Elsewhere, Pierre Lemieux asked In two sentences, what do you think of the Monty Hall paradox? Unless I construct sentences loaded with conjunctions (which would seem to violate the spirit of the request), an answer in just two sentences will be unsatisfactory (though I provided one). Here in my 'blog, I'll write at greater length.

The first appearance in print of what's called the Monty Hall Problem seems to have been in a letter by Steve Selvin to The American Statistician v29 (1975) #1. The problem resembles those with which Monty Hall used to present contestants on Let's Make a Deal, though Hall has asserted that no problem quite like it were presented on that show. The most popular statement of the Monty Hall Problem came in a letter by Craig Whitaker to the Ask Marilyn column of Parade:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, Do you want to pick door No. 2? Is it to your advantage to switch your choice?

(Before we continue, take car and goat to stand, respectively, for something that you want and something that you don't want, regardless of your actual feelings about cars and about goats.)

There has been considerable controversy about the proper answer, but the text-book answer is that, indeed, one should switch choices. The argument is that, initially, one has a 1/3 probability that the chosen Door has the car, and a 2/3 probability that the car is behind one of the other two Doors. When the host opens one of the other two Doors, the probability remains that the car is behind one of the unchosen Doors, but has gone to 0 for the opened Door, which is to say that the probability is now 2/3 that the car is behind the unchosen, unopened Door.

My first issue with the text-book answer is with its assignment of initial, quantified probabilities. I cannot even see a basis for qualitative probabilities here; which is to say that I don't see a proper reason for thinking either that the probability of the car being behind a given Door is equal to that for any other Door or that the probability of the car being behind some one Door is greater than that of any other Door. As far as I'm concerned, there is no ordering at all.

The belief that there must be an ordering usually follows upon the even bolder presumption that there must be a quantification. Because quantification has proven to be extremely successful in a great many applications, some people make the inference that it can be successfully applied to any and every question. Others, a bit less rash, take the position that it can be applied everywhere except where it is clearly shown not to be applicable. But even the less rash dogma violates Ockham's razor. Some believe that they have a direct apprehension of such quantification. However, for most of human history, if people thought that they had such literal intuitions then they were silent about it; a quantified notion of probability did not begin to take hold until the second half of the Seventeenth Century. And appeals to the authority of one's intuition should carry little if any weight.

Various thinkers have adopted what is sometimes called the principle of indifference or the principle of insufficient reason to argue that, in the absence of any evidence to the contrary, each of n collectively exhaustive and mutually exclusive possibilities must be assigned equal likelihood. But our division of possibilities into n cases, rather than some other number of cases, is an artefact of taxonomy. Perhaps one or more of the Doors is red and the remainder blue; our first division could then be between two possibilities, so that (under the principle of indifference) one Door would have an initial probability of 1/2 and each of the other two would have a probability of 1/4.

Other persons will propose that we have watched the game played many times, and observed that a car has with very nearly equal frequency appeared behind each of the three Doors. But, while that information might be helpful were we to play many times, I'm not aware of any real justification for treating frequencies as decision-theoretic weights in application to isolated events. You won't be on Monty's show to-morrow.

Indeed, if a guest player truly thought that the Doors initially represented equal expectations, then that player would be unable to choose amongst them, or even to delegate the choice (as the delegation has an expectation equal to that of each Door); indifference is a strange, limiting case. However, indecision — the aforementioned lack of ordering — allows the guest player to delegate the decision. So, either the Door was picked for the guest player (rather than by the guest player), or the guest player associated the chosen Door with a greater probability than either unchosen Door. That point might seem a mere quibble, but declaring that the guest player picked the Door is part of a rhetorical structure that surreptitiously and fallaciously commits the guest player to a positive judgment of prior probability. If there is no case for such commitment, then the paradox collapses.

Well, okay now, let's just beg the question, and say not only that you were assigned Door Number 1, but that for some mysterious reason you know that there is an equal probability of the car being behind each of the Doors. The host then opens Door Number 3, and there's a goat. The problem as stated does not explain why the host opened Door Number 3. The classical statement of the problem does not tell the reader what rule is being used by the host; the presentation tells us that the host knows what's behind the doors, but says nothing about whether or how he uses that knowledge. Hypothetically, he might always open a Door with a goat, or he might use some other rule, so that there were a possibility that he would open the Door with a car, leaving the guest player to select between two concealed goats.

Nowhere in the statement of the problem are we told that you are the sole guest player. Something seems to go very wrong with the text-book answer if you are not. Imagine that there are many guest players, and that outcomes are duplicated in cases in which more than one guest player selects or is otherwise assigned the same Door. The host opens Door Number 3, and each of the guest players who were assigned that Door trudges away with a goat. As with the scenario in which only one guest player is imagined, more than one rule may govern this choice made by the host. Now, each guest player who was assigned Door Number 1 is permitted to change his or her assignment to Door Number 2, and each guest player who was assigned Door Number 2 is allowed to change his or her assignment to Door Number 1. (Some of you might recall that I proposed a scenario essentially of this sort in a 'blog entry for 1 April 2009.) Their situations appear to be symmetric, such that if one set of guest players should switch then so should the other; yet if one Door is the better choice for one group then it seems that it ought also to be the better for the other group.

The resolution is in understanding that the text-book solution silently assumed that the host were following a particular rule of selection, and that this rule were known to the guest player, whose up-dating of probabilities thus could be informed by that knowledge. But, in order for the text-book solution to be correct, all players must be targeted in the same manner by the response of the host. When there is only one guest player, it is possible for the host to observe rules that respond to all guest players in ways that are not not possible when there are multiple guest players, unless they are somehow all assigned the same Door. It isn't even possible to do this for two sets of players each assigned different Doors.

Given the typical presentation of the problem, the typical statement of ostensible solution is wrong; it doesn't solve the problem that was given, and doesn't identify the problem that was actually solved.

[No goats were harmed in the writing of this entry.]

The law has long treated the images of living persons as something like trademarks, so that the use of such images without the consent of those persons is restricted in various ways. Over the last few decades, there have been efforts — some successful — to turn these images into property of a sort that may legally be bequeathed upon death, as opposed to such images lapsing into the public domain.

The potential monetary rewards increased simply as celebrity became more culturally important. And the evolution of CGI has made it possible to fabricate the appearance of persons in video, not only increasing opportunities to make money from such images but to use those images in ways that many of us would see as grossly abusive (for example, in pornography).

Reflexively, quite a few people want law at a Federal level to protect the images of the dead. But there is some reasonable question as to whether the US Constitution empowers the Federal government to act.

The rub comes by way of Article I §8, which enumerates the powers of Congress. It specifically empowers Congress

To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;

As I've explained, this enumeration did not creäte copyrights; it instead gave Congress limited power to protect them; without that empowerment, the matter would simply have been left in the hands of common law and of the legislation of the constituent states. But neither §8 nor any other part of the unamended Constitution makes explicit mention of intellectual property of any other sort, and it is an unreasonable stretch to suggest that there is implicit reference to similar such property, exactly because there had been a felt need for explicit mention of the rights of authors and of inventors. Any prerogative to protect the images of the dead was left in the hands of the constituent states.

I used the word unamended advisedly, because one might try to make a case that the Fourteenth Amendment empowers the Congress to treat personal images as continuing to be property beyond personal death. But one can legitimately make that claim only if somehow the associated rights are basic rights of persons (or of US citizens as such) or can be shown to derive from basic rights; the Fourteenth Amendment doesn't empower Congress to reconfigure legal rights ad libitum.

There's a wide-spread propensity to confuse great desirability with moral necessity. But the penalties of law are always ultimately acts of violence, and there's a need for more than emotional appeal when the law forbids something. So, while it would be greatly desirable for the images of the celebrated dead to be treated with something like the respect that they would have received when alive, a solid case should be made for regarding them as property, or indeed they should be regarded as not property.

Some efforts to make personal images into property that remains such beyond the death of the persons have focussed on getting constituent states to have it treated as such in law. It's perhaps worth noting that the Fourteenth Amendment might be read to block the constituent states from converting these images to property (though I am sure that no court to-day would accept that reading).

To-day in the bistro, an unfamiliar girl perhaps six years old sat near me on the same bench. She was joined after a few minutes by a woman, probably her mother, who sat on the other side of their table. The little girl was interested in me and in my attention. Years ago, the drill for me would have been to engage her in brief conversation, asking her name and so forth, and probably answering questions about what I were doing. To-day, it was to turn briefly to give a friendly smile to her, and then turn quickly back to my business, all without pause.

Our notions of proper behavior have changed because Americans are generally far more concerned and otherwise anxious about threats to children, especially sexual threats from adult men. I share that concern and anxiety. I don't know whether things have become more or less dangerous than once they were, but honestly I think that question is secondary. Even if our world is less dangerous for children than in the past, I want us to be concerned; if it was once less perilous, none-the-less I wish that we'd even then been more vigilant.

(The Economist used to make a practice of mocking Americans for our fear for children. Perhaps they still do. I don't expect that it has occurred to them, in the wake of the various scandals concerning the sexual exploitation of children in the UK, that perhaps they have once again been mistaken in their presumptions of superiority.)

Yes, I'm saddened that I couldn't have had that short conversation. But I don't live in the world that ought to be, and in this case I cannot make ours a better world by acting as I would if it were. Had I interacted with the child in a more inviting way, I would have helped to foster norms and expectations that are exploited by predators. She didn't much need to talk to me. She does need to be spared some of the awful possible outcomes of the world in which we live.

Because my father watches Supergirl, I have now seen a few episodes. I note that they were written on the presumption that Hillary Clinton would be elected President, and thus that the character of the President is played by Lynda Carter imitating the voice and speaking patterns of Ms Clinton — so far, no cackle — albeït with the character named Olivia Marsdin.

And here's what is truly telling: In this fantasy, people who do not freely support Madam President are physically assaulted by state officials. For saying that she is Not my President. a fellow has his thumb wrenched by DEO agent Alex[andra] Danvers, who later begins to beat information out of him even though he is not even so much as a suspect.

It seems not to have occurred to writers, to producers, to directors, nor to starring actors that their heroes in an imagined world guided by Hillary Clinton were doing things that would seem thuggery if done by champions of a social order directed by Donald Trump.

Yet the shoes were merely on the other feet — or, in this case, mistakenly presumed to be so.

In Chapter 6 of Through the Looking Glass by Charles Lutwidge Dodgson (writing as Lewis Carroll), a famous and rather popular position on language is taken:

When I use a word, Humpty Dumpty said, in rather a scornful tone, it means just what I choose it to mean — neither more nor less.

If Mr Dumpty's words simply mean whatever he intends them to mean, then the rest of us are not in a position to understand them. If he provides us with verbal definitions, we must know what the defining words mean. He could not even declare in a manner intelligible to us that he meant most words in the same sense as do you or I. We might attempt to tease-out meanings by looking for correlations, but then we would be finding meanings as correlations, which assumes properties (such as stability) that represent more than pure choice on the part of Mr Dumpty. Having been made perfectly private, his vocabulary as such would have no practical value except for internal dialogue. There is a paradox here, which Dodgson surely saw, yet which so very many people don't: If Mr Dumpty's apparent declaration were true, then it could not be understood by us. He might actually just be making some claim about breakfast. We might take (or mistake) his claim for a true proposition (that his vocabulary were purely idiosyncratic), but any co-incidence between his intention and our interpretation would be a result of chance. We could not actually recognize it for whatever proposition it actually expressed.

In order to communicate thoughts with language to other persons, we must have shared presumptions not only about definitions of individual words, but also about grammar. The more that such presumptions are shared, the more that we may communicate; the more fine-grained the presumptions, the more precise the communication possible. In the context of such presumptions, there are right ways of using language in attempt to communicate — though any one of these ways may not be uniquely right or even uniquely best — and there are ways that are wrong.

Those who believe that there are right ways and wrong ways to use language are often called prescriptivist, and generally by those who wish to treat prescriptism as wrong-headed or as simply a position in no way superior to the alternatives. Yet, while one could find or imagine specific cases where the beliefs concerning what is right or wrong in language-use were indeed wrong-headed, forms of prescriptivism follows logically from a belief that it is desirable for people to communicate, and especially from a belief that communication is, typically speaking, something rather a lot of which is desirable. As a practical matter, altogether rejecting prescriptivism is thoughtless.

To the extent that the same presumptions of meaning are shared across persons, the meanings of words are independent of the intentions of any one person. Meanings may be treated as adhering to the words themselves. Should Mr Dumpty take a great fall, from which recovery were not possible, still his words would mean exactly what they meant when he uttered them. A very weak prescriptivism would settle there, with the meaning of expressions simply being whatever were common intention in the relevant population. This prescriptivism is so weak as not often to be recognized as prescriptivism at all; but even it says that there is a right and wrong within the use of language.

Those more widely recognized as prescriptivists want something rather different from rude democracy. In the eyes of their detractors, these prescriptivists are dogmatic traditionalists or seeking to creäte or to maintain artificial elites; such prescriptivists have existed and do exist. But, more typically, prescriptivism is founded on the belief that language should be a powerful tool for communication as such. When a typical prescriptivist encounters and considers a linguistic pattern, his or her response is conditioned by concern for how it may be expected to affect the ability to communicate, and not merely in the moment, but how its acceptance or rejection will affect our ability to understand what has been said in the past and what will be said in the future. (Such effects are not confined to the repetition of specific pattern; other specific patterns may arise from analogy; which is to say that general patterns may be repeated.) Being understood is not considered as licensing patterns that will cause future misunderstandings.

In opposing the replacement of can with the negative can't in can hardly, the typical prescriptivist isn't fighting dogmatically nor to oppress the downtrodden, nor merely concerned to protect our ability to refer to the odd-ball cases to which can't hardly with its original sense applies; rather, the prescriptivist is trying to ward-off a more general chaos in which we can hardly distinguish negation from affirmation. (Likewise for the positive could care less standing where the negative couldn't care less would be proper.) When the prescriptivist objects to using podium to refer to a lectern, it's so that we continue to understand prior use and so that we don't lose a word for the exact meaning that podium has had. We already have a word for lecterns, and we can coin new words if there is a felt need for more.

The usual attempt to rebut prescriptivism of all sorts notes that language evolves. Indeed it does, but prescriptivisms themselves — of all sorts — play rôles in that evolution. When a prescriptivist objects to can't hardly being used where can hardly would be proper, he or she isn't fighting evolution itself but participating in an evolutionary struggle. Sometimes traditional forms are successfully defended; sometimes old forms are resurrected; sometimes deliberate innovations (as opposed to spontaneous innovations) are widely adopted. Sometimes the results have benefitted our ability to communicate; sometimes they have not; but all these cases are part of the dynamic of real-world linguistic evolution.

The Evolution Card is not a good one to play in any event. Linguistic evolution may be inevitable, but it doesn't always represent progress. It will not even tend to progress without an appropriate context. Indeed, sometimes linguistic evolution reverses course. For example: English arose from Germanic languages, in which some words were formed by compounding. But English largely abandoned this characteristic for a time, only to have it reïntroduced by scholarly contact with Classical Greek and Latin. (That's largely why our compounds are so often built of Greek or Latin roots, whereäs those of Modern German are more likely to be constructed with Germanic roots.) It was evolution when compounding was abandoned, and evolution when it was reädopted. If compounding were good, then evolution were wrong to abandon it; if compounding were bad, then evolution were wrong to reëstablish it. And one cannot logically leap from the insight that evolution is both inevitable and neither necessarily good nor necessarily bad to the conclusion that any aspect of linguistic practice is a matter of indifference, that nothing of linguistic practice is good or bad. One should especially not attempt to apply such an inference peculiarly to views on practice that one dislikes.

In his foundational work on probability,[1] Bernard Osgood Koopman would write something of form α /κ for a suggested observation α in the context of a presumption κ. That's not how I proceed, but I don't actively object to his having done so, and he had a reason for it. Though Koopman well understood that real-life rarely offered a basis for completely ordering such things by likelihood, let alone associating them with quantities, he was concerned to explore the cases in which quantification were possible, and he wanted his readers to see something rather like division there. Indeed, he would call the left-hand element α a numerator, and the right-hand element κ the denominator.

He would further use 0 to represent that which were impossible. This notation is usable, but I think that he got a bit lost because of it. In his presentation of axiomata, Osgood verbally imposes a tacit assumption that no denominator were 0. This attempt at assumption disturbs me, not because I think that a denominator could be 0, but because it doesn't bear assuming. And, as Koopman believed that probability theory were essentially a generalization of logic (as do I), I think that he should have seen that the proposition didn't bear assuming. Since Koopman was a logicist, the only thing that he should associate with a denominator of 0 would be a system of assumptions that entailed a self-contradiction; anything else is more plausible than that.

In formal logic, it is normally accepted that anything can follow if one allows a self-contradiction into a system, so that any conclusion as such is uninteresting. If faced by something such as X ∨ (Y ∧ ¬Y) (ie X or both Y and not-Y), one throws away the (Y ∧ ¬Y), leaving just the X; if faced with a conclusion Y ∧ ¬Y then one throws away whatever forced that awful thing upon one.[2] Thus, the formalist approach wouldn't so much forbid a denominator of 0 as declare everything that followed from it to be uninteresting, of no worth. A formal expression that no contradiction is entailed by the presumption κ would have the form ¬(κ ⇒ [(Y ∧ ¬Y)∃Y]) but this just dissolves uselessly ¬(¬κ ∨ [(Y ∧ ¬Y)∃Y])
¬¬κ ∧ ¬[(Y ∧ ¬Y)∃Y]
κ ∧ [¬(Y ∧ ¬Y)∀Y]
κ ∧ [(¬Y ∨ ¬¬Y)∀Y]
κ ∧ [(¬Y ∨ Y)∀Y]
κ (because (X ⇔ [X ∧ (Y ∨ ¬Y)∀Y])∀X).

In classical logic, the principle of non-contradiction is seen as the bedrock principle, not an assumption (tacit or otherwise), because no alternative can actually be assumed instead.[3]. From that perspective, one should call the absence of 0-valued denominators simply a principle.

[1] Koopman, Bernard Osgood; The Axioms and Algebra of Intuitive Probability, The Annals of Mathematics, Series 2 Vol 41 #2, pp 269-292; and The Bases of Probability, Bulletin of the American Mathematical Society, Vol 46 #10, pp 763-774.

[2] Indeed, that principle of rejection is the basis of proof by contradiction, which method baffles so many people!

[3] Aristoteles, The Metaphysics, Bk 4, Ch 3, 1005b15-22.

Science is reasoned analysis of — and theorizing about — empirical data. A scientific conclusion cannot be recognized as such unless one understands the science.

It might be imagined that one can recognize a conclusion as scientific without understanding the science, by recognizing the scientists as such. But the popular formula that science is what scientists do is vacuous when taken literally, and wrong in its usual interpretation. Someone can can have an institutional certification as having been trained to be a scientist, and have a paid position ostensibly as a scientist, and yet not be a scientist; for those who actually understand some scientific area, it is fairly easy to find historical examples or perhaps present cases.[1] To recognize a scientist as such one must recognize what he or she does as science, not the other way around.

Even if it is in some contexts reasonable to accept conclusions from such persons on the basis of their social standing, it is not scientific literacy to accept conclusions on that basis; it is simply trust in the social order.

The full understanding of a scientific expert isn't always necessary to have a scientific understanding of the reasoning behind some of the broad conclusions of a scientific discipline. But in some cases of present controversy with significant policy implications, the dispute over the relevant conclusions turns upon issues of applied mathematics, and perhaps other things such as thermodynamics. No one can be scientifically literate in the areas of controversy without understanding that mathematics and so forth.

In many of the disputations amongst lay-persons over these issues, I observe people in at least one group who assert themselves to be scientifically literate, when they are no such thing, and to accept science, when they are not positioned to know whether what they are accepting is science. These are actually people who simply trust some part of the social order — typically, those state-funded institutions that declare themselves to engage in scientific research.

[1] It is certainly easy to find what lay-persons will acknowledge as examples. However, some of these ostensible examples are actually spurious.

A few years ago, in the title of an entry discussing the implications for the world of the failing health of Hugo Chávez, I alluded to a motto that ends leave a beautiful corpse[1]. That entry considered an observed practice:

When a charismatic leader dies aburptly while still in power, his or her supporters quickly begin building a mythology of what would have been accomplished had he or she lived.

I drew attention to how this mythologizing bears upon social policy:

The mythological episode of such leadership is treated as having the same standing for purposes of comparison as does historical fact. When an opponent tries to construct an argument founded on logic and general fact against policies associated with that leader, supporters treat the mythology as if it is a disproof by counter-example. What’s really happening then is that Faith is being mistaken for empirical data.

While death significantly amplifies the power of the mythologizing of a leader who was not given full opportunity to effect the programmes that he or she chose, death isn't essential for there to be some mythologizing; I noted that there was a developing narrative of what President Obama would have done had his party retained a majority in both chambers of Congress for the whole of his terms.

As it happens, charisma is also inessential, though it very much helps. And an odd substitute for direct charisma has been demonstrated. Barack Obama inflamed so much inverted narcissism on the part of his followers that a great many of them chose to treat his successor, Hillary Rodham Clinton, as if she were magnificent though she is signally lacking in charisma.

At the same time, her health is failing her, and had she been elected to the Presidency, she would not likely have served through a full term. There would have been an odd sort of race between how rapidly she did things that repelled those who had been her supporters, and when she left office. Depending upon the outcome of that race, she might have left a beautiful corpse.

But Ms Clinton has lost the race for Presidential Electors. Although a few of her supporters cling to an implausible hope that the Electoral College will not merely turn its back on the detestable Donald John Trump but will elect Clinton (as opposed to some Republican other than Trump), she will not be President. And the mythologizing is already under-way, even to the level of having Ms Clinton imagined as rather prettier than she is.

One does not have to regard Mr Trump as even tolerable to resist the mythologizing and to see Ms Clinton for what she has been. She has repeatedly been one of the people causing the United States military to engage in the slaughter of innocent people, for stated goals that haven't been obtained because they haven't been obtainable. She has engaged in calculated support of domestic policies such as the War of Drugs and aggressive incarceration policies that have literally led to many thousands of deaths and to the ruin of many thousands of other lives. She and her husband have got rich exactly as brokers of political influence. She has privately spoken against some policies as corrosive while publicly supporting them — or vice versa — depending upon the expected flow of dollars and of votes. She has casually disregarded laws, in the expectation (thus far vindicated) that her connections will insulate her from being charged, let alone convicted.

If Ms Clinton is to be made into a beautiful corpse, it is rather fitting that this transformation be effected while she is undead.

[1] In full, the motto is Live fast; die young; leave a beautiful corpse. It is an elaboration of an earlier motto of live fast and die young. A popular variant is Live fast; die young; leave a good-looking corpse.

[An earlier version of this entry was posted to Facebook on 30 September.]

A bad leader whose leadership is accepted with little resistance is more frightening than a bad leader whose leadership is accepted grudgingly, and who knows that the acceptance is reluctant.

A sense that Trump would have the freer hand will make some people vote for Clinton who might otherwise have voted for him; a sense that Clinton would have the freer hand will make some people vote for Trump who might otherwise have voted for her. Where these particular calculations are concerned, Clinton has an actual advantage in there being a present Republican majority in both chambers of Congress, because it is expected that Congress would frustrate Clinton more than it would thwart Trump.

But a bad leader is more frightening if he or she has many loyal followers even if these followers are outside of government. The composition of the Congress could change in the upcoming election or in one to follow; and, even if it did not, a President with greater popular support can accomplish more than otherwise, even without his or her party in the majority in either chamber.

Thus, the failure of the vast majority of the most vocal supporters of each of these two candidates truthfully to acknowledge their candidate for what he or she is makes each candidate far more scary to those who are undecided or weakly decided.

Almost no one who is now undecided or weakly decided thinks that either Clinton or Trump is merely not perfect; the voters most likely to be moved see both Clinton and Trump as awful people, and see this with good reason. To be less scared of these candidates, these voters need to read and to hear acknowledgments, from supporters, of just how flawed their own candidates are. (Becoming still more scared of one candidate is not at all the same thing as becoming less scared of the other, though indeed an increase in fear of one could strengthen support for the other.)

Were these supporters more rational, they would change their pitch. But, psychologically, they cannot. Some of them are simply swept-up in the urges of inverted narcissism;[1] and, more generally, supporters cannot admit the truth to others without to some extent recognizing the truth and acknowledging it to themselves. The world would have to be faced as a bleaker and more uncertain place.

[1] Inverted narcissism (popularly confused with covert narcissism, a markèdly different condition) is the felt need to treat some individual as magnificent, even if careful consideration would show him or her not to be so. The inverted narcissist is thus of a sort of complement to the narcissist, supplying the admiration that the narcissist needs for comfort. Inverted narcissism plays a hugely important rôle in politics.

The original definition of racism, and the one still found in standard dictionaries, is a theory or an adherence to a theory that merit is in part intrinsically a function of race

However, a few decades ago, some social theorists began insisting upon a new definition of racism, under which one could not be called a racist unless one not only were prejudiced against some racial group, but had social power. Devotees of this new definition variously baldly restate it, as if the restatement makes it so, or cite the theorists, as if such citation makes it so.

Those who make a special study of a subject sometimes take a term in popular use, and give it a peculiar, somewhat new definition. (For examp!e, we see that in physics, with the uses of energy, force, and work; and we see that in economics, with the definition of unemployment.) But what usually characterizes these redefinitions is that somewhat loose notions are replaced with more explicit, more precise, and otherwise more workable definitions. (For example, when an economist uses unemployment, she usually excludes people who have quit one job for another, but have not yet started that next job, because joblessness of this transitory sort is not typically considered to be a social ill.)

Alarms really ought to go-off about the redefinition of racism. The original concept was quite coherent and useful; if it were not coherent, then the redefinition (which essentially adds a condition) would inherit the incoherence. Racism on the part of people with little social power still has significant social consequences; any legitimate use of the new concept is far more sharply limited than that of the original concept.

Let's imagine that someone prejudiced against those outside his own major racial group makes a solo walking tour of Los Angeles. As he travels from one neighborhood to another, he gains or loses social power as the ethnic compositions of those neighborhoods vary. His beliefs about the relation between race and merit needn't change (and should not be expected to do so much if at all). Yet by the mere act of travel through a large city in which ethnic groups are not uniformly distributed, under the redefinition he would repeatedly go from being a racist, to not being a racist, to again being a racist. It would be extraordinary and dangerous to make a solo walking tour of all of Los Angeles, but a great many people regularly move across communities of different ethnic composition. Application of the proposed redefinition of racism would routinely become unworkable, under circumstance in which the standard definition remains quite workable.

There are certainly legitimate applications of the concept of socially empowered racism, but in those applications we can call it socially empowered racism or something similar.

When a concept loses its associated symbol, it becomes harder to discuss or even to think about that concept. Further, the response to symbols is largely emotive. Whether people learn by reason that something is good or that it is bad, or they are simply led to accept some valuation by imitation of those in their society, people come to associate positive or negative feelings with the words used for those things. Old concepts given new words don't provoke the same response; old symbols given new meanings carry with them some or all of the old feelings. Those who have adopted a new redefinition of racism can thus escape the recognition of racism, and the felt need to condemn some instances of racism, by allowing themselves to believe that some people simply cannot be racists, by virtue of their social standing.

We are simply dealing with an attempted hijacking of language, for purposes of subverting clear thought and discussion. That is most plain when the word racism has been introduced into some discourse with its standard definition, and in response it is insisted that something conforming to that original definition is not racism because it does not conform to the proposed redefinition. But any non-standard use that is not flagged as such is still a subversion of rationality. Those who have participated in the attempted hijacking are knaves or fools or both.