Fairly inexpensive hair combs made of hard rubber — rubber vulcanized to a state in which it is as about firm as a modern plastic — could be found in most American drugstores at least into the mid-'90s. Now-a-days, they have become something of a premium item. I was looking at listing on Amazon supposedly of hard rubber combs and discovered, to my annoyance, that a careful reading of the descriptions showed that most of the combs explicitly described as hard rubber were made of plastic. To me, the situation seemed to be of pervasive fraud, as it will to many others.

But then I realized that it is more likely to be something else. Fraud, after all, involves deliberate misrepresentation. Whereäs we live in a world in which a great many people believe that no use of a word or phrase is objectively improper — that if they think that hard rubber means a rubbery plastic or a plastic that looks like another substance called hard rubber, then it indeed means just that. (Of course, we cannot trust any verbal explanation from them of these idiosyncratic meanings, as they may be assigning different meanings to any words with which they define other words.)

My defense of linguistic prescriptivism has for the most part been driven by concerns other than those immediate to commercial transactions. And, when I've seen things such on eBay as items described with mint condition for its age or with draped nude, my inclination has been merely to groan or to laugh. But it seems to me that the effects of ignoring or of rejecting linguistic prescription have found their way into commercial transactions beyond the casual.

Well, those who are not prescriptivists are hypocrites if they complain, and they're getting no worse than they deserve.

I often hear or read someone objecting to judging an historical person or act by present moral standards. Although there seems to be some element of reasonableness entangled in this objection, it's very problematic.

It is especially problematic as expressed. Technically, we cannot judge anyone or anything at all, except by whatever may be our present standards. If we judge historical people and acts differently from how we do present-day people and acts, it is exactly because our present standards incorporate a recognition of historical context.

I don't see that the real issue is historical context as such, but context more generally. If we are to make allowances for historical person or acts, it is because of what informed them and what did not inform them; and, similarly, acts by persons in some present-day contexts are very differently informed from acts by other persons in other present-day cultures. As L.P. Hartley usefully noted, The past is a foreign country: they do things differently there.

Cultural relativism, in application to other places or to other times, is sensible when it warns one against presumption that one's own culture is doing things the only right way. (One's culture may be doing things a wrong way, or there may be other ways that are just as good.) But a cultural relativism that instead claims that something is automatically acceptable simply because it prevails in the culture of that place or prevailed in the culture of that time dissolves into nihilism because each person at each time and at each place is him- or herself a subculture.

And I think that some allowances should be made; but I think that too much allowance is often made.

For example, is the case against slavery now available really all that much better than the case that was available in America a few hundred years ago? Inverting that question, was the case against slavery available a few hundred years ago really much worse than the case available now? There is a sound argument, even to-day, for not waging war against slavery in the territories ruled by other states; and there may be a case for making treaties or even forming alliances with such states; but those are different practices from engaging in slavery or actively enabling slavery. Is there really a meaningfully better defense of the slavery of two hundred years ago than there would be of slavery now?

I   don't   think   so.

Nor do I think so for a great deal else that I am told not to judge by modern standards.

Those who support locking-down in response to SARS-CoV-2 are like weird locusts. Instead of eating the crops; these locusts prevent growth and harvest. That is to say that they prevent economic activity, which is an implicit consumption of an especially perverse sort. In any case, they leave despair and literal starvation in their wake.

State officials should not use tasers as devices to compel positive acts. I have made and explained this point elsewhere, but I believe that I have failed to do so previously in this 'blog.

When tasers were introduced to policing, they were presented to the public as devices to stop attackers, without potentially lethal force. It would take some contrivance to present a situation in which such use of a taser would not be preferable to lethal force.

But tasers also inflict pain. And police officers quickly began using them to hurt people until those people complied, even when compliance was a positive act, such as moving one's body in some way. The pain inflicted by a taser is sufficiently severe that it will cause people to act in ways that will lead to their convictions, as when a taser was used to induce a suspect to produce a urine sample. Used to motivate behavior, a taser is a device of torture. Judges have acquiesced to this use of torture to compel positive acts. Almost no one speaks out against it. The taser has become a socially accepted device of torture.

To my chagrin, I find that I made a transcription error for an axiom in Formal Qualitative Probability. More specifically, I placed a quantification in the wrong place. Axiom (A6) should read I've corrected this error in the working version.

I found an article that, had I known of it, I would have noted in my probability paper, A Logic of Comparative Support: Qualitative Conditional Probability Relations Represented by Popper Functions by James Allen Hawthorne
in Oxford Handbook of Probabilities and Philosophy, edited by Alan Hájek and Chris Hitchcock

Professor Hawthorne adopts essentially unchanged most of Koopman's axiomata from The Axioms and Algebra of Intuitive Probability, but sets aside Koopman's axiom of Subdivision, noting that it may not seem as intuitively compelling as the others. In my own paper, I showed that Koopman's axiom of Subdivision was a theorem of a much simpler, more general principle in combination with an axiom that is equivalent to two of the axiomata in Koopman's later revision of his system. (The article containing that revision is not listed in Hawthorne's bibliography.) I provided less radically simpler alternatives to other axiomata, and included axiomata that did not apply to Koopman's purposes in his paper but did to the purposes of a general theory of decision-making.

I wasn't otherwise informed of the change, but when I checked this morning I found that a version of my probability paper had been posted to the First View list (and the listing amongst accepted manuscripts removed). So, except for pagination, the final form has been created. (I hope that the error to which I last directed attention of the productions office was corrected.)

On 3 September, I received a galley proof of my probability paper. Setting aside issues of style,[1] there were various minor problems. Of a bit greater importance was that the paper was reported as received on 20 Februrary 2020, the date that the publisher received it from the editors, which was months after the editors had received it from me. But the most important matter was the replacement in a citation of 1843 with 1943.[2] I responded on the same day, noting most of these issues.[3] On 10 September, I was queried about which version of the MSC I'd used for the code that I'd provided, and as to whether there were truly a space in my surname. Again I responded on the same day.

On 6 October, I received a new galley proof. I found no new problems. All of the minor issues that I'd noted were fixed. However, the paper was still reported as received on 20 Februrary, and the citation still had the wrong year. I decided to ignore the first of these two issues, and simply to note the problem with the citation. Again, I responded on the same day.

I have not since received communication from the production office. My paper remains on the accepted manuscripts list, and has not appeared in the FirstView list.

[1] I think that I just have to accept things such as punctuation being moved within quotation marks even when it's not part of the quotation, spaces being removed from either side of em-dashes, and artefact being respelled artifact, though I use the former for a different notion from the latter.

[2] The first clear frequentist challenge to the classical approach to probability seems to have been made in a paper by Richard Leslie Ellis published in 1843.

[3] One thing that I decided not to note was my discomfort over the space between left-hand quotation marks and quoted formulæ.

My work and the problems that most interest me are difficult to discuss with friends and even with colleagues because so much infrastructure is unfamiliar to them.

As repeatedly noted by me and by many others, there are multiple theories about the fundamental notion of probability, including (though not restricted to) the notion of probabilities as objective, logical relationships amongst propositions and that of probabilities as degrees of belief.

Though those two notions are distinct, subscribers to each typically agree with subscribers to the other upon a great deal of the axiomatic structure of the logic of probability. Further, in practice the main-stream of the first group and that of the second group both arrive at their estimates of measures of probability by adjusting initial values through repeated application, as observations accumulate, of a principle known as Bayes' theorem. Indeed, the main-stream of one group are called objective Bayesian and the mainstream of the other are often called subjective Bayesian.[1] Where the two main-streams differ in practice is in the source of those initial values.

The objective Bayesians believe that, in the absence of information, one begins with what are called non-informative priors. This notion is evolved from the classical idea of a principle of insufficient reason, which said that one should assign equal probabilities to events or to propositions, in the absence of a reason for assigning different probabilities. (For example, begin by assume that a die is fair.) The objective Bayesians attempt to be more shrewd than the classical theorists, but will often admit that in some cases non-informative priors cannot be found because of a lack of understanding of how to divide the possibilities (in some cases because of complexity).

The subjective Bayesians believe that one may use as a prior whatever initial degree of belief one has, measured on an interval from 0 through 1. As measures of probability are taken to be degrees of belief, any application of Bayes' theorem that results in a new value is supposed to result in a new degree of belief.

I want to suggest what I think to be a new school of thought, with a Bayesian sub-school, not-withstanding that I have no intention of joining this school.

If a set of things is completely ranked, it's possible to proxy that ranking with a quantification, such that if one thing has a higher rank than another then it is assigned a greater quantification, and that if two things have the same rank then they are assigned the same quantification. If all that we have is a ranking, with no further stipulations, then there will be infinitely many possible quantifications that will work as proxies. Often, we may want to tighten-up the rules of quantification (for example, by requiring that all quantities be in the interval from 0 through 1), and yet still it may be the case that infinitely many quantifications would work equally well as proxies.

Sets of measures of probability may be considered as proxies for underlying rankings of propositions or of events by probability. The principles to which most theorists agree when they consider probability rankings as such constrain the sets of possible measures, but so long as only a finite set of propositions or of events is under consideration, there are infinitely many sets of measures that will work as proxies.

A subjectivist feels free to use his or her degrees of belief so long as they fit the constraints, even though someone else may have a different set of degrees of belief that also fit the constraints. However, the argument for the admissibility of the subjectivist's own set of degrees of belief is not that it is believed; the argument is that one's own set of degrees of belief fits the constraints. Belief as such is irrelevant. It might be that one's own belief is colored by private information, but then the argument is not that one believes the private information, but that the information as such is relevant (as indeed it might be); and there would always be some other sets of measures that also conformed to the private information.

Perhaps one might as well use one's own set of degrees of belief, but one also might every bit as well use any conforming set of measures.

So what I now suggest is what I call a libertine school, which regards measures of probability as proxies for probability rankings and which accepts any set of measures that conform to what is known of the probability ranking of propositions or of events, regardless of whether these measures are thought to be the degrees of belief of anyone, and without any concern that these should become the degrees of belief of anyone; and in particular I suggest libertine Bayesianism, which accepts the analytic principles common to the objective Bayesians and to the subjective Bayesians, but which will allow any set of priors that conforms to those principles.

[1] So great a share of subjectivists subscribe to a Bayesian principle of updating that often the subjective Bayesians are simply called subjectivists as if there were no need to distinguish amongst subjectivists. And, until relatively recently, so little recognition was given to the objective Bayesians that Bayesian was often taken as synonymous with subjectivist.