems with answering 'Yes'. The problem is that (2), while it looks like it is similar to (3), can't be. The dilemma proposes a contrast between God's being able to cause Himself to be unable to do something, in which case we have an inability 'nested in' an ability, and God's being unable to cause Himself to be unable to do something, in which we have an 'unnested' inability. But in sophisticated positions (as opposed to mere crude simplifications) that do take omnipotence to be the ability to do anything (e.g., broadly Cartesian accounts of omnipotence), these will not function in the same way. For if we think of the ability to be able or unable (as one chooses), it always means that if you are unable to do something it is because of a logically prior ability. But these positions on omnipotence in these contexts are then essentially claims that there is an infinite series of such abilities: for any or ability inability you might name, God has the ability not to have that ability or inability, directly or indirectly, and that ability to have or lack the ability is logically prior. (And, indeed, broadly Cartesian accounts of omnipotence are sometimes explicit in one way or another about such an infinite series.) The modal operators for these abilities cannot collapse, so any claim of inability is relativized by its place in the infinite series; and thus saying that "God can create a stone He cannot lift" does not problematize the omnipotence in question because the inability is derivative: affirming means merely that God both can and cannot lift the stone, in different senses. He cannot lift it in the sense that He is exercising His ability not to be able to lift it; He could lift it simply by no longer exercising His ability not to be able to lift it.

We can find analogues in finite cases, of course. If I inject my legs with a chemical that produces indefinite paralysis, and I also have handy the antidote, can I or can't I walk to the store? 'Can' and 'Can't' depend on which abilities you have in view: the immediate ability of my legs to move or my ability with the antidote to make my legs movable. My overall abilities are branched, with a paralysis branch (in which I can't move my legs) and an antidote branch (in which I can). What the omnipotence case does is guarantee that for any 'paralysis' in the series there is an 'antidote' branch in the ability and that there can be no extrinsic impediment intervening; any 'paralysis' about the stone implies a previously available 'antidote' to the 'paralysis'. Thus the antecedent of (2) does not guarantee the consequent.

Such accounts of omnipotence are not at all the best accounts of omnipotence; but the paradox of the stone is not a particularly good reason for rejecting them. At least, it lacks the analytical sophistication to do much; you would needed a more logically advanced argument than stone paradoxes usually are to pin any actual logical problems on even the crude notion of omnipotence.

Surrexit Christus

Christus resurrexit a mortuis,
Morte mortem calcavit,
Et entibus in sepulchris
Vitam donavit.