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.

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.

Reading a book first published in 1951, I am reminded that, at one time, the definition of humanities included sciences of human behavior within its scope. Now, one seldom encounters that inclusion in contemporary use, and the Merriam-Webster Dictionary explicitly excludes the study of social relations (though it says nothing explicit about that part of behavior outside of the social).

In the earlier period, there was a question of whether the study of human behavior were fundamentally different from the study of the properties of other things. Those who insisted upon such a difference would speak and write of science and the humanities as if of two separate things.

But the tools by which the physical, biological, and behavioral science were studied were increasingly shared. The physical and biological sciences took-up probability and statistics; the biological sciences have taken-up chemistry, mechanics, and game theory; the behavioral science have taken-up biological explanation and mathematical modelling. All have been affected by the same philosophic theories of method. A dichotomy of science and the humanities cannot prevail so long as the behavioral sciences are included amongst what are called humanities.

Apparently that dichotomy was so dear to some of those who insisted upon it that they attempted its preservation by implicitly changing what they intended with humanities in order to hold fast to it. Of course, the newer definition doesn't maintain the original dichotomy; but replaces it with a new one.

For several months, just two manuscripts were in the listing of manuscripts accepted by The Review of Symbolic Logic, one on an application of modal logic to set theory which article had been listed on 4 October and mine on probability which had been listed on 20 February. On 25 June, another was added, followed by nine more on 29 June; on 2 July, four more.

I don't know why the oldest two on the list have still not been typeset and moved to the FirstView list. And I don't think that my article will find many readers before it has, further, been assigned to a specific issue. It seems unlikely that the last will happen before 2021.

I have been working on a paper concerned with De Morgan's contribution to an area of probability theory. I had wanted to mention that contribution in the introduction to my probability paper, but saw no way of doing it that would be succinct without seeming occult. I began the new paper thinking that I would finish it in a very few days, but as I engaged in some of the requisite research I found that the task of properly explaining things was going to be still more challenging than I had anticipated.

In the end, the paper on De Morgan will be seen as a minor contribution to the history of thought. Had I known at the beginning how troublesome would be the task of writing it, I would have postponed the undertaking.

In a paper on which I'm working, I needed a block quotation, within which there were hanging paragraphs — for each every line except for the first was indented — effected in a way that naturally complemented ordinary block quotations as defined in article.cls. Not being a master of LAΤΕΧ, I made a search for how to do this, but I did not find anything that quite did the job. I arrived at this

\newenvironment{hangquotation}
    {\list{}{%
        \setlength{\itemindent}{-1.5em}%
        \setlength{\listparindent}{\itemindent}%
        \setlength{\rightmargin}{\leftmargin}%
        \addtolength{\leftmargin}{1.5em}%
        \setlength{\parsep}{\z@ \@plus\p@}%
    }%
    \item\relax}
    {\endlist}

which I am posting for the benefit of someone which the same problem, or with a problem sufficiently similar that my solution is readily adapted to his or to hers.

Here's an example of the output:

To use the code, place it in the LAΤΕΧ preamble, and then nest each block of paragraphs for which it is to be used between \begin{hangquotation} and \end{hangquotation}.

In a previous entry, I asserted that Voigt's Zahl und Mass in der Ökonomik contain[s] more error than insight. Here, I'll discuss one of the more egregious errors. In section V, Voigt writes

An die Spitze der Erörterung dieses vielberufenen Begriffes sollte gestellt werden, dass es Einheiten des Wertes giebt, dass man also untersuchen kann, wievielmal so gross ein Wert als ein anderer ist und Güter gleichen Wertes durch einander ersetzen kann, dass also der Wert ein eigentliches in einer Kardinalzahl ausdrückbares Mass hat.

which may be translated as

At the forefront of discussion of this much used concept should be placed that there are units of value that one thus can investigate how many time as large a value is as another and can replace goods of the same value with each other, that thus the value has a real measure expressible in a cardinal number.

I'll deal first with the point that it seems that one can investigate how many times as large a value is as another.

Numbers are used in many ways. Depending upon the use, what is revealed by arithmetic may be a great deal or very little. Sometimes numbers are ascribed with so little meaning that we may as well consider them strings of numerals, the characters that we use for numbers, and not numbers at all. Sometimes numbers do nothing but provide an arbitrary order, good for something such as a look-up table but nothing else. Sometimes they provide a meaningful order, but one in which the results of most arithmetic operations are meaningless, as when items produced at irregular intervals are given sequential serial numbers. (The difference between any two such numbers tells one which was produced before the other, but little else.) Sometimes the differences between the differences are meaningful, as when items are produce at regular intervals and given sequential serial numbers. And so forth.

Monetary prices are quantities, but they are more specifically quantities of money; that does not make them quantities of value nor proxies of quantities of value. One would have to show that the results of every arithmetic operation on such a quantity of money said something about value for it to be shown that value were itself a quantity.

The second part of Voigt's claim is that one Güter gleichen Wertes durch einander ersetzen kann [can replace goods of the same value with each other]. But an equivalence between things corresponding to the same numbers doesn't make results of the application of arithmetic to those numbers meaningful. (Consider lots of items produced at irregular intervals, with each item in the lot given the same serial number, unique to the lot but otherwise random.) And we should ask ourselves under just what circumstances we can and cannot ersetzen one set of commodities of a given price with another of the same price.

Nor does somehow combining the use of quantities of money for prices with a property of equivalence imply that value is a quantity.

Voigt is unusual not in making this unwarranted inference, but in so clearly expressing himself as he does. From the observation that prices are usually quantities of something, which quantities increase as value increases, most people, and even most economists blithely infer that value itself behaves as a quantity.

In early 2013, I made freely available a transcription of Zahl und Mass in der Ökonomik: Eine kritische Untersuchung der mathematischen Methode und der mathematischen Preistheorie (1893) by Andreas Heinrich Voigt. I have to-day completed a first pass of a translation of this as Number and Measure in Economics: A Critical Examination of Mathematical Method and of Mathematical Price Theory. Although I believe that there are many errors to be corrected in that translation, I am making it available. I do not plan to use a different URI for corrected versions.

I have been very disappointed by my reading of Voigt's article. I regard it as containing more error than insight.

In the course of translation, I found and corrected extremely minor errors in the transcription of the original. A name was at one point misspelled by me, and I failed to capitalize a word beginning a sentence. I also marked a die die as questionable which I've since concluded was deliberate. I do not believe that anyone could have been led to a mistaken reading as a result of those errors, but I have naturally corrected them.

I may change the URI for the transcription, moving it from another domain to place it amongst the uploads for this 'blog. If so, then I will edit entries to reflect that change.

On 20 February 2020, a year to-the-day after I submitted my paper Formal Qualitiative Probability to The Review of Symbolic Logic and nearly five months after I was notified that a revised version had been accepted, Cambridge University Press published the manuscript on-line.

(I believe that an unchanging DOI 10.1017/S1755020319000480 will be used for whatever is the latest version of the article, as it is type-set for paper publication and eventually assigned to a specific issue.)

This work was badly treated across journals of philosophy. Regardless of whether any of my future work is perhaps best regarded as philosophic, I will henceforth avoid submitting to such journals.

I recently started reading Psychology from an Empirical Standpoint, a translation of Psychologie vom empirischen Standpunkt[e] by Franz Brentano. My copy happens to be of the 1973 Humanities Press edition.

In the translation of the 1874 foreword, I hit a sentence

I was prompted to undertake a rather detailed study of these opinions because at the present time they enjoy an undue popularity and exert a lamentable influence upon a public which, in matters of psychology even less than in other fields, has not yet learned to demand scientific cogency.

This sentence is a muddle, with restrictions and negations working to say something contrary to what Brentano must surely have intended. A scan of the original is available on-line, the German reads

Und was mich dazu trieb, auch auf sie weitläufiger einzugehen, waren nur eine ungebührliche Verbreitung und ein beklagenswerther Einfluss, welche sie gegenwärtig auf ein Publicum gewonnen haben, das in sachen der Psychologie weniger noch als anderwärts auf wissenschaftliche Strenge Anspruch zu machen gelernt hat.

That refers to

a public, who in matters of psychology less still than elsewhere have learned to make a demand for scientific rigor

So the muddle is not in the original, but is an artefact of translation that doesn't strive to be as close to the original as possible while conforming to the conventions of the target language.

I checked a scan of the 1995 second edition of the translation, and found the same muddle as in the 1973 edition.

Naturally, I'm wondering to what extent I can reasonably trust the remainder of the translation. I reälize that passages recognized as crucial will probably have been treated with greater care and received more scrutiny, but there may be passages the importance of which has not been recognized. And even passages whose importance were recognized might be poorly translated. (I certainly saw such cases in translations of the work of Aristoteles.)