As expected, my brief paper was quickly rejected by the third journal to which I sent it. The rejection came mid-day on 19 July; the editor said that it didn't fit the general readership of the journal. He suggested sending it to a journal focussed on Bayesian theory, or to a specific journal of the very same association as that of the journal that he edits. I decided to try the latter.

On the one hand, I don't see my paper as of interest only to those whom I would call Bayesian. The principle in question concerns qualitative probability, whether in the development of a subjectivist theory or of a logicist theory, and issues of Bayes' Theorem only arise if one proceeds to develop a quantitative theory. On the other hand, submitting to that other journal of the same association was something that I could do relatively quickly.

I postponed an up-date here because I thought that I'd report both rejections together if indeed another came quickly. But, so far, my paper remains officially under review at that fourth journal.

The paper is so brief — and really so simple — that someone with an expertise in its area could decide upon it minutes. But reviewing it isn't just a matter of cleverness; one must be familiar with the literature to feel assured that its point is novel. A reviewer without that familiarity would surely want to check the papers in the bibliography, and possibly to seek other work.

Additionally, a friend discovered that, if he returned papers as quickly as he could properly review them, then editors began seeking to get him to review many more papers. Quite reasonably, he slowed the pace of at which he returned his reviews.

The second journal to which I submitted my brief article quickly rejected it (on 11 July) as being unsuited to their readership, and suggested that it may be that your work would be better directed to a journal specialising on statistical theory, or foundations/philosophy. (The journal to which I submitted arguably is one of statistical theory; but it leans heavily towards review rather than towards innovation.)

As 13 July neared its end, I submitted to yet another journal. This time, I'm pretty sure that I'm playing a long-shot, but a rejection should come very quickly if it comes, the paper would get relative many readers if were published there, and people in and around my field would be impressed; so I think that the gamble is a good one.

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 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 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.

Yester-day evening, I was using a publicly accessible WLAN to connect with the Internet. I found my access to this 'blog blocked by a Norton-branded product, which declared the 'blog to be pornographic.

Erotica really hasn't figured large in this 'blog. You can find the relevant entries with the tag erotica. I think that the two or three entries that caused Norton to damn this thing are specifically my entry of 2 July 2009, my entry of 26 March 2010, and perhaps my entry of 30 June 2010; the entry of 30 January 2011 may have weighed against me as well.

Of these, the entry of 2 July 2009 is the one that most likely set-off alarms. It contains an overtly erotic image (by Carolyn Weltman), and has a key-word of cunnilinctus.[1] Do a Google image-search using that key-word, and a link to that entry is currently the second returned. And, because of a couple of the other key-words in that entry, other images are also found, including one by Karel Šimůnek than many would regard as pornographic.

In the '50s, the drawings by Joe Shuster in the entry of 30 June 2011 would have been regarded as pornographic, though now the word pornography would typically be regarded as too strong. (Actually, a hundred years ago, many would have insisted that the picture in my entry of 2 February 2011 were pornographic, while now-a-days it could appear in a children's book without fuss.) Still, the text in that entry contains the term sado-masochistic and there are pictures, and Norton's classification was probably mediated with weak AI; indeed, once other flags were thrown, the appearance of the word dominatrix in a follow-up entry may have been seen as further PoP.

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Most WLANs that filter do so by way of a DNS table. When a browser seeks content located in terms of a URI or of a URL, and that specification includes a domain name, the domain name is converted to an IP number by way of a DNS table. By censoring the table that is used, the WLAN can block domains.

Some people subvert this censorship by way of a proxy server, which is no more than some site that will act as an intermediary; fetching content from the blocked domain. The obvious problem here is that the proxy may be identified and blocked as well.

A better subversion is to use a different table than whatever is being supplied by the WLAN. In particular, one may configure one's system to use DNS tables provided by Google, or perhaps by some other third party. But be alert that using an alternative DNS table may not be a good idea in other contexts. (For example, when using a subscription ISP that places quotas on content for most sites, but with exceptions.)

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[1]The words cunnilinctus and cunnilingus are synonymous in English and in some other languages; but in Latin cunnilinctus referred to the act, while cunnilingus referred to a performer of that act. The latter word acquired its more recent meaning as a result of incompetent posturing (something that has figured more than once in attempts to borrow foreign terms and phrases). Efforts to clean-up this particular mess have repeatedly failed, but I avoid participating in it, by using the word that is both proper English and proper Latin. Hence my use of the less common term.

The term ambiguity is often applied to matters that are in fact not at all ambiguous. Sometimes the mis-application is simple carelessness, but in one application it is hard not to see a more active perversion.

Characters (fictional or actual) who are called morally ambiguous almost never are. Instead, the label is most often applied to characters of two sorts.

One sort is morally compromised. Those characters are not all bad; they may even be mostly good; but they are discernibly not all good. The person labelling them as morally ambiguous typically very much seems to be trying for special pleading if a sort on behalf of the character or of the moral short-comings exhibited by the character.

The other sort exhibits a combination of characteristics, some of which the audience will find attractive but some of which the person applying the label finds disagreeable, without his or her being able to make a sound case (or seemingly sound case) against those traits. By labelling the character as morally ambiguous, the labeller is insinuating doubt without reasoned foundation. Challenged, he or she will likely deny having issued a condemnation of the characteristics against which he is directing that doubt.

In application to situations, the term moral ambiguity is more likely to be legitimately applied than in application to characters. But calling a situation morally ambiguous is also often an attempt to introduce by back door a special plea for bad behavior.

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(One of the papers on which I am presently working, and the paper of that lot that is likely to end-up the least mathematical, compares and contrasts some decision-theoretic states that are often mistaken one for another. One sort of these states entails ambiguity. So I have been thinking about real and specious ambiguity more generally.)