84 Lumber bought airtime within the broadcast of the 2017 Superbowl, and presented a video of a Latina mother and daughter travelling through what seems to be Mexico, plainly in hopes of entering America. Inter-spliced with the scenes of their travel are scenes of Americans, clearly constructing something. When the mother and daughter reach the border, they are confronted by a grey and terrible wall. But, as they seek for some hope, they find it — sunlight somehow shining through a section of that wall. Running to it, they find a door. In the awful wall, it was a great door that the Americans in the other scenes were building.

84 Lumber is being attacked for their video, on a theory that its purpose were to defend illegal immigration. Naturally, 84 Lumber denies that their message were any such defense; they now claim that the door were a metaphor for the institutions of legal entry.

I don't encounter a lot of people who will honestly speak in favor of illegal immigration. They ought to do so. There is nothing wrong with illegal immigration. Nothing.

The vast majority of people who oppose illegal immigration or want greater legal restriction on immigration do not do so from racism, and I am very sorry that they have been slandered and libelled; but recognizing the inappropriateness of that accusation doesn't serve to support a case for denying people entry.

Indeed, immigrants might come to our nation and do a variety of things that are violations of the rights of the people who are here now, or that are otherwise undesirable; but every genuine right that might violated by an immigrant could also be violated by someone born and raised here; more generally, every socially corrosive act that might be perpetrated by an immigrant could also be perpetrated by a native. A man or woman who was born here can violate the property and person of someone else; a man or woman who was born here can demand that his or her religion or language be give a privileged legal status; a man or woman who was born here can live at the expense of the taxpayers. None of these behaviors is made better or worse by virtue of where the person were born, nor by whether he or she were allowed to immigrate by the law. I will grant that groups coming from some foreign cultures have a greater share of members likely to do undesirable things of some sorts; but some groups native to America have a greater share of members likely to do undesirable things of some sorts.

There is a dire confusion of the legal with the moral, both on the part of those who insist that illegal immigrants are already in the wrong by virtue of having broken laws that are ostensibly ours in coming here, and by those who insist that there is no such thing as an illegal immigrant. Law can be wrong, and when it is wrong then it may be ignored without doing wrong. Those immigrants here in violation of law are neither wrong simply for being illegal, nor legal because they are not wrong to be here.

America is not a club nor a corporation. The persons and properties within the area occupied by America are not ipso facto in any way the property of all Americans. The right to trade, the right to give without condition, and the right to take that which is freely offered are not rights that in any way reflect nationality. Those who would do business with newcomers are within their rights; newcomers who would do business with those Americans are within their rights.

It's offensively absurd to claim an entitlement to exclude people by pointing to state-managed infrastructure and programmes. They weren't brought into existence through some sort of social contract; ultimately, they were effected through threats of violence; and generally they crowded-out alternative institutions that would have been created by free people. Of course, the welfare state cannot survive in a world of such freedom; it could not survive even if the progressives were allowed to pursue their wildest dreams of taxation, nationally or globally. But so much the worse for the false generosity and false security of the welfare state, which cannot avoid bankruptcy in this century, regardless of whether it keeps all of us trapped on one side or another of its jurisdictional boundaries.

Many people who are going or went through the process of legal immigration may feel that it is unfair for others now to jump the queue; but the queue should never have existed in the first place, and one only compounds the injustice by imposing it upon others.

There should be no queue, no wall, no need for doors.

Thinking about there already being an effort to persuade voters that they must support whomever the Democratic Party nominates in 2018 and in 2020, I was naturally led to wonder what sort of candidates those would be; and thence, more generally, what politics would be like in about three years.

What politics will be is something within the context of what they can be, so I try to imagine the plausible scenarii. To me, these look very grim.

I expect the Republican Party to continue to reshape itself around Donald Joseph Trump, to be more informed by his poison. I don't expect the dissenters within the Republican Party to enjoy much success, especially as I don't expect them to find any help either from main-stream of the media or from the alternative led by Fox. Some of the better people in that tribe whom we call the political right will leave it, and even some people who were enthusiastic about Trump will see or sense where things are leading, and turn away; however, it will continue to recruit people who were not previously its members but are attracted to Trump or to Trumpism. And a very large share of those who were already members of that tribe will reshape their ostensible beliefs to fit the pronouncements and actions of Donald Trump.

(If Trump should leave office early, then the Party will presumably work to reshape itself around Michael Richard Pence, who will attempt to segue from whatever Trumpism then is, to a frightening social conservatism. But I don't expect Trump to be removed.)

Meanwhile, the aforementioned Democrats are in a dark political death-pit. Their most recent nomination was decided as a struggle between what progressivism has become (and was always destined to be) and crony capitalism posturing opportunistically as that progressivism. The leadership ensured that the crony capitalist got the nomination, but the subsequent result was, if anything, to intensify the need of the leadership to pander to the progressive urges of the Party's base. And the response of the base to Trump's election has been to move still further left and to become more overtly violent.

That base is about 25% of the nation and of the voters. It likes to imagine itself as a plurality, as a majority, or sometimes even as the other 98% or as the 99%. But the political left has inflated its apparent size by taking disproportionate control of the commanding heights of our social institutions, and by implicitly coöperating with the political right (also only about a quarter of the population) to marginalize those with views that do not conform to the left-right framework; remarkably, the political right has kept the political left viable, and vice versa. (These days, about a third of the American population wants the state to be less involved both in matters of sex and of religion and in matters ordinarily classified as economic. That makes them a larger group than either the left or the right, but not larger than the two combined.) Given how small they actually are, the left (like the right) cannot take political power without getting votes from those outside their tribe. If the Democratic Party cannot free itself from the influence of those who continue down the path of progressivism, then it cannot return to power based upon a positive appeal; its hopes would lie only in Republican over-reach.

Which over-reach would certainly have recent precedence. In 2006 and 2008, the Republican Party was in its own death-pit. They'd stumbled into it under the influence of neo-conservatism. The neo-conservatives pursued two wars, guided by a theory that the people in Afghanistan and in Iraq were aching for liberal democracy and prepared to fight for it. And they pursued fiscal and regulatory policies that triggered a major financial crisis. The Republicans lost control of both chambers of Congress, and then of the White House.

What pulled them from that death-pit was the Tea Party, which began coälescing with rallies, and then organized itself well enough to displace candidates of the Republican establishment in primary races. Those in the Republican establishment who held onto their positions fought vigorously with the Tea Party, which served to burnish the credentials of the Tea Party candidates and office-holders. Attempts by the left to treat the Tea Party Republicans as responsible for the prior actions of the neo-conservative Republicans were unsuccessful in persuading those outside the Democratic base. Ultimately, it seems that the Tea Party failed in its objectives; they did not succeed in capturing the leadership of the Republican Party, and some office-holders who had cultivated the support of the Tea Party betrayed their trust. The Tea Party appears now itself displaced by an uglier and angrier populism. But the Tea Party had the effect of allowing the Republican Party largely to free itself from association with the awful policies of the Administration of George Walker Bush.

That brings me to the Women's March on Washington, and to its sister Marches in other cities. It is not impossible that these rallies could be the beginning of a process that could reälign the Democratic Party, pulling it from its death-pit as the Tea Party pulled the Republican Party from its own. The odds, however, are very much against that reälignment.

First, though a great many of the women who participated wanted to be heard, rather that to be told what to say by celebrities and by icons — definitely shouting No! to goddamn'd Donald Joseph Trump, but not all saying Yes! to what the Democratic Party or its progressive base have been offering — the objective of most of those who called and led these marches in the first place was not to reälign the Party, but to reälign women. A new leadership of reformers would have to be found.

Second, while the Tea Party did not much have to fight the Republican base, that is exactly what anyone seeking fundamentally to reälign the Democratic Party would have to do.

Those without much hope for the Republican or Democratic Parties as instruments of positive change sometimes turn to third parties. Some exist, others could be creäted. We've already seen a collapse of the institutionalized myth that third parties must always be formed either around one issue or around one candidate. The left and the right will join together, through the media that they control and through bi-partisan commissions, to fight the emergence of a real alternative; but, if the left continues to get ever more repulsive to those voters outside of the left and right, then the right will have a greatly weakened partner in their unholy alliance to exclude rival views. I don't imagine that I myself will find a party or Presidential candidate whom I can, in good conscience, support; but perhaps 2020 will be made less awful by the emergence of a better major party.

I have previously explored the logical absurdity of insisting that those who don't vote for one of the two foremost candidates in an election are effectively voting for the other of these two candidates. That analysis could easily be generalized to include ballot measures; where abstaining from voting has sometimes been claimed to be the same as opposing a measure, and sometimes been claimed to be the same as supporting the measure.

The primary purpose of claims of these forms is to pressure someone into voting for a candidate whom — or measure which — the potential voter finds unappealing. We especially see these claims when there are actual candidates, or formulated ballot measures. But we also see that purpose at play when an election has been held and candidates and proposal for the next election are not yet identified. Some of those declaring You are now to blame for X because you did not vote for Y! are hoping to motivate the audience to tolerate whatever is demanded by the claimant's faction in that next election. An alternative would be to promise to offer something better than Y in that next election; but they are engaged in brinksmanship, threatening to take the community off a cliff if a plurality don't agree to their demands.

Other motivations for such claims in the wake of an election are simple ventilation and blame-shifting. It is frustrating to lose an election, and a blow to the ego to acknowledge that one's own faction may be largely responsible for that loss.[1]

There's another, unrecognized motivation for these claims. Although there is a very great logical distance between refusing to support one of the two major political tribes and thinking as do members of the other major tribe, it is easy enough for tribal members to disregard that distinction almost perfectly. Thus, these absurd claims that refusal to support Y is operationally the same thing as supporting X implicitly become part of a more general psychological device of treating politics as all falling along a left-right spectrum, and thereby avoiding any challenge to one's thought or behavior that cannot be dismissed from the left by pointing to the right or from the right by pointing to the left, and saying You guys are worse!, even if the challenger is not one of those guys. The challenge may even be spuriously taken as proof that, after all, the challenger were really a member of the other tribe, as he or she is not challenging them, and them alone.

[1] For example, James Henry (Jim) Webb could have beaten any of the Republican candidates for President in 2016, and it is at least plausible that Bernard (Bernie) Sanders could have beaten Donald J[oseph] Trump; but the Democratic Party chose its weakest or second-weakest candidate. (Martin Joseph O'Malley might have been a still worse choice, as his mythology of Baltimore collapsed in the face of the police murder of Freddie Carlos Gray jr.)

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.]

My paper on indecision is part of a much larger project. The next step in that project is to provide a formal theory of probability in which it is not always possible to say of outcomes either that one is more probable than another or that they are equality likely. That theory needs to be sufficient to explain the behavior of rational economic agents.

I began struggling actively with this problem before the paper on indecision was published. What I've had is an evolving set of axiomata that resembles the nest of a rat. I've thought that the set has been sufficient; but the axiomata have made over-lapping assertions, there have been rather a lot of them, and one of them has been complex to a degree that made me uncomfortable. Were I better at mathematics, then things might have been put in good order long ago. (I am more able at mathematics than is the typical economist, but I wish that I were considerably still better.) On the other hand, while there are certainly people better at mathematics than am I, no one seems to have accomplished what I seek to do. Economics is, after all, more than its mathematics.

What has most bothered me has been that complex axiom. There hasn't seemed much hope of resolving the general over-lap and of reducing the number of axiomata without first reducing that particular axiom. On 2 January, I was able to do just that, dissolving that axiom into two axiomata, each of which is acceptably simple. Granted that the number of axiomata increased by one, but now that the parts are each simple, I can begin to see how to reduce their overlap. Eliminating that overlap should either pare or vindicate the number of axiomata.

I don't know whether, upon getting results completed and a paper written around them, I would be able to get my work published in a respectable journal. I don't know whether, upon my work's getting published, it would find a significant readership. But the work is deeply important.

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.

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.