Archive for the ‘philosophy’ Category

Policy Paralogism

Thursday, 22 February 2018

Confronted with a real or imagined social problem, most people first grab for an ostensible solution that appeals to their prejudices, and then for an argument (in favor of this policy) that seems plausible to them. That approach is not ideal, but might still result in good policy if people would poke at each such argument, to see whether it were actually logical, and move away from proposed solutions in cases in which none of the arguments withstood examination. Unfortunately, people don't generally test their arguments; words strung together in emotionally satisfying ways are embraced as if any reasonable person would accept them.

I came upon an epitomal example of this behavior, in the wake of a recent mass shooting at a school. Someone posted a graphic macro suggesting how guns might be treated analogously to motor vehicles and and declared

Let’s go through this one more time…maybe they will get it. And yes, people will obtain guns illegally. And yes, people kill people. But doing nothing means more die.

(Underscore mine.) Now, there are various problems with the suggestion that guns should be treated analogously to motor vehicles, and perhaps someday I'll labor all that occur to me. But here I want to focus on that assertion doing nothing means more die. To the poster, it apparently seems that any reasonable person would accept that this assertion is an argument for the policy that he favors. Let's poke at this use, to see whether it is actually logical.

It is surely true that if we do nothing different, then people who have not yet died will die, and in this sense more will die. But, as a matter of logic, that doesn't mean that there is something that we can do such that people would not die, or even that fewer would die. If we somehow had an optimal social policy, and found that people died, we could still say that if we did nothing different then people would die. So, one question that we might ask is of whether a change in social policy would cause fewer or more people to die.

And I'm not simply talking about whether a change in social policy would cause fewer or more people to die at the hands of shooters who are not state officials, or even about the more general question of whether a change in policy would cause fewer or more people to to die at the hands of shooters of all sorts, but about the question of whether the change in policy would result in fewer or in more deaths across all causes. For example, a policy change might lead to greater use of IEDs. (The deadliest mass murder at a school in American history was effected by a bomb.) The answer is not known a priori.

There is also the issue of other costs. For example, some jurisdictions have a lower rate per capita of homicide, but a higher rate of rape. One doesn't want to switch from one set of policies to another simply on the basis that if we do nothing then more will be raped, and likewise one doesn't want to switch from one set of policies to another simply on the basis that if we do nothing then more will die. I don't think that any utilitarian calculus is actually reasonable, but one that simply counts lives is plainly inhumane. And it would be childlike to think and childish to insist that, with some set of policies, the global minimum for each costs could be achieved simultaneous to that for every other, let alone that such a fantastic minimum could be found by first finding the local minimum for one cost and then seeking the local minimum for another.

The poster has presented an example from just one class of policies, and declared doing nothing means more die. Plainly, there are other possible policy responses, so that the relevant comparison is not simply between adopting the policy that he favors and maintaining the status quo.

Moreover, if his argument were adapted to the defense of other policies, he and others might be provoked to examine that argument more carefully. His words might be left essentially unchanged, but the macro replaced with one discussing a policy of a different sort. For example, someone might propose that each person above the age of 10 years old be interned in a mental-health camp, until and unless experts appointed by the state certified that he or she was not a danger to society. I'd like to think that, if the original poster had earlier seen the very same words used in defense of an internment policy, then he would have immediately poked at the argument to find the illogic. I'm quite sure that most people who applauded or would have applauded his words in the context in which he did use them would have found their illogic in the context of an argument for rounding-up American youth and throwing them into camps. Well, the should have poked at the argument where they actually found it.

Again into the Breach

Monday, 15 January 2018

As occasionally noted in publicly accessible entries to this 'blog, I have been working on a paper on qualitative probability. A day or so before Christmas, I had a draft that I was willing to promote beyond a circle of friends.

I sent links to a few researchers, some of them quite prominent in the field. One of them responded very quickly in a way that I found very encouraging; and his remarks motivated me to make some improvements in the verbal exposition.

I hoped and still hope to receive responses from others, but as of to-day have not. I'd set to-day as my dead-line to begin the process of submitting the paper to academic journals, and therefore have done so.

The process of submission is emotionally difficult for many authors, and my past experiences have been especially bad, including having a journal fail to reach a decision for more than a year-and-a-half, so that I ultimate withdrew the paper from their consideration. I even abandoned one short paper because the psychological cost of trying to get it accepted in some journal was significantly impeding my development of other work. While there is some possibility that finding acceptance for this latest paper will be less painful, I am likely to be in for a very trying time.

It is to be hoped that, none-the-less, I will be able to make some progress on the next paper in the programme of which my paper on indecision and now this paper on probability are the first two installments. In the presumably forth-coming paper, I will integrate incomplete preferences with incompletely ordered probabilities to arrive at a theory of rational decision-making more generalized and more reälistic than that of expected-utility maximization. A fourth and fifth installment are to follow that.

But the probability paper may be the most important thing that I will ever have written.

Hume's Abstract of His Treatise

Thursday, 14 December 2017

In an attempt to promote his work A Treatise on Human Nature (1738), David Hume anonymously wrote and in 1740 had published a booklet, An Abstract of a Book Lately Published, Entituled, A Treatiſe of Human Nature, &c. It went nearly unnoticed and unrecognized until republished in 1938, with an introduction by John Maynard Keynes and Piero Sraffa. That edition was reprinted in 1965. The introduction may still be protected by copyright, as may be images of the reset text.

In any event, I did not find any editions of the booklet itself freely available on-line; so I have created one.

Well, actually, two editions. The first retains the use of long ess (‘ſ’) and the convention by which longer passages were quoted, which was a matter of prefixing a quotation mark to each line which continued a quotation from the previous line. The second replaces the long esses with now ordinary lower-case esses, and uses block quotation where now conventional, though the second version otherwise preserves the spelling and punctuation of the original.

The Abstract is about 6,500 words. The booklet was just thirty two pages, one of which was a title page and one of which was blank. My transcriptions come each to less than nine pages of twelve-point type.

Addendum (2017:12/15): After I posted my transcriptions, a Google search on an Android tablet returned a link not previously returned by a Google search on my Linux box, to a transcription by Carl Mickelsen lacking the original preface contained in the booklet, and with the remaining text extensively editted to change spellings, punctuation, italicization, &c I also found a wholesale paraphasing of the Abstract by Jonathan Bennett, with changes far more extensive than the reader is led to believe

Hyper-Vigilance and Feedback

Tuesday, 14 November 2017

Psychologists vary in precisely what they mean when using the term vigilant or hyper[-]vigilant to describe a personality type. What is common across notions and here relevant is an acute concern about — and sensitivity to — behavior by others that may carry information about intention, about propensity, or about capacity. Hyper-vigilance typically arises as an attempted adaptation in response to seriously hurtful experience; it is in any case a self-defense behavior more focussed on identifying hostile or otherwise threatening intentions, propensities, or capacities, and should be expected to be associated with other defensive behaviors and more generally with personality attributes that arise from injury.

Hyper-vigilance itself is not the same thing as paranoia. When there is an element of irrationality to hyper-vigilance as such, it is in an over-commitment of resources to the tasks of awareness or of interpretation. The hyper-vigilant may otherwise be for the most part rational in their interpretations of behavior. (And one cannot reasonably infer that there is an over-commitment of resources simply from the fact that a hyper-vigilant person is seeking greater awareness.) A paranoid systematically makes important inferences that are themselves unreasonable.

The skills of the hyper-vigilant (and, for that matter, the unreasonable inferential practices of the paranoid) aren't always employed for purposes of self-defense. People may be identified as well-intentioned or peculiarly talented, and cultivated as friends; people may be perceived as having concealed vulnerabilities, and quietly given protection.

When two people interact — whether either is hyper-vigilant or not and so long as they are at all social — they consciously or unconsciously each size-up the other. The behavior of each usually adjusts to anything learned in the present encounter, and that adjustment of behavior may then communicate something new to the other, causing a counter-adjustment on his or her part. When two people have complementary emotional responses each to the other, a feedback loop is creäted, and the responses amplify to some extent. These feedback loops can cause people to take relatively quick and markèd likings or dislikings each to the other.

When hyper-vigilant people interact, complementarity has a still more pronounced effect. They can move to attack or become friends or come to love or indeed fall in love with a speed that startles everyone — including the two people in the feedback loop if they've never considered the dynamic or if they haven't each discerned that the other is not merely ill- or good-willed but also hyper-vigilant. Because hyper-vigilance is a behavior of self-defense, it is likely to be accompanied by a suppression or masking of behaviors that would otherwise expose emotions or reveal defensive abilities or propensities, and hyper-vigilance itself would be one of those behaviors; additionally, a hyper-vigilant person may conceal vigilance to avoid censure (especially as hyper-vigilance is widely equated with paranoia). Thus one or both of two hyper-vigilant people may miss this important insight in the implicit challenge of reading the other, especially when vigilance is operating largely at an unconscious level.

Responsible Voting

Wednesday, 18 October 2017

It was once socially accepted that people were not responsible for acts of a wide variety if the persons engaged in them while intoxicated, even if the intoxication were quite voluntary and the engagement active. Over time that attitude has eroded. After all, a person who chooses to be intoxicated chooses to engage in increased probability that he or she will effect those acts. If a person who chose to drink passes-out on the front lawn, drives his vehicle into a pedestrian, or beats his domestic partner, few people would insist that he didn't choose to do such a thing. And, should we meet one of those few people, we rightly suspect that they cannot be trusted to use intoxicants responsibly.

In response to the campaign of Bernard (Bernie) Sanders, a great many people embraced things that they called democratic socialism. They didn't actually agree amongst themselves as to what this term meant. Many of them insisted that democratic socialism weren't socialism, which insistence did not provoke as often as it should a question as to why then its name should contain socialism. The answer simply was that Sanders had long referred to what he advocated with this term; they were stuck with socialism if they held onto Sanders. Whether they admitted that democratic socialism referred to socialism or not, all of the folk calling for something by that name sought to neutralize the dire associations of socialism with various outcomes that had been observed when regimes had been identified by that label. And all of these folk, whether or not they acknowledged that they were referring to socialism, agreed that what they called democratic socialism would indeed be democratic.

That insistence has afforded them a rhetorical ploy for dealing not only with socialistic regimes that were never democratic, but with socialistic regimes that have lost popular support, such as that in Venezuela. Absenting that support, these regimes are said not to be democratic, and hence plainly not to represent whatever might properly be called democratic socialism. But when a socialistic regime is brought to power by democratic means, in a framework of law that was effected by democratic means, and then uses that law to take unpopular actions, to insist that the regime is undemocratic begins to resemble claiming that the neighbors passed-out on the lawn, driving their cars into pedestrians, or beating their domestic partners did not choose to do such things. Oh yes they did. And anyone who insists otherwise is to be regarded as dangerous with the relevant intoxicants, including ballots.

Indeed, for most of recent history, popular opinion was not treated as particularly important in application to America by most Americans who came to call for democratic socialism. They had earlier thought it perfectly democratic when the Democratic Party, democratically elected to majority control of both Chambers of Congress and to the Presidency, effected various measures that were in fact widely unpopular with the more general population. President Obama advised the Republicans to win some elections. When they did, so that the Democrats lost first the House of Representatives and then the Senate, he and most of these folk for democratic socialism held to the idea that his democratic election to the Presidency legitimized his actions in defiance both of the votes of the Congress and of popular opinion amongst the wider population. Popular opinion in Venezuela and elsewhere has emerged as ostensibly relevant to democratic socialism exactly and only because, once again, socialism — even socialism within a framework democratically effected — has devolved as it always will if allowed to persist. There is no magic in democracy.

The state is a terrible institution, to be checked by an institutional framework that resists its growth, instead of enabled to grow by fantasies that amateurs or experts can use it expansively to bring about a more humane world.

Helmholtz's Zählen und Messen

Monday, 16 October 2017

When I first encountered mention of Zählen und Messen, erkenntnisstheoretisch betrachtet [Numbering and Measuring, Epistemologically Considered] by Hermann [Ludwig Ferdinand] von Helmholtz, which sought to construct arithmetic on an empiricist foundation, I was interested. But for a very long while I did not act on that interest.

A few years ago, I learned of Zahl und Mass in der Ökonomik: Eine kritische Untersuchung der mathematischen Methode und der mathematischen Preistheorie (1893), by Andreas Heinrich Voigt, a early work on the mathematics of utility, and that it drew upon Helmholtz's Zählen und Messen, which impelled me to seek a copy of the latter to read. To my annoyance, I found that there was no English-language version of it freely available on-line. I decided to create one, but was distracted from the project by other matters. A few days ago, I recognized that my immediate circumstances were such that it might be a good time to return to the task.

I have produced a translation, Numbering and Measuring, Epistemologically Considered by Hermann von Helmholtz It is not much better than serviceable. I don't plan to return to the work, to refine the translation, except perhaps where some reader has suggested a clear improvement and I effect a transcription.

I have not inserted what criticisms I might make of this work into the document. Nor have I presented my thoughts on how Helmholtz's ostensible empiricism and Frege's logicism are not as far apart as might be thought.

Vocal Cues

Monday, 26 June 2017

Many animals, across different classes, have two distinct sounds that may be classified as growls or as whines, respectively. The growls signal threat; the whines signal friendship or appeasement.

The bark of a dog is actually a combination of a growl with a whine; it is thus not a pure signal of aggression, as many take it to be; it is literally a mixed signal, perhaps indicating confusion on the part of the dog, perhaps signalling both that the dog is prepared to fight and that the dog would consider a peaceful interaction.

When women talk with men whom they find attractive, women tend to raise the pitches of their voices. Men tend to do something different when talking with women whom they find attractive; they mix deeper tones than they would normally use with higher tones than they would normally use. The deep tones are signals of masculinity, of being able to do what men are expected to do. The higher tones of men carry much the same significance as do the higher tones of women — with the additional point in contrast to the deep tones that the man does not mean to threaten the woman.

It amused me to reälize consciously that this behavior by men is at least something like barking. Then I grimly considered that some men are actually barking, telling the woman that he can be nice to her if she is nice to him, but will actively make things unpleasant if she is not. But at least it should typically be possible to disambiguate the threatening behavior, based upon where the low notes are used, and of course the choice of words.

On the Meaning of Sexism

Thursday, 11 May 2017

In a previous entry, I noted that the original definition of racism was a theory or an adherence to a theory that merit is in part intrinsically a function of race. It was exactly by analogy with the word racism that the word sexism was introduced in 1968, thus referring to a theory or an adherence to a theory that merit is in part intrinsically a function of sex.

Now, here is where matters get tricky. In any case in which one rejects sexism, it is regarded as an inappropriate response to the sex of people; and, in particular, the treatment is likely to be seen as unethical. A very great many folk employ the concept of unethical response to the sex of people as if that were the very definition of sexism. That notion is going to operationalize very much like the actual definition whenever and wherever the issue at hand is one of ethics and ethics actually call for neutrality — for a rejection of the relevance of sex to the issue. But nearly all of us regard people of one sex as better suited to some rôles that are of importance. For example, if I presume that sexism must refer to something unethical, then I am compelled either to associate sexism with something other than neutrality of a sort, or as a matter of justice to try to entertain thoughts of accepting a man as a potential spouse for myself. (People are led astray by the analogy with racism; the cases in which sex is relevant to selection loom larger because of the importance of reproduction.) And the substituted notion is not going to operationalize at all like the original definition exactly when someone believes that merit is a function of sex in a far wider range of cases than do folk such as I; then the substitution is going to get things almost perfectly twisted around. He or she will label anti-sexism as sexism and will label some sort of sexism — perhaps quite an intense sexism — as anti-sexism.

The spurning of a claim of relevance is the maintenance or adoption of indifference. This indifference is an equality of one sort — and we often see the words equal and equality used in antonymy to sexism — but it is not an equality of various other sorts. Advancement of a conflicting equality would itself be sexist. Such conflicting equalities can arise when the equality sought is equality of outcome. If people, regardless of sex, may be presumed to respond to a framework in essentially identical ways, and we observe markèdly different outcomes for one sex compared to those for another, then this difference is prima facie evidence that the framework is sexist. But if it is recognized that people of one sex behave differently in that framework, then the presumption that the framework is sexist does not follow from the mere presence of a difference. If we say that the different behaviors must be treated as of equal merit because otherwise a difference in outcomes emerges, then the merit that is ascribed to the behavior is treated as a function of the sex of the people who engage in that behavior; that prescription is itself intrinsically sexist.

For example, the rates at which men are arrested for, charged with, and convicted of criminal behavior of various sorts are much higher than the corresponding rates at which women are arrested, charged, and convicted. We cannot conclude simply from these differences that the system of criminal law is sexist, because it may be that men simply engage in that behavior more often; indeed, most of us are fairly sure that this latter case holds. If we insist that the behaviors themselves must be decriminalized in order to reduce the rates at which men are arrested, charged, and convicted, then we are inferring the relative merit of the behavior from the sexes of those who engage in it. The very same sort of analysis would apply to hiring practices and to the wages or salaries paid to those in various occupations.[1]

(Many people, including certainly me, would argue that an unfortunate sexism prior to whatever exists in the legal system is one factor contributing to greater criminality by men, but few-if-any people propose that part of an appropriate response would be an adjustive sexism, giving more tolerance to male criminalized behavior than to female criminalized behavior. Likewise, some of us assert that an unfortunate sexism prior to whatever exists in the jobs market is one factor leading to different career outcomes for women, but we don't propose an adjustive sexism attempting to compel employers to pay women more than the expected values of their marginal products.)

The confused presumptions that only an unethical discrimination can count as sexism and that sexism is found where there is some sort of inequality other than non-neutralityan attention to sex — causes people in all sincerity to misapply the word sexism and to fail to see legitimate application of the word, perhaps to their own attitudes and actions. If substitutions of these sorts are not recognized by those who use the word sexism in accordance with its definition, then interactions will be characterized by mutual incomprehension, quite possibly enraged. Attempts to employ logic and facts won't be persuasive because one of the two groups will actively misunderstand a word central to any communication. Additionally, there are people who implicitly believe that ethical significance clings to symbols, such that by changing labels what was wrong may be made to be right and vice versa. In dealing with them, the principal point that ought to be made is not that words cannot be redefined, but that, if we should for any reason redefine sexism, then whatever case was made against what was originally called sexism isn't thereby logomantically transformed into a case against whatever is now to be called sexism, nor is a case against something that was originally called sexism somehow invalidated by ceasing to call it by that name.[2] Of course, there are also those who effect the substitution as a device of unconscious projection, and others who opportunistically seek to sow further confusion.


[1] In the absence of a coherent explanation otherwise, if any population really could be hired at bargain rates, then not only should we expect all members of that population to be hired before any members of any other population; we should expect employers to bid-up the wages and salaries of this less expensive population to the point that they matched those of other populations, before hiring any members of those other populations. If there is some occupation such that the cost of hiring workers for it is notably less than the expected values of their marginal products, then we should expect employers to increase their hirings for those occupations, and in doing so (each in competition with the others and in the face of otherwise ever more reluctant workers) to bid-up the wages or salaries of those workers until the difference disappears.

[2] The same principle of course applies to efforts to redefine racism.

On Deductibility of Local Taxes

Monday, 8 May 2017

In my field of awareness, there has recently been more discussion than usual about deductibility of constituent-state taxes and of municipal taxes from income computed for purposed of Federal taxation. I think that most of the discussion has been fundamentally wrong-headed.

In the textbooks of middle-schools, of high-schools, and of introductory courses in college on civics, on politics, or on economics, there are discussions of various proposed guidelines for taxation, based on ostensible or insinuated theories of justice. One commonly offered theory is that people should be compelled to pay based upon supposed ability; another is that they should be compelled to pay based upon the amount of services that they receive from the state.[1] I've yet to see such a discussion in such a textbook that could withstanding much critical examination.

In any case, these homilies don't serve to explain how-and-why taxation is effected in the real world, except in-so-far as some of their prescriptions are invoked to argue for a tax of one sort, even as conflicting rationalizations are offered (often by the very same people) to argue for taxes of other sorts. Historically and to the present day, taxation has been fundamentally opportunistic. That which has been taxed is whatever seemed to be most readily taxable. Targets of convenience have been wealth or income that has been thought to be easily tracked and measured, difficult to relocate outside of the jurisdiction, or for the taxation of which there is wide-spread acquiescence if not support within the community. (It is with respect to that last aspect that textbook theories have their real relevance.)

The state is not satiated by some steady extraction of wealth from the community. When extractions are greater than were expected, the state will not return the surplus to the taxpayer as such, except under extraordinary pressure; and, here-to-fore, states have always moved towards attempting to extract as much tax from their communities as the communities will suffer. This tendency is natural, as the people who make-up the state generally see their positions within society improve as they have increasing command over resources; mechanisms that exist in sectors whose rewards are determined by markets which cause participants to identify and pursue efficiencies simply have no correspondents within the state; the state is able to cultivate dependencies in the wider population; and many people imagine a very extensive rôle for the state within society (especially those people who lose sight of the distinction between the state and its subjects). The state grows ever larger and becomes ever worse at the allocation of resources, and so seeks ever greater extractions.

When, within the jurisdiction of a constituent state or within a municipality, there is greater community resistance than elsewhere to taxation, there is less taxation than there otherwise might be. That difference is a target of opportunity for a federal state, whose jurisdiction encompasses a wider community. There is a mechanism for obtaining the acquiescence of that wider community without typically triggering a significantly intensified resistance on the part of the communities subjected to a federal surtax in the face of lower taxes by other entities. That mechanism involves allowing taxpayers to deduct what taxes they pay to those other entities from the calculated worth of something that the federal state taxes; because, in the face of those deductions, parts of the wider community become less resistant to rate increases.

Let's say that people in jurisdictions A, B, and C, which are all of roughly the same size, face a federal tax of 30% on income, and that people in jurisdictions A and B face a more local 10% tax on pre-tax income, while people in jurisdiction C face a no such tax. If the federal tax is increased to 1/3 on taxable income, but local income taxes are made fully deductible, then the people of jurisdictions A and B face no net increase in income tax, and so may acquiesce; the people in jurisdiction C may thus find themselves out-voted and their taxes increased by about 3%.

A great many people imagine what thus happens is that, given deductibility of more local taxes, people in jurisdictions with lower local taxes are force to subsidize those in jurisdictions with higher local taxes; but that conclusion is spurious. It would in some sense follow if the quantity or quality of goods and services delivered by the state were well correlated with the amount of resources that it extracts from the community, but there is no such correlation, except in transitory cases in which the state deliberately impairs performance to provoke acquiescence to greater extractions. The people paying lower taxes than they otherwise might are not getting something from those paying higher taxes than would be tolerated without the mechanism of deductibility. They are simply less victimized. One would be no less mistaken in claiming that people who live in other nations with lower income taxes are ipso facto subsidized by American taxpayers.

(For purposes of economic analysis of some sorts, tax-cuts and subsidies are equivalent, but those in the jurisdictions that are less taxed by the federal state have not received a tax cut, they have instead not been subjected to tax increases imposed elsewhere. And the aforementioned equivalence holds only if either there is no prior property in resources, or the state has a prior claim on whatever resources are involved. If no one has a claim prior to taxation and subsidization, then no one is paying taxes; they are being extracted from resources that are un-owned. If the state has a prior claim, then there are again no tax-payers; there are people who are granted more or less wealth or income belonging to the state. And, if there are no tax-payers, then the tax-payers subsidize no one.)

Eliminating the deductibility of other taxes would create greater resistance to federal taxes, as some who had previously not been subjected to higher levels then would be. But not everyone thus penalized would previously have been a supporter of imposing those levels on others. Innocent by-standers would be dragged into a fight; there could not be justice in that.


[1] When I say state, I don't necessarily mean one of the constituent states of a federation such as the United States. I certainly don't mean the jurisdicational area of one of those states, nor the inhabitants of such an area. A state is an organization that successfully claims an effective monopoly of some sort in the control of violence.

Theories of Probability — Perfectly Fair and Perfectly Awful

Tuesday, 11 April 2017

I've not heard nor read anyone remarking about a particular contrast between the classical approach to probability theory and the Bayesian subjectivist approach. The classical approach began with a presumption that the formal mathematical principles of probability could be discovered by considering situations that were impossibly good; the Bayesian subjectivist approach was founded on a presumption that those principles could be discovered by considered situations that were implausibly bad.


The classical development of probability theory began in 1654, when Fermat and Pascal took-up a problem of gambling on dice. At that time, the word probability and its cognates from the Latin probabilitas meant plausibility.

Fermat and Pascal developed a theory of the relative plausibility of various sequences of dice-throws. They worked from significant presumptions, including that the dice had a perfect symmetry (except in-so-far as one side could be distinguished from another), so that, with any given throw, it were no more plausible that one face should be upper-most than that any other face should be upper-most. A model of this sort could be be reworked for various other devices. Coins, wheels, and cards could be imagined as perfectly symmetrical. More generally, very similar outcomes could be imagined as each no more probable than any other. If one presumes that to be no more probable is to be equally probable, then a natural quantification arises.

Now, the preceptors did understand that most or all of the things that they were treating as perfectly symmetrical were no such thing. Even the most sincere efforts wouldn't produce a perfectly balanced die, coin, or roulette wheel, and so forth. But these theorists were very sure that consideration of these idealized cases had revealed the proper mathematics for use across all cases. Some were so sure of that mathematics that they inferred that it must be possible to describe the world in terms of cases that were somehow equally likely, without prior investigation positively revealing them as such. (The problem for this theory was that different descriptions divide the world into different cases; it would take some sort of investigation to reveal which of these descriptions, if any, results in division into cases of equal likelihood. Indeed, even with the notion of perfectly balanced dice, one is implicitly calling upon experience to understand what it means for a die to be more or less balanced; likewise for other devices.)


As subjectivists have it, to say that one thing is more probable than another is to say that that first thing is more believed than is the other. (GLS Shackle proposed that the probability of something might be measured by how surprised one would be if that something were discovered not to be true.)

But most subjectivists insist that there are rationality constraints that must be followed in forming these beliefs, so that for example if X is more probable than Y and Y more probable than Z, then X must be more probable than Z. And the Bayesian subjectivists make a particular demand for what they call coherence. These subjectivists imagine that one assigns quantifications of belief to outcomes; the quantifications are coherent if they could be used as gambling ratios without an opponent finding some combination of gambles with those ratios that would guarantee that one suffered a net loss. Such a combination is known as a Dutch book.

But, while quantifications can in theory be chosen that insulate one against the possibility of a Dutch book, it would only be under extraordinary circumstances that one could not avoid a Dutch book by some other means, such as simply rejecting complex contracts to gamble, and instead deciding on gambles one-at-a-time, without losing sight of the gambles to which one had already agreed. In the absence of complex contracts or something like them, it is not clear that one would need a preëstablished set of quantifications or even could justify committing to such a set. (It is also not clear why, if one's beliefs correspond to measures, one may not use different measures for gambling ratios.) Indeed, it is only under rather unusual circumstances that one is confronted by opponents who would attempt to get one to agree to a Dutch book. (I don't believe that anyone has ever tried to present me with such a combination, except hypothetically.) None-the-less, these theorists have been very sure that consideration of antagonistic cases of this class has revealed the proper mathematics for use across all cases.


The impossible goodness imagined by the classical theorists was of a different aspect than is the implausible badness of the Bayesian subjectivists. A fair coin is not a friendly coin. Still, one framework is that of the Ivory Tower, and the other is that of Murphy's Law.