In the wee hours of 8 July, I rewrote my brief article on one of the proposed axiomata of probability, and sent it to a journal of statistical theory.

The principal reason for doing some rewriting was to add a paragraph reporting an interesting point made by one of my former professors. (I wish that I'd seen that point on my own, but I didn't, so I've duly creditted him.) Additionally, I tightened-up the abstract.

In the absence of being given a reason why my note was rejected by the previous journal, my conjecture is that it was considered to present what would be viewed as a technicality from the perspective imputed to the readership. So I'm turning to a journal with a different sort of readership.

Years ago, I planned to write a paper on decision-making under uncertainty when possible outcomes were completely ordered neither by desirability nor by plausibility.

On the way to writing that paper, I was impressed by Mark Machina with the need for a paper that would explain how an incompleteness of preferences would operationalize, so I wrote that article before exploring the logic of the dual incompleteness that interested me.

Returning to the previously planned paper, I did not find existing work on qualitative probability that was adequate to my purposes, so I began trying to formulating just that as a part of the paper, and found that the work was growing large and cumbersome. I have enough trouble getting my hyper-modernistic work read without delivering it in large quantities! So I began developing a paper concerned only with qualitative probability as such.

In the course of writing that spin-off paper, I noticed that a rather well-established proposition concerning the axiomata of probability contains an unnecessary restriction; and that, over the course of more than 80 years, the proposition has repeatedly been discussed without the excessiveness of the restriction being noted. Yet it's one of those points that will be taken as obvious once it has been made. I originally planned to note that dispensibility in the paper on qualitative probability, but I have to be concerned about increasing clutter in that paper. Yester-day, I decided to write a note — a very brief paper — that draws attention to the needlessness of the restriction. The note didn't take very long to write; I spent more time with the process of submission than with that of writing.

So, yes, a spin-off of a spin-off; but at least it is spun-off, instead of being one more thing pending. Meanwhile, as well as there now being three papers developed or being developed prior to that originally planned, I long ago saw that the original paper ought to have at least two sequels. If I complete the whole project, what was to be one paper will have become at least six.

The note has been submitted to a journal of logic, rather than of economics; likewise, I plan to submit the paper on qualitative probability to such a journal. While economics draws upon theories of probability, work that does not itself go beyond such theories would not typically be seen as economics. The body of the note just submitted is only about a hundred words and three formulæ. On top of the usual reasons for not knowing whether a paper will be accepted, a problem in this case is exactly that the point made by the paper will seem obvious, in spite of being repeatedly overlooked.

As to the remainder of the paper on qualitative probability, I'm working to get its axiomata into a presentable state. At present, it has more of them than I'd like.

I've never voted in a General Election for a Republican Presidential nominee; and, the one time that I registered as a Republican, it was to vote against Ronald Reagan in the 1980 primary election by voting for a candidate who had withdrawn. One may fairly conclude that I was anti-Reagan; I remain so. But I was-and-am also anti-Carter and anti-Mondale; indeed, I have never voted in a General Election for a Democratic Presidential nominee. And my dog in the fight over Reagan's legacy is truth as such, not the development or defense of one of the narratives of either of the two major political tribes.

Part of the conventional narrative of progressives and of Democrats is that our problem of homeless people became a crisis as a result of a ruthless expulsion of mentally ill people from hospitals, by the Reagan Administration, simply to save money. One problem with this part of that narrative was that, at the time that people were being deïnstitutionalized, there was very little in the way of protest from the other tribe, nor much from any other part of the political continuum.

The forceable incarceration of the mentally ill simply for being mentally ill was and remains deeply problematic; it operationalizes as the criminalization of victimless behaviors. Further, like almost every other state programme (essential or otherwise), actual practice bore little resemblance to supportive pontifications by educators and by journalists, regardless of which party were in power. The captivity of the mentally ill was a great injustice, which many progressives, classical liberals, and indeed conservatives wanted to see ended. Not a lot of thought was given to what was to happen to the inmates upon release.

Some of these people had been getting-by before they were locked-up. But the problem now was that the structures that they had earlier found or created in order to get-by were largely demolished by their incarceration. They had spent months or years — sometimes many years — in an peculiar society in which all or nearly all of the people around them were ill-adapted to ordinary life. Most of the possessions of those deïnstitutionalized had been dispersed or destroyed during their institutionalization. The victims didn't have homes. Those released had the stigma of having been locked-up. But, no, few people, regardless of ideological commitments, had much considered what the incarceration itself implied for the ability of the incarcerated to reädapt to the outside world.

We have a very similar problem coming upon us even as I write. It's not coming at us so fast or so slowly that the speed-of-approach should blind anyone; but none-the-less almost everyone is again blind, regardless of ideological commitment.

Our nation may be moving in the general direction of decriminalization of drug-crimes. Some constituent states are decriminalizing marijuana, and the Federal state seems to be allowing that decriminalization. The Presidential Administration is looking to scale back the penalties for crimes involving crack cocaine. And these changes ought to be happening. Consenting adults ought to be able to buy and ingest whatever they want. (Unfortunately, contrary to the apparent trend of decriminalization, many progressives are looking to outlaw tobacco products and to turn sugars into controlled substances.)

But with decriminalization would come the release of a great many institutionalized people. Once again, those released would have spent months or years or even many years in an environment where most of the people around them were ill-adapted to ordinary society. Most of their possessions would have been dispersed or destroyed. Many wouldn't have homes. They'll confront the stigma of having been imprisoned. (If they don't report their imprisonments on job forms and rental applications, then they'll have large, unexplained gaps in their histories!)

I don't offer you a solution to the problems to come. If the progressives wake-up to the problems before any large-scale release, then they'll devise some scheme of half-way houses that in practice will bear little resemblance to progressive theory, and assuredly victimize tax-payers.

No matter what, narratives will be formulated that obscure the current failure to anticipate a predictable, large-scale problem.

It is recurringly claimed that omission and commission are morally equivalent, that failing to assist someone is as blameworthy as injuring that person. But, were that really the case then, by the same token, failing to injure someone would be as every bit as laudable as acting to prevent his or her injury by some other agency. The man who did not kill a random stranger upon whom he chanced would be as much the hero as one who rushed in to save one stranger from another.

I've previously touched on the matter of there being markèdly differing notions all associated with the word probability. Various attempts have been made by various writers to catalogue and to coördinate these notions; this will be one of my own attempts.

[an attempt to discuss conceptions of probability]

I don't know that 'Net-neutrality were, in fact, a good thing; but, even on the assumption that it were, state action is not the proper way to promote it.

'Net-neutrality can be promoted by how people do business with ISPs. At one end, subscribers can consistently migrate towards those ISPs who deviate least from neutrality. At the other end, website owners can impede access by ISPs that do not practice an acceptable degree of neutrality.

In fact, Google and Facebook could effectively impose neutrality by announcing that, in one year, they would begin blocking access by providers who did not make pledges, renewed annually but each extending for ten years, to practice 'Net-neutrality. It might, however, require state inaction for these heavy-hitters to make such a demand. Specifically, Congress might need to clear a path in anti-trust law to allow such a policy.

I started reading Rethinking the Western Understanding of the Self by Ulrich Steinvorth, and in its first chapter came upon this passage

As subjects we desire satisfaction of our desires; as selves we strive for the enactment of reason and free will.

(Underscore mine.) It is not auspicious to find a claim of this sort early in the work.

To say that something desires the satisfaction of its individual desires is no more than to say that it desires what it desires; nothing fails to do this, as things without desire present us with the trivial case of a null set.

The pursuit of satisfaction of each individual desire does not logically entail global satiation of desires (bliss) unless those desires are themselves somehow bounded. It's not clear what Steinvorth means by desire (a point that I will labor), but let's assume that he means something along the lines of uncontemplated cravings and the things that are craved, as for sensual pleasures or for hoards of material goods. I don't see that they're naturally bounded. I don't see that most people make a presumption, one way or another, about whether such cravings are bounded. The impulse to bound them by attaining ἀπάθεια or nirvana seems far from universal to me (and anyway is probably not an expression of what Steinvorth calls subject, but of what he calls self).

It's evident that he wants to distinguish desire as a verb from one more generally meaning to have a directed psychological impulse, and as a noun from one more generally meaning objective; but nowhere prior has Steinvorth given a definition of desire, as noun or as verb; the remainder of the chapter and use of the index indicate that he's not going to do it at all. I see declarations such as X desires the satisfaction of X's desires as the unconscious attempt to fill the need for a definition with a logically unassailable tautology. (Simply say X desires and the need for definition is more apparent.) The problem is that the latter cannot do the work of the former, and the tautology is vacuous.

It's further evident from the first chapter that Steinvorth wants to distinguish happiness from a noun simply meaning an emotional sense of attaining or of having attained one's objectives; and to distinguish utility from a noun simply meaning usefulness. One can tell that he means to equate or approximate what he means by happiness with what he means by utility. But nowhere in the first chapter does he actually provide more positive definitions. He does insist that if we consider such things as the glory of suffering to be a form of happiness then the idea of happiness becomes inflated and loses its meaning, but I want to know what meaning it would lose. Again using the index, it doesn't seem that he bothered with providing any of these definitions anywhere else in the book.

Time is measured by sequences of changes. Classic examples of sequences that have been used are beats of the heart, apparent positions of the sun and of the moon, and the solstices. In theory, any sequence might be used.

When one measure of time is gauged against another, it is ultimately a matter of counting how many changes of each sort occur. When the rate of some different changes seems to be constant relative to those by which time has been measured, if these different changes occur in greater number then it may be decided to substitute these changes as the primary measure of time, and thus have a finer-grained measure.

Speeds and frequencies are not normally recognized as conversion factors for measures of time against each other, but that is exactly what they are. In the case of speeds generally, the changes are quantifications (of physical position, perhaps). In the more specific case of frequencies, one has a sequence of changes that are attainment of — or departure from — what is regarded as a recurring state; a count of these attainments or departures might be quantified as a pure number.

To say that some changes take place at a constant rate over time is simply to say that there is an invariant correspondence between the number of the changes by which we measure time and the number of the changes whose rate is being measured.

Such constancy occurs trivially when the changes that are used to measure time are measured against time — they're just being measured against themselves. If time is measured by appearances of the sun above the horizon, then the conversion factor for the frequency with which the sun appears above the horizon is necessarily 1. If we use these appearances to meaure the frequency with which the heart beats, that frequency will almost certainly be inconstant; but if we use heart-beats as our measure of time, then their frequency will necessarily be 1 (and the frequency with which the sun appears will almost certainly be inconstant).

If someone should ask about using the average rate at which the heart beats as the measure of time, then he or she is implicitly presuming something other than heart-beats in measuring them, or their average frequency will necessarily be 1. Any comfort in imagining that the reference changes are being averaged is a comfort in confusion.

Someone else will insist that it is obvious that the rate at which any reference-heart beats is objectively inconstant, but it is no such thing. Rather, the convenience for the formulation of descriptions of the world around us of some measures is so limited, and that of others so pronounced as to make it seem that some are closer to objective constancy than are others.

If the measure of time were in terms of Scott's heart-beats, then his mood would figure into descriptions of the universe (the rest of the world would be slower when Scott were excited), and we'd need his pulse whenever we timed things (in particular, all other changes would happen infinitely fast after Scott died). These characteristics make Scott's heart-beats grossly inconvenient for everyone excepting, perhaps, Scott.

What one wants of measures of time are accessibility, for them to result in manageable descriptions of rest of the world, and for them to not to deviate intolerably from our subjective experiences of time. There is a certain amount of rivalry at least between the first two desiderata. Those measurements that are most easily made don't correspond to the simplest descriptions of the rest of the world. But some measurements of time result in many fairly simple descriptions (some of those descriptions are even of other rates as constants) that appear perfectly accurate. It is the latter sort of measurement that is mostly likely to be taken as objective, but if the measurements that supported the simplest statements of physical laws made a very poor fit for subjective experiences of time, then these measurements would not widely be accepted (even by scientists) as measurements of time at all, objective or otherwise!

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We're often told that the speed of light (in vacuo) is constant. Many people wonder why this constancy is so; others whether it is so. But what is actually meant by the assertion itself that the speed of light be constant is that the changes in the position of light maintain a fixed ratio with the changes by which we have chosen to measure time. In effect, those (such as Einstein) who said that this speed were constant were declaring that we ought to measure time in a manner that made the speed of light constant. And the reason that we ought to measure it thus was because accurate descriptions of the behavior of things of interest would be as simple as possible (or, at the least, as simple as possible without resulting in a measure unrecognizable as time).

The real question is not of why or whether the speed of light is constant; the real question is of why treating it thus simplifies accurate descriptions. And the basic answer is because light and stuff very much like it do a lot. One whoozit affects another by way of that stuff.

Of course, that basic answer shouldn't satisfy anyone with more than passing curiosity. My point is just that the idea that the speed of light is constant doesn't represent a mystery of the sort that many people take it to be.

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This entry was primarily motivated by my desire to get the point about the constancy of the speed of light off my chest, but the more general part of it actually has application to questions of method in economics.

When I was in the graduate programme at UCSD, there was a student who wanted to do some sort of econometric work where the changes by which time were measured would be transactions, rather than ticks of an ordinary clock — he called this alternate measure market time. (I don't know whether he arrived at the concept or at this term on his own, but he didn't cite a prior source.) Sadly, his initial presentation was a disaster; when he attempted to explain this idea to the professors who were to judge his work, he came across to them and to most of the rest of the audience as incoherent. I might well have been the only other person in the room who really understood what he was trying to say. (I had for some while been thinking skeptically about the propensity of economists to use the physicists' t.)

Afterwards, I sat down with him and tried to explain to him what he had to communicate; but he seemed not to listen to me as he insisted that the response of the professors were unfair. And, the next time that he gave a presentation on the idea, he essentially repeated his previous performance.

It is at least plausible to me that a major part of the reason that he could not communicate what he was proposing to do was that he had only a vague intuïtion about the nature of measures of time and about distinctions amongst them.

I would note that the particular measure of time that he suggested is certainly not the one for economists to use in all or even most cases, and that it has never been one that had distinctively useful application to a problem that I've investigated.

Yester-day, I finished reading the 1969 version of Choice without Preference: A Study of the History and of the Logic of the Problem of Buridan's Ass by Nicholas Rescher, which version appears in his Essays in Philosophical Analysis. An earlier version appeared in Kantstudien volume 51 (1959/60), and some version has or versions have appeared in later collections. I have only read the 1969 version, and some of the objections that I raise here may have been addressed by a revision.

The problem of Buridan's ass may not be familiar by name to all of my readers, but I imagine that all of them have encountered some form of it. A creature is given a choice between two options neither of which seems more desirable than the other. The question then is of how, if at all, the creature can make a choice. In the classical presentation, the creature is a donkey or some other member of the sub-genus Asinus of Equus, the choice is between food sources, and a failure to make a choice will result in death by starvation. The problem was not first presented by the Fourteenth-Century cleric and philosopher Jean Buridan, but it has come to be associated with his name. (Unsurprisingly, my paper on indifference and indecision makes mention of Buridan's ass.)

Rescher explores the history of the problem, in terms of the forms that it took, the ultimate purposes for which a principle were sought from its consideration, and the principles that were claimed to be found. Then he presents his own ostensible resolution, and examines how that might be applied to those ultimate purposes.

One of the immediate problems that I have with the essay is that nowhere does Rescher actually define what he means by preference. I feel this absence most keenly when Rescher objects that there is no preference where some author and I think there to be a preference.

As it happens, in my paper on indifference and indecision, I actually gave a definition of strict preference: which is to say that X₁ is strictly preferred to X₂ if X₂ is not in the choice made from the two of them.[1] So, in that paper, strict preference really just refers to a pattern of choice. I didn't in fact define choice, and I'll return to that issue later.

The Merriam-Webster Dictionary essentially identifies preference as a gerund of prefer, and offers two potentially relevant definitions of prefer:

1. to promote or advance to a rank or position
2. to like better or best

The first seems to be a description of selection as such. The second might be taken to mean something more. But when I look at the definition of like, I'm still wondering what sense I might make of it other than an inclination to choose.

I'm not claiming that Rescher is necessarily caught-up in an illusion. Rather, I'm claiming, first, that he hasn't explained something that is both essential to his position and far from evident; and, second, that his criticism of some authors is based upon confusing their definitions with his own.

When I used the notion of a choice function C( ) in my paper, my conception of choice was no more than one of selection, and that's what I was unconsciously taking Rescher to mean until, towards the end of his essay, speaking of decisions made by flips of coins (and the like), he writes

In either event, we can be said to have "made a choice" purely by courtesty. It would be more rigorously correct to say that we have effected a selection.

Well, no. This isn't a matter of rigor, whatever it might be. The word choice can rigorously refer to selection of any sort. It can also refer to selection with care of some sort, which seems to be what he had in mind.

Some of the authors whom Rescher cites, and Rescher himself, assert that when a choice is to be made in the face of indifference, it may be done by random means. Indeed, Rescher argues that it must be done by such means. But he waits rather a long time before he provides any explicit definition of what he means by random, and he involves two notions without explaining why one must invoke the other, and indeed seemingly without seeing that he would involve two distinct notions. When he finally gives an explicit notion, it to characterize a choice to be made as random when there is equal weight of evidence in favor of each option. However, when earlier writing of the device by which the selection is to be made, he insists

The randomness of any selection process is a matter which in cases of importance, shall be checked by empirical means.

Now, one does not test the previously mentioned equal weight of the evidence by empirical means. An empirical test, instead, adds to the fund of evidence. We can judge the weight of the present evidence about the selection device by examining just that present evidence. The options are characterized by equal plausibility, yet Rescher has insisted that the selection device must instead be characterized by equal propensity. It isn't clear why the device can't simply also be characterized by equal plausibility.[2]

Rescher makes a somewhat naïve claim just before that insistence on empirical testing. For less critical choices, he declares

This randomizing instrument may, however, be the human mind, since men are capable of making arbitrary selections, with respect to which they can be adequately certain in their own mind that the choice was made haphazardly, and without any reasons whatsoever. This process is, it is true, open to possible intrusions of unrecognized biases, but then so are physical randomizers such as coins.

Actually, empirical testing of attempts by people to generate random numbers internally show very marked biases, such that it's fairly easy to find much less predictable physical selectors.

Rescher's confusion of notions of randomness is entangled with a confounding taxonomy of choice which is perhaps the biggest problem with Rescher's analysis. The options that he allows are

1. decision paralysis
2. selection favoring the first option
3. selection favoring the second option
4. random selection, in which random entails a lack of bias

And, proceeding thence, he seems to confuse utterly the notion that choice without some preference somewhere is impossible with the notion that choice without some preference somewhere is unreasonable. In any case, Rescher insists that only the last of these modes of selection is reasonable, and this insistence would tell Buridan's ass that it must starve unless it can find a perfectly unbiased coin![3] Reason would be a harsher mistress than I take her to be!

Another term that Rescher uses without definition is fair and its coördinates, as when he writes

Random selection, it is clear, constitutes the sole wholly satisfactory manner of resolving exclusive choice between equivalent claims in a wholly fair and unobjectionable manner.

I certainly don't see that random selection should be seen as wholly satisfactory (though I believe it to often be the least unsatisfying manner), and I don't know what Rescher imagines by fair. My experience is that when the word fair is used, it is typically for something more appealing than justice to those inclined to envy. In the case of allotments by coin-flip, there may be no motivation for envy ex ante, but things will be different ex post. People do a great deal of railing against the ostensible unfairness of their luck or of that of another.

I recall one final objection, which moves us quite out of the realm of economics, but which I have none-the-less. One of the applications of these questions of choice without preference (or, at least, without preference except stemming from meta-preference) has been to choices made by G_d. In looking at these problems, Rescher insists that G_d's knowledge must be timeless; I think that he ought to allow for the possibility that it were not.

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[1] That might seem an awkward way of saying that X₁ is strictly preferred to X₂ if only X₁ is in the choice from the two of them, but it actually made the proofs less awkward to define strict preference in this odd manner.

[2] Even if one insists that the selection device must be characterized by equal propensity, there is in fact little need for empirical testing, if one accepts the presumptions that a coin may be considered to have unchanging bias and that flips of a coin may be independent one from another. Implicitly making these assumptions, my father proposes a method for the construction of a coin where the chances of heads and of tails would be exactly equal. One starts with an ordinary coin; it comes-up heads sometimes, and tails others. Its bias is unknown; at best approximated. But, whatever the bias may be, says my father, in any pair of flips, the chances of heads-followed-by-tails are exactly equal to the chances of tails-followed-by-heads. So a pair of flips of the ordinary coin that comes-up heads-tails is heads for the constructed coin; a pair of flips of the ordinary coin that comes-up tails-heads is tails for the constructed coin; any other pair for the ordinary coin (heads-heads, tails-tails, or one or both flips on edge) is discarded.

[3] I don't know that my father could explain his solution to a donkey. I've had trouble explaining it to human beings.

I'm going to step into a debate that no one has asked me to join, concerning the implications of a belief system that I reject.

In Matthew 12:31, Jesus declares that there is exactly and only one unforgiveable sin, and that is to blaspheme against the Holy Spirit. (It would here be tangential to discuss why he declared such a thing; the relevant point is that he said it.) Every other sin is declared to be forgiveable.

So let's apply that proposition to an issue about which the 'Net has been stupidly buzzing — suicide. A clergyman's son has killed himself, and some are insisting that this son is necessarily going to Hell, or at least that Christianity must hold as much. But how, exactly, can the act of suicide, if indeed a sin, be both forgiveable and at the same time ensure that one goes to Hell?

If, between every suicidal act and actual death, there were opportunity to regret and to repent, then perhaps this would be the way to forgiveness; which would of course imply that suicide weren't unforgiveable. But it seems that, in some cases, there just isn't enough time. Yet, somehow, if the act is a sin, it has to be forgiveable, even without the possibility of post factum repentance in this life. We must therefore conclude that, within Christian doctrine, either suicide is not a sin at all (which appears doubtful, in that the prohibition against homicide doesn't seem to make an exception for killing oneself), or that it is a forgiveable sin — that a person who'd otherwise been saved would not be lost for having deliberately killed him- or herself — which sin doesn't even require specific repentance in this life.

(I'm acutely aware that there are those who will claim that to commit suicide is, really, to blaspheme against the Holy Spirit. In other contexts, I've heard some people go so far as to claim that any sin is, really, every sin. But, if this sort of logic holds, then the claim of Jesus that blasphemy against the Holy Spirit were an exception wouldn't. There would be nothing operational to the rule but that exception, and everyone would be going to Hell, regardless of works and of faith. The notion that people somehow more greatly insult the Holy Spirit by killing themselves than by other homicides or by other sins more generally is in sore need of more than hand-waving accompanied by beatific smiles or by stern looks.)

The mainstream Christian doctrine that suicide is a sure route to Hell just isn't supported by their Holy Scriptures. It arose because the existence of the Church here on Earth was threatened by the possibility of believers attempting a short-cut to Paradise. The Earthy flock would be reduced in number, and questions would be asked about the sincerity of those who lingered.