Malebranche on the Science of Man

The most beautiful, the most pleasant, and the most necessary of all our knowledge is, undoubtedly, the knowledge of ourselves. Of all the human sciences, the science of man is the most worthy. Yet this science is neither the most cultivated nor the most complete that we possess; ordinary men neglect it altogether. Even among those who take pride in science, there are very few who apply themselves to this science, and there are still fewer who apply themselves to it with any success.

Nicolas Malebranche, The Search after Truth, Lennon & Olscamp, trs. (Cambridge: 1997) xxxix. 'Science' here is used more broadly than we tend to use it.

Links for Thinking

* Chris has an excellent post on the conceptual metaphor theory of our temporal attributions (the view that we conceive of time metaphorically by mapping it onto space).

* Ben Witherington provides an excerpt (about the Epistle of James) from his forthcoming commentary on Hebrews, James, and Jude. (As a complete aside, surely it's a bit unusual to link Jude with Hebrew and James rather than the Petrine epistles? I wonder what the reasoning behind it was.)

* If you ever happen to be on any of the worlds in the Empire, check to see if the Gideons are leaving the Klingon-language paraphrase or translation in hotel rooms. (The latter is being done by the same people who are working hard to restore the complete works of Shakesepeare to the 'original Klingon'.) The weblog mu''a'vo'mu' has regular reflections on the Klingon language version of the Bible. You never know when these things will come in handy.

* Clark has an interesting post on Heidegger and the Hebrews.

* The 127th Christian Carnival is the Voltron Edition.

* Everyone who can should contribute something to the DonorsChoose.org drive at Science Blogs, even if it's only $10. The drive is to provide students, especially underprivileged ones, with adequate science materials for school. Since I have a soft spot for third and fourth graders (in undergrad I tutored third & fourth grade math), and Janet Stemwedel's Adventures in Ethics and Science has quite a few challenges for these grades, I recommend this, this, this, this, or this from her challenge. The first link goes to a challenge already 26% complete, so only a few more donations would be enough to complete it. The second-to-last link goes to a challenge that is 35% complete, to provide science materials for 4th-graders in Katrina-devastated St. Bernard Parish (all their science textbooks were ruined in the flooding). Even if you don't have the means to donate, or if you can't (it only accepts U.S. donations, unfortunately), you can still pass the word. The drive ends July 1st.

* Wilson has an excellent post called Language, empire, and hope. Well worth reading!

* You can read Hippolyte Delehaye's classic 1907 work on the principles of historio-hagiography, The Legends of the Saints at Medieval Sourcebook.

* More on the Christian tradition of God as Mother. (HT: verbum ipsum)

Hume on Thomas More

In the Catholic liturgical calendar, the feast of Thomas More (and John Fisher) is tomorrow, but I'll be out of town, so I'm posting this today. I thought it would be interesting to look at Thomas More through the eyes of someone who admires him even despite a stern disapproval of his Catholicism, namely, David Hume. From his History of England:

After the prorogation, Sir Thomas More, the chancellor, foreseeing that all the measures of the king and parliament led to a breach with the church of Rome, and to an alteration of religion, with which his principles would not permit him to concur, desired leave to resign the great seal; and he descended from his high station with more joy and alacrity than he had mounted up to it. The austerity of this man’s virtue, and the sanctity of his manners, had no wise encroached on the gentleness of his temper, or even diminished that frolic and gaiety, to which he was naturally inclined. He sported with all the varieties of fortune into which he was thrown; and neither the pride, naturally attending a high station, nor the melancholy incident to poverty and retreat, could ever lay hold of his serene and equal spirit. While his family discovered symptoms of sorrow on laying down the grandeur and magnificence, to which they had been accustomed, he drew a subject of mirth from their distresses; and made them ashamed of losing even a moment’s chearfulness, on account of such trivial misfortunes. The king, who had entertained a high opinion of his virtue, received his resignation with some difficulty; and he delivered the great seal soon after to Sir Thomas Audley....

The oath regarding the succession was generally taken throughout the kingdom. Fisher, bishop of Rochester, and Sir Thomas More, were the only persons of note, that entertained scruples with regard to its legality. Fisher was obnoxious on account of some practices, into which his credulity, rather than any bad intentions, seems to have betrayed him. But More was the person of greatest reputation in the kingdom for virtue and integrity; and as it was believed, that his authority would have influence on the sentiments of others, great pains were taken to convince him of the lawfulness of the oath. He declared, that he had no scruple with regard to the succession, and thought that the parliament had full power to settle it: He offered to draw an oath himself, which would ensure his allegiance to the heir appointed; but he refused the oath prescribed by law; because the preamble of that oath asserted the legality of the king’s marriage with Anne, and thereby implied, that his former marriage with Catherine was unlawful and invalid. Cranmer, the primate, and Cromwel, now secretary of state, who highly loved and esteemed More, entreated him to lay aside his scruples; and their friendly importunity seemed to weigh more with him, than all the penalties attending his refusal. He persisted, however, in a mild, though firm manner, to maintain his resolution; and the king, irritated against him as well as Fisher, ordered both to be indicted upon the statute, and committed prisoners to the Tower....

John Fisher, bishop of Rochester, was a prelate, eminent for learning and morals, still more than for his ecclesiastical dignities, and for the high favour, which he had long enjoyed with the king. When he was thrown into prison, on account of his refusing the oath which regarded the succession, and his concealment of Elizabeth Barton’s treasonable speeches, he had not only been deprived of all his revenues, but stripped of his very cloaths, and, without consideration of his extreme age, he was allowed nothing but rags, which scarcely sufficed to cover his nakedness. In this condition, he lay in prison above a twelvemonth; when the pope, willing to recompense the sufferings of so faithful an adherent, created him a cardinal; though Fisher was so indifferent about that dignity, that, even if the purple were lying at his feet, he declared that he would not stoop to take it. This promotion of a man, merely for his opposition to royal authority, rouzed the indignation of the king; and he resolved to make the innocent person feel the effects of his resentment. Of Sir Thomas More. Fisher was indicted for denying the king’s supremacy, was tried, condemned, and beheaded.

The execution of this prelate was intended as a warning to More, whose compliance, on account of his great authority both abroad and at home, and his high reputation for learning and virtue, was anxiously desired by the king. That prince also bore as great personal affection and regard to More, as his imperious mind, the sport of passions, was susceptible of towards a man, who in any particular opposed his violent inclinations. But More could never be prevailed on to acknowledge any opinion so contrary to his principles as that of the king’s supremacy; and though Henry exacted that compliance from the whole nation, there was, as yet, no law obliging any one to take an oath to that purpose. Rich, the solicitor general, was sent to confer with More, then a prisoner, who kept a cautious silence with regard to the supremacy: He was only inveigled to say, that any question with regard to the law, which established that prerogative, was a two-edged sword: If a person answer one way, it will confound his soul; if another, it will destroy his body. No more was wanted to sound an indictment of high treason against the prisoner. His silence was called malicious, and made a part of his crime; and these words, which had casually dropped from him, were interpreted as a denial of the supremacy.y Trials were mere formalities during this reign: The jury gave sentence against More, who had long expected this fate, and who needed no preparation to fortify him against the terrors of death. Not only his constancy, but even his cheerfulness, nay, his usual facetiousness, never forsook him; and he made a sacrifice of his life to his integrity with the same indifference that he maintained in any ordinary occurrence. When he was mounting the scaffold, he said to one, "Friend, help me up, and when I come down again, let me shift for myself." The executioner asking him forgiveness, he granted the request, but told him, "You will never get credit by beheading me, my neck is so short." Then laying his head on the block, he bade the executioner stay till he put aside his beard: "For," said he, "it never committed treason." Nothing was wanting to the glory of this end, except a better cause, more free from weakness and superstition. But as the man followed his principles and sense of duty, however misguided, his constancy and integrity are not the less objects of our admiration. He was beheaded in the fifty-third year of his age.

That's a bit long, but I think it's interesting enough to warrant it. Jennifer Herdt, in her wonderful Religion and Faction in Hume's Moral Philosophy, notes that this appraisal of Thomas More is something of an anomaly for Hume's view on the psychology of religion. Generally speaking, Hume holds that (monotheistic, and particularly institutional monotheistic) religion induces an 'artificial life' -- an unnatural way of living -- that is characterized by gloom, hypocrisy, and irrationality. These make sympathetic understanding impossible; they interfere with an outsider's ability to put themselves in the religionist's shoes. The only understanding available is to identify causes external to the religious viewpoint (supposedly) affirmed: secret motives, passions, political factions. The religious viewpoint in itself is incomprehensible. None of these apply to More, however. As Herdt notes:

The virtues of constancy and integrity are hardly those which Hume should in theory discover in a theist, even the most sincere. So Hume in this instance seems to give the lie to his own assumptions about the nature of theistic belief and therefore to the limits of sympathetic understanding of a theist by a non-theist.

[Jennifer Herdt, Religion and Faction in Hume's Moral Philosophy. Cambridged (1997) p. 214]

So Hume's account of religion has no place for people like More. Of course, as Herdt goes on to note, Hume's account of religion, insofar as it is directed at anybody, is directed at the very narrow Scottish Calvinism that Hume knew growing up; and seen in this light a lot can still be said for Hume's account. The anomaly of More isn't a counterexample for the account, strictly speaking; it just marks a way in which it is limited.

Duhem on Teaching Physics by History

Despite the familiarity of most philosophers today with Duhem's name, many of his actual arguments are rather neglected. One of the more interesting of these is his argument that the proper method for teaching physics is historical:

To give the history of a physical principle is at the same time to make a logical analysis of it. The criticism of the intellectual processes that physics puts into play is related indissolubly to the exposition of the gradual evolution by which deduction perfects a theory and makes of it a more precise and better-ordered representation of laws revealed by observation.

Besides, the history of science alone can keep the physicist from the mad ambitions of dogmatism as well as the despair of Pyrrhonian skepticism.

This passage summarizes the three basic functions of teaching physics by teaching the history of physics.

(1) Analysis. The sort of history Duhem has in mind is a somewhat idealized one. When teaching physics according to the historical method, you are using history to get the point of the physics across, not doing history for history's sake. So it's OK to abstract a bit from anything that might interfere with or distract from understanding the physics. What you are looking for is the general interplay between theory and experiment that gives the theory its content.

(2) Moderation of Ambition. The history of science is a history of error: brilliant people using ingenious methods to come to wrong conclusions. By giving students of physics an idea of this history of dead-ends, confusions, hesitations, wrong assumptions, etc., you help to give them the sense that it's not enough to do the experiments and come up with the theories the way we usually imagine scientists do; you also must be self-critical and willing to be wrong many times before you get something workable -- and when you get something workable, you must be willing to recognize that it, too, could be superceded. Since Duhem is a positivist, he also thinks it helps to underscore the fact that physics represents provisionally rather than explains definitively; for instance, on this view, Newton's theory doesn't explain anything, but it represents a certain range of phenomena so astoundingly well that it can still be used after everyone has learned its flaws and limitations. And by learning physics historically, Duhem thinks you're more likely to recognize that newer theories will be fortunate if they do even half so well. When the physicist is tempted to put too much weight on his own pet theories, the history of physics can remind him that such dogmatism contributes nothing of value to physics. Against presumption, the history of physics teaches humility.

(3) Encouragement. But if the history of science is a history of error, it is also a history of progress, and the progress sometimes comes about through even serious errors. Each era in physics draws strength from the earlier eras and is pregnant with the eras to come. When you teach physics historically, you don't merely teach that physical theory is representation; you teach that it is a representation that approaches "natural classification and an increasingly clearer reflection of realities which experimental method cannot contemplate directly." When the physicist is tempted to despair of the possibility of progress, the history of physics can remind her that physics has come through worse with astounding feats of progress. Against despair, the history of physics teaches hope.

Such is Duhem's argument, anyway. It represents a sort of philosophy of science that I wish were more common, namely, the kind that thinks seriously and carefully about ways to improve scientific pedagogy.
***
All quotes are from Pierre Duhem, The Aim and Structure of Physical Theory. Philip Wiener, tr. Atheneum (New York: 1962) 269-270.

The Womb of the Father and the Son our Mother

You may have read recently about the possibility that the Presbyterian General Assembly may allow the language 'Mother, Child, Womb' (among others) for the Trinity in church services. The general reaction to this particular combination has usually been incredulous, since it isn't clear what it means. However, my reaction is a bit of puzzlement at it, since it apparently ignores the Trinitarian tradition its proponents want it to be a part of.

Contrary to what one might think, the term 'womb' is actually already a technical term in Trinitarian theology. A fairly standard usage is in the Symbol of Faith of the Eleventh Council of Toledo (675):

We must believe that the Son is begotten or born not from nothing or from any other substance, but from the womb of the Father, that is from His substance. Therefore the Father is eternal, and the Son is also eternal. If He was always Father, He always had a Son, whose Father He was, and therefore we confess that the Son was born from the Father without beginning. We do not call the same Son of God a part of a divided nature, because He was generated from the Father, but we assert that the perfect Father has begotten the perfect Son, without diminution or division, for it pertains to the Godhead alone not to have an unequal Son. This Son of God is also Son by nature, not by adoption; of Him we must also believe that God the Father begot Him neither by an act of will nor out of necessity, for in God there is no necessity nor does will precede wisdom.

De Patris utero, id est, de substantia ejus. We find a similar usage in a sermon on Mary (fourth century, I think) misattributed to Chrysostom:

You have found a Spouse who will protect your virginity instead of corrupting it; you have found a Spouse who wants to become your Son because of His great love for men. The Lord is with you! He who is everywhere is in you; He is with you, and He comes from you, the Lord in heaven, the Most High in the abyss, the Creator of all, Creator above the cherubim, Charioteer above the seraphim, Son in the womb of the Father, Only-begotten in your womb, the Lord--He knows how--entirely everywhere and entirely in you. Blessed are you among women!

There is a connection to the Vulgate translation of Ps. 110:3, which is, roughly, 'From the womb, before the daystar, I have begotten you'. Compare Augustine:

But this is put off, this will be granted afterwards: what is there now? "From the womb I have begotten Thee, before the morning star." What is here? If God hath a Son, hath He also a womb? Like fleshly bodies, He hath not; for He hath not a bosom either; yet it is said, "He who is in the bosom of the Father, hath declared Him." But that which is the womb, is the bosom also: both bosom and womb are put for a secret place. What meaneth, "from the womb"? From what is secret, from what is hidden; from Myself, from My substance; this is the meaning of "from the womb;" for, "Who shall declare His generation?"

I have seen, once or twice, an argument that the Spirit could be considered 'the womb of the Father', but this just messes things up; the Son is not born from the Spirit, and the Spirit is not the divine substance. So it seems no-go, at least without the sorts of explanation you can't stop a church service to give.

It's similar with the name 'Mother'. Julian of Norwich applies the label to the Trinity, in a completely orthodox way; but she's thought it through enough to recognize which person of the Trinity is most fittingly called 'Mother'. Just a few such passages:

The Second, most precious, Person, who is our substantial mother has now become our sensual mother, for we are double by God's making, that is to say, substantial and sensual. Our substance is the higher part that we have in our father, God Almighty.

The Second Person of the Trinity is our mother in nature, in our substantial making. In him we are grounded and rooted, and he is our mother by mercy in our sensuality, by taking flesh.

Thus our mother, Christ, in whom our parts are kept unseparated, works in us in various ways. For in our mother, Christ, we profit and increase, and in mercy he reforms and restores us, and by virtue of his passion, death, and resurrection joins us to our substance. This is how our mother, Christ, works in mercy in all his beloved children who are submissive and obedient to him.

And identifying the Second Person as Mother is far easier than identifying the First Person as Mother, because the Second Person bears distinctive mother-like characteristics toward us (e.g., by his pains upon the cross we are birthed into new life), whereas the Father does not. This is not intra-Trinitarian language, as the Father-Son-Spirit language is supposed to be; but it is orthodox, thought out well, and easily incorporated into liturgy in a way that Mother-Child-Womb language is not. (As most people are saying in response to it, What in the world does that mean?) Whereas Julian's route is only obscure when you jumble it all up with other language without explanation (as I do in the title to this post).

Some Passages in Butler on Self-Deception

I missed observing the anniversary of Butler's death on June 16, so I want to do something now. One of the topics which Butler discusses with great ingenuity is self-deception. So here are a few passages from him on the subject.

The Sermon before the House of Lords on the Occasion of the Martyrdom of King Charles I:

Here is a general supposition, that what is wrong cannot be avowed in its proper colours, but stands in need of some cloke to be thrown over it. God has constituted our nature, and the nature of society, after such a manner, that generally speaking, men cannot encourage or support themselves in wickedness upon the foot of there being no difference between right and wrong, or by a direct avowal of wrong; but by disguising it, and endeavouring to spread over it some colours of right. And they do this in every capacity and every respect, in which there is a right or a wrong. They do it, not only as social creatures under civil government, but also as moral agents under the government of God; in one case to make a proper figure in the world, and delude their fellow-creatures; in the other to keep peace within themselves, and delude their own consciences. And the delusion in both cases being voluntary, is, in Scripture, called by one name, and spoken against in the same manner: though doubtless they are much more explicit with themselves, and more distinctly conscious of what they are about, in one case than in the other....

These false professions of virtue, which men have, in all ages, found it necessary to make their appearance with abroad, must have been originally taken up in order to deceive in the proper sense: then they became habitual, and yet often still, to civility is often intended merely by way of form serve their original purpose of deceiving.

There is doubtless amongst mankind a great deal of this hypocrisy towards each other: but not so much as may sometimes be supposed. For part which has, at first sight, this appearance, is in reality that other hypocrisy before mentioned; that self-deceit, of which the Scripture so remarkably takes notice. There are indeed persons who live "without God in the world": and some appear so hardened as to keep no measures with themselves. But as very ill men may have a real and strong sense of virtue and religion, in proportion as this is the case with any, they cannot be easy within themselves but by deluding their consciences. And though they should, in great measure, get over their religion, yet this will not do. For as long as they carry about with them any such sense of things, as makes them condemn what is wrong in others, they could not but condemn the same in themselves, and dislike and be disgusted with their own character and conduct, if they would consider them distinctly, and in a full light. But this sometimes they carelessly neglect to do, and sometimes carefully avoid doing. And as "the integrity of the upright guides him," guides even a man's judgment; so wickedness may distort it to such a degree, as that he may "call evil good, and good evil; put darkness for light, and light for darkness"; and "think wickedly, that God is such an one as himself." Even the better sort of men are, in some degree, liable to disguise and palliate their failings to themselves: but perhaps there are few men who go on calmly in a course of very bad things, without somewhat of the kind now described in a very high degree. They try appearances upon themselves as well as upon the world, and with at least as much success; and choose to manage so as to make their own minds easy with their faults, which can scarce be without management, rather than to mend them.

From a Sermon upon the Character of Balaam (in Fifteen Sermons):

This was the man, this Balaam, I say, was the man, who desired to die the death of the righteous, and that his last end might be like his; and this was the state of his mind when he pronounced these words. So that the object we have now before us is the most astonishing in the world: a very wicked man, under a deep sense of God and religion, persisting still in his wickedness, and preferring the wages of unrighteousness, even when he had before him a lively view of death, and that approaching period of his days, which should deprive him of all those advantages for which he was prostituting himself; and likewise a prospect, whether certain or uncertain, of a future state of retribution; all this joined with an explicit ardent wish that, when he was to leave this world, he might be in the condition of a righteous man. Good God! what inconsistency, what perplexity is here! With what different views of things, with what contradictory principles of action, must such a mind be torn and distracted! It was not unthinking carelessness, by which he ran on headlong in vice and folly, without ever making a stand to ask himself what he was doing: no; he acted upon the cool motives of interest and advantage. Neither was he totally hard and callous to impressions of religion, what we call abandoned; for he absolutely denied to curse Israel. When reason assumes her place, when convinced of his duty, when he owns and feels, and is actually under the influence of the divine authority; whilst he is carrying on his views to the grave, the end of all temporal greatness; under this sense of things, with the better character and more desirable state present--full before him--in his thoughts, in his wishes, voluntarily to choose the worse--what fatality is here! Or how otherwise can such a character be explained? And yet, strange as it may appear, it is not altogether an uncommon one: nay, with some small alterations, and put a little lower, it is applicable to a very considerable part of the world. For if the reasonable choice be seen and acknowledged, and yet men make the unreasonable one, is not this the same contradiction; that very inconsistency, which appeared so unaccountable? To give some little opening to such characters and behaviour, it is to be observed in general that there is no account to be given in the way of reason, of men's so strong attachments to the present world: our hopes and fears and pursuits are in degrees beyond all proportion to the known value of the things they respect. This may be said without taking into consideration religion and a future state; and when these are considered, the disproportion is infinitely heightened. Now when men go against their reason, and contradict a more important interest at a distance, for one nearer, though of less consideration; if this be the whole of the case, all that can be said is, that strong passions, some kind of brute force within, prevails over the principle of rationality. However, if this be with a clear, full, and distinct view of the truth of things, then it is doing the utmost violence to themselves, acting in the most palpable contradiction to their very nature. But if there be any such thing in mankind as putting half-deceits upon themselves; which there plainly is, either by avoiding reflection, or (if they do reflect) by religious equivocation, subterfuges, and palliating matters to themselves; by these means conscience may be laid asleep, and they may go on in a course of wickedness with less disturbance. All the various turns, doubles, and intricacies in a dishonest heart cannot be unfolded or laid open; but that there is somewhat of that kind is manifest, be it to be called self-deceit, or by any other name.

The sermon on Balaam is worth reading in full; it's one of the great classical texts on self-deception.

Proving a Negative

Ed Brayton at Dispatches from the Culture Wars:

My guess is that there is no evidence because it is nearly impossible to prove a negative. It's a bit like someone claiming that there is an invisible leprauchan that makes it rain; we can point to all sorts of "naturalistic" theories and the data that support them on how rain is produced, but the question will still remain, "Well, what evidence do you have that the invisible leprachaun doesn't guide the whole process?" And the answer is "none", because there is no hypothetical evidence to prove such a negative - there just isn't any reason to believe it to be the case, and Occam's razor would certainly be germane here.

This has started me thinking about the matter. It's often said that it is nearly impossible to prove a negative, but I think it's a case of a cliché running on without adequate basis. 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. Brayton's invisible leprechaun is a good example. Unless the existence of the invisible leprechaun is suggested by 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 the claim has no straightforward relevance to the actual phenomena.

This sort of issue arises in a lot of skeptical scenarios in philosophy. Someone suggests that I am a brain in a vat, and that what I think is the external world really isn't. The challenge, then, is to prove that I'm not a brain in a vat. I look around me; all my senses show me a world (and a me) that seems to exclude that supposition. If we're accepting this level of proof as the standard, I've proven that I'm not a BIV. If, as is more often the case, the skeptic wishes to say, by an additional supposition, that my senses are deceived and that I am a BIV in a way that cannot be registered by any means of sensory proof or disproof, the relevance of the BIV supposition to what I experience is no longer well-defined. Now it's difficult to prove that I'm not a BIV, because there isn't any clear way in which such a supposition is relevant to anything I experience. This is what I sometimes call the Berkeleyan solution to external world skepticism. By becoming irrelevant to anything, the claim has become harder to refute; it has also become clear that it's not in need of any refutation. To handle a given domain of thought adequately, you don't need to be bothered about things irrelevant to it.

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. While this is possible, in practical cases it's often prohibitively difficult, 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 not exclusive to negatives, it should be pointed out; there are positive statements that are prohibitively difficult to prove at this level of proof.) If the relevance problem for the invisible leprechaun could be fixed (there is excellent reason to think it can't), and if we can't show that our induction is an exhaustive search over the possibilities, and if we can't show that our evidence rules it out, the only reasonable thing to do would be to admit the possibility that the invisible leprechaun is a hidden factor, if there are any hidden factors. The problem here, though, is much like the ones we've already noted. The problem is not that negatives are difficult to prove but that for this particular negative we've ruled out our means of proof (in the above cases arbitrarily, in this case in a principled way).

So the real maxim should be that it is nearly impossible to prove a negative when either you or the facts have made it nearly impossible. As a maxim it's not as catchy, though.