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.)

When I went for dinner, I encountered someone slipping into madness. He was polite and pleasant, but going mad.

He was fixated upon improving the world globally. I don't know whether he were going mad because he wanted somehow to improve the world globally, or were obsessively focussed upon improving the world globally because he was going mad; my guess would be that the aspiration and the madness were each feeding upon the other. In any case, he was writing and drawing chaotically with bright marker on loose sheets of paper, and trying to engage random people in his efforts to figure-out How to Save the World. I was a random person.

I sometimes talk to madmen. No less or more comes out of my conversations with them than those with most other people. In this case, I wasn't much occupied at the time with anything else but eating.

He found talking with me to be discouraging. It's not that I don't think that the world might be saved, or that I might do something towards that end. It's that I think that most people, mad or otherwise and including him, fundamentally misconceive the nature of the problem and the potential methods of solution. The Good isn't subject to arithmetic; concern for others is no guarantee against actions that produce horrific outcomes; the meek are capable of over-estimating what can typically be done and thence what they can do; and any attempt to call a convention of the best-and-brightest in each field would attract a different sort (or none at all).

He took his madness to a different table.

I am making freely available a PDF file of Zahl und Mass in der Ökonomik: Eine kritische Untersuchung der mathematischen Methode und der mathematischen Preistheorie (1893), by Andreas Heinrich Voigt, which is encoded as text rather than as graphics.

I wanted a transcription for my own purposes — a resource that might be used for a paper on which I am working — and decided that I should make it available to other researchers, and do a proper job of its assembly.

Up-Date (2020:04/09): I have made the first-pass of an English-language translation as Number and Measure in Economics: A Critical Examination of Mathematical Method and of Mathematical Price Theory.

Without some basis in fact — without at least a basis in the recognized structure of reality on some general level — fiction would instead be gibberish. And most fiction involves considerable factual elements — it describes a familiar world and may even involve passing reference to specific, familiar, real-life persons. Some fiction makes more than passing reference.

Satire normally involves more literal truth than does ordinary fiction. because some element of the real-world is a target,[1] perhaps for purposes of commentary or perhaps merely as an opportunity for absurdity.

Harlan Ellison has sometimes asserted that he might be called a paid liar. He does, after all, state things as if they were true that he knows to be false. But his fiction doesn't quite fit the ordinary notion of lying. Under this notion, to lie is to make a statement which one knows to be false, and to make it with intent to deceive. Ellison makes false statements, but presumably expects his readers to identify the fiction as such, and hence not to be deceived. Backing-up, the key is not merely that the false statement is presented in just any way as if true, but in a manner that one might hope and expect to be presuasive. Even if we should insist that any statement that one knows to be false would constitute a lie, clearly there is an important difference between willfully false statements which are hoped to mislead and those which are expected to be treated as falsehoods.

Sometimes the author of fiction relies upon immediate context to indicate the work as fiction — the work is wrapped (as by the label novel). In other cases, the content is sufficiently at odds with expectations that it would not be believed by anyone with at least an ordinary degree of rationality.

Satire — genuine satire — reveals its fictional content, as distinct from its factual content, in that the fictional component is presented to amuse by violating established expectations, while the non-fictional component does not itself seem an attempt to be funny.

Unfortunately, this convention, like many social institutions, is not consciously discerned by most of those who rely upon it, and that lack of awareness creätes an opportunity to use ostensible satire as a vehicle for deception. If one insinuates false-yet-unamusing assertions within a work, these may be taken as part of the factual component by a large share of the audience. If someone should protest that false statements are being presented as fact, that someone can be dismissed as ignoring that the work be satirical. (This dismissal will be more effective if the work also has falsehoods that few would take seriously.) Few people will be positioned to respond that genuine satire does not present deliberate falsehood as fact is presented. And so purported satire becomes a vehicle for deliberately false statements made with the intent to deceive. Lying is labelled satire, and ordinary defenses fail against it.

The use of ostensible satire to lie has been very popular since the rise of the Baby Boom Generation. But it's not as if one can give a public lecture on how to lie in this manner without undermining the device. In consequence, a lot of people are using it to lie without quite understanding how and why it works; others, more oblivious, have concluded that all these falsehoods really have been amusing, and imagine that when they too string-together falsehoods, these must likewise be amusing.

Yester-day and to-day, there was a fiasco on the American political left. First, Roger Simon made what seems an attempt to satirize the circumstances of Paul Ryan. The attempt was perhaps sincere, but it's hard to find much funny in it. And it was taken to be mostly factual by some of Simon's own tribe, including various prominent members. Tobin Harshaw is blaming this confusion on the literalism of Americans, but the primary cause is not so much literalism as it is the degeneration of the concept of satire.

(Of course, I expect those on the left who believed Simon's claims to attempt to excuse themselves by claiming that the political right has become so absurd that it is practically impossible to tell fact from fiction.)

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[1] The real thing satirized may be a story or idea of something that is itself unreal; but, without some real referent (such as a story or idea), one does not have satire.

Yester-day or this morning, I encountered yet another instance of argumentation over what Keynes really meant in The General Theory of Employment, Interest and Money. I don't plan to labor here what I believe that Keynes intended to say; rather I want to draw attention to something about many of these arguments over the meaning or intention of some works.

When I consider the meaning or intention of the works of people who in turn attempt to interpret something else, I regard my interpretation of their interpretation as concerned with thought as such; I am thinking about how someone is or was thinking; my interpretation might be informed by my own understanding of the subject about which they thought, but the interpretation is of their thought.

It's good to know what any one of these people intended to say; it's good to know what they actually did say (whether intended or not); but it's almost always more desirable to have best approximations of the truth about which they ostensibly spoke than to have best approximations of the claims that they intended to make. It is a fortunate error when someone gets closer to the truth about the underlying subject by misinterpretting the work of someone who was mistaken about that subject. And, if one simply doesn't know which interpretation to make, but finds the truth amongst the possibilities, then there isn't even a positive misinterpretation.

It's different when one is attempting to interpret words which themselves impose rules, as in the cases of legislation, of formalized games, or of works of fiction. In those cases, the words creäte the relevant reälity.

Some people believe in prophets. By prophet I do not mean simply a forecaster, but a person through whom G_d (or something like G_d) speaks (perhaps about the future, but perhaps not). Amongst ostensible prophets I would count those believed to have a direct knowledge of external reälity, unmediated by the senses. Unsurprisingly, I do not believe in prophecy.

But, if one does believe in prophecy, then it makes sense to concern oneself with its meaning as-if resolving its meaning were the same thing as getting a best approximation of the underlying subject — because, indeed, prophecy would be just that best approximation. Of course, I take exception to the presumption that this-or-that work were holy scripture; but I take rather greater exception to an unacknowledged presumption to such effect.

And that brings me to what is so wrong with so many of the arguments about what Keynes really meant: Too many of the participants are perfectly sure that, whatever he really intended, it must have been right, and that it is for this reason that we must discover what he intended. One sees even more of this sort of thinking in debates about what Marx really meant. And I've seen basically the same thing in discussions about what Ayn Rand really meant. These three (and various others) are unacknowledgedly being treated as prophets. As far as I'm concerned, in such cases discussion has run off the rails.

Now, there are those who would insist that Marx, by way of dialectical reasoning, or Rand, by way of thorough-going objectivist epistemology, could apprehend things so very clearly that we should just take for granted that, indeed, whatever they said must be right. But those propositions each would strike me as highly dubious even if I didn't already possess what I regard as counter-proofs. (Certainly there would seem to be a claim of personal infallibility or a fallible claim on the part of whomever were testifying to the infallibility of Marx or of Rand.) And I've not encountered even that much of an argument for treating Keynes as if he were a prophet. (I have seen his economic intuïtion championed by reference to his having made a fortune investing in stocks, but I wasn't much persuaded by this argument even before I learned that, earlier, he had faced financial ruin through such investments, and been rescued by his father.)

[This entry may be superfluous, in that people who fall for any of the fallacies discussed are unlikely to read the entry, people who employ one of the fallacies are unlikely to reform if they do read the entry, and people who recognize that fallacies are involved may not see much use to analyzing them.]

I often encounter an argument, whose form is

P does A₁;
A₂ is better than A₁;
therefore it would be acceptable/desirable for P to do A₂.

It's easy to find P, A₁, and A₂ such that the intuïtion recoils from the conclusion that

it would be acceptable/desirable for P to do A₂.

and, in the face of such intuïtions, most people will acknowledge the non sequitur (acknowledged or otherwise) in the argument. We could even add a further premise, that

P ought to be persistently active (if not necessarily in their present manner).

and still find P, A₁, and A₂ such that the intuïtion recoils from that conclusion. (Consider that non-profit institutions do facilitate child abuse, and that child abuse is worse than many other things that are still themselves unacceptable.)

Yet one encounters this argument frequently with P as the state, A₂ is something that somebody wants done (such as space exploration) and A₁ is something disturbing that the state is doing or has done recently.

A variation on this can be found with form

P₁ approves when P₂ does A₁;
A₂ is better than A₁;
therefore P₃ should not object to P₂ doing A₂.

A non sequitur is evident in cases where P₃ is plainly no subset of P₁; but this argument is often presented in a manner so as to obscure a distinction, as when an everyone or a no one is used as-if loosely (which is to say inaccurately) in the first premise, but P₃ is some person or group of persons who aren't actually in the set labelled everyone or actually are in a non-empty set labelled no one.

However, this argument is fallacious even when P₃ simply is P₁. There may in fact be an incoherency in approving of A₁ while objecting to A₂, but that inconsistency could be resolved by changing one's position on A₁. For example, if forcing people to pay for birth control is better than forcing them to pay for war with Iraq, then perhaps someone who objects to the former should cease approving of the latter, rather than embracing the former.

(And resistance from P₁ to coherence wouldn't itself license A₂ when A₂ victimizes yet some additional party P₄. One doesn't force atheists to distribute copies of Al Qu'ran on the grounds that neoconservatives would object to such distribution even while supporting worse things.)

Sometimes one even sees an argument of the form

P₁ does not object when P₂ does A₁;
A₂ is better than A₁;
therefore P₃ should not object to P₂ doing A₂.

Variations of this even go so far as to replace objection with more active opposition.

P₁ does not actively oppose P₂ doing A₁;
A₂ is better than A₁;
therefore P₃ should not actively oppose P₂ doing A₂.

The appeal for those who present these arguments is that, if they were accepted, then almost no A₂ could be practicably challenged, as the objector could be dismissed for not having tackled each and every greater evil.

Of course, if this argument held, then it could virtually always be turned around against the claimant. For every P₂ and A₂, there is a P'₂, A'₁, and A'₂ such that A'₂ is the supposed ill addressed by A₂, P'₂ effects A'₂, and A'₁ is some greater ill effected by P'₂. In other words, even if A₂ were good, it would itself almost never address the greatest evil, so that there would always be something else that one would be required to do before ever getting to A₂.

On Sunday, 27 May, I received a pair of e.mail messages announcing formal acceptance for publication of my paper on indecision, and I ceased being braced for rejection. From 15 June, Elsevier had a version for sale on-line (first the uncorrected proof, then the corrected proof, now the version found in the journal). The issue itself (J Math Econ v48 #4) was made available on-line on 3 August. (I assume that the print copies will be received by subscribers soon.)

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Reader may recall that, not very long ago, I was reading A Budget of Paradoxes by Augustus de Morgan, and that when de Morgan used the term paradox he did not use in in the sense of an apparent truth which seems to fly in the face of reason, but in the older sense of a tenet opposed to received opinion. De Morgan was especially concerned with cases of heterodoxy to which no credibility would be ascribed by the established mainstream.

Some paradoxes would later move from heterodoxy to orthodoxy, as when the Earth came to be viewed as closely approximated by a sphere, and with no particular claim to being the center of the universe. But most paradoxes are unreasonable, and have little chance of ever becoming orthodoxy.

I began reading de Morgan's Budget largely because I have at least a passing interest in cranky ideas. But reading it at the time that I did was not conducive to my mental health.

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Under ideal circumstances, one would not use a weight of opinion — whether the opinion were popular or that of experts — to approximate most sorts of truth. But circumstances are seldom ideal, and social norms are often less than optimal whatever the circumstances. When confronted with work that is heterodox about foundational matters, the vast majority of people judge work to be crackpot if it is not treated with respect by some ostensibly relevant population.

In cases where respect is used as the measure of authority, there can be a problem of whose respect is itself taken to have some authority; often a layering obtains. The topology of that layering can be conceptualized in at least three ways, but the point is that the layers run from those considered to have little authority beyond that to declare who has more authority, to those who are considered to actually do the most respected research, with respected popularizers usually in one of the layers in-between. In such structures, absurdities can obtain, such as presumptions that popularizers have themselves done important research, or that the more famous authorities are the better authorities.

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As I was reading de Morgan's book, my paper was waiting for a response from the seventh journal to which it had been offered. The first rejection had been preëmptory; no reason was given for it, though there was some assurance that this need not be taken as indicating that the paper were incompetent or unimportant. The next three rejections (2nd, 3rd, 4th) were less worrisome, as they seemed to be about the paper being too specialized, and two of them made a point of suggesting what the editor or reviewer thought to be more suitable journals. But then came the awful experience of my paper being held by Theory and Decision for more than a year-and-a half, with editor Mohammed Abdellaoui refusing to communicate with me about what the Hell were happening. And this was followed by a perverse rejection at the next journal from a reviewer with a conflict of interest. Six rejections[1] might not seem like a lot, but there really aren't that many academically respected journals which might have published my paper (especially as I vowed never again to submit anything to a Springer journal); I was running-out of possibilities.

I didn't produce my work with my reputation in mind, and I wouldn't see damage to my reputation as the worst consequence of my work being rejected; but de Morgan's book drew my attention to the grim fact that my work, which is heterodox and foundational, was in danger of being classified as crackpot, and I along with it.

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Crackpots, finding their work dismissed, often vent about the injustice of that rejection. That venting is taken by some as confirmation that the crackpots are crackpots. It's not; it's a natural reäction to a rejection that is perceived to be unjust, whether the perception is correct or not. The psychological effect can be profoundly injurious; crackpots may collapse or snap, but so may people who were perfectly reasonable in their heterodoxy. (Society will be inclined to see a collapse or break as confirmation that the person were a crackpot, until and unless the ostensible authorities reverse themselves, at which point the person may be seen as a martyr.)

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As things went from bad to worse for my paper, I dealt with how I felt by compartmentalization and dissociation. When the paper was first given conditional acceptance, my reäction was not one of happiness nor of relief; rather, with some greater prospect that the paper would be published, the structure of compartmentalization came largely undone, and I felt traumatized.

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Meanwhile, some other things in my life were going or just-plain went wrong, at least one of which I'll note in some later entry. In any case, the recent quietude of this 'blog hasn't been because I'd lost interest in it, but because properly to continue the 'blog this entry was needed, and I've not been in a good frame-of-mind to write it.

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[1] Actually five rejections joined with the behavior of Abdellaoui, which was something far worse than a rejection.