## Posts Tagged ‘measurement’

### Voigt and Value

Friday, 10 April 2020

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.

### A Translation of Voigt's Zahl und Mass in der Ökonomik

Wednesday, 8 April 2020

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.

### Helmholtz's Zählen und Messen

Monday, 16 October 2017

When I first encountered mention of Zählen und Messen, erkenntnisstheoretisch betrachtet [Numbering and Measuring, Epistemologically Considered] by Hermann [Ludwig Ferdinand] von Helmholtz, which sought to construct arithmetic on an empiricist foundation, I was interested. But for a very long while I did not act on that interest.

A few years ago, I learned of Zahl und Mass in der Ökonomik: Eine kritische Untersuchung der mathematischen Methode und der mathematischen Preistheorie (1893), by Andreas Heinrich Voigt, a early work on the mathematics of utility, and that it drew upon Helmholtz's Zählen und Messen, which impelled me to seek a copy of the latter to read. To my annoyance, I found that there was no English-language version of it freely available on-line. I decided to create one, but was distracted from the project by other matters. A few days ago, I recognized that my immediate circumstances were such that it might be a good time to return to the task.

I have produced a translation, Numbering and Measuring, Epistemologically Considered by Hermann von Helmholtz It is not much better than serviceable. I don't plan to return to the work, to refine the translation, except perhaps where some reader has suggested a clear improvement and I effect a transcription.

I have not inserted what criticisms I might make of this work into the document. Nor have I presented my thoughts on how Helmholtz's ostensible empiricism and Frege's logicism are not as far apart as might be thought.

### Consciousness and Science

Tuesday, 9 June 2015

The January-February 2012 issue of American Scientist contains an abridged reprinting of an article by BF Skinner, followed by a newer piece, frequently polemical, by a behaviorist, Stephen F. Ledoux.[0] In his polemic, Ledoux contrasts what he insists to be the scientific approach of behaviorology[1] with the ostensibly untestable and mystical approach of reference to an inner agent.

There's a problem here, but it's not unique to behaviorists. A large share of those who would study human nature scientifically do not know what science is.

Although courts and journalists and sociologists have declared that science is what scientists do, this formula is either a perverse begging of the question or simply wrong. The nature of science is not definitionally what is done by those recognized as scientists by academia nor by some narrower or wider society. Science does not start with academic degrees nor with peer review nor with the awarding of grants.

Science is reasoned analysis of — and theorizing about — empirical data.

Some want to use science more narrowly. It's in no way essential to the principal purpose of this essay that all rational analysis and theorizing about empirical data should count as science; but it is essential to see that whatever sort of analysis and theorizing is employed must be rational and that the data must ultimately be empirical. (I doubt that, at this stage, a behaviorist would feel a need to disagree.) To side-step absurd semantic arguments, I will sometimes write rational empiricism for the concept that I would simply call science.

An ostensible science that accepts as fact unjustified empirical propositions is no science at all. That is not to say that each thing that, in everyday language, we call a science (eg, biology) must be a self-contained set of explanations. It is perfectly acceptable for one such science to be built upon the results of a prior rational empiricism (eg, for chemistry to build upon physics).

If we carefully consider what we take to be fact (and which may indeed be fact), we recognize that there is a theoretical or conjectural support to our acceptance of most of it. Such propositions taken as fact cannot be the foundation of rational empiricism because the aforementioned support must itself have been rational empiricism for rational empiricism to proceed from these propositions. Rational empiricism cannot start with measurement[1.50] nor with notions of things to be measured such as with mass or as with the speed of light; rational empiricism cannot start with a geometry. These notions arise from interpretation and conjecture.[2]

Rational empiricism starts with what may be called brute fact — data the awareness of which is not dependent upon an act of interpretation.[3] If the belief in a proposition depends upon any such act, regardless of how reasonable the act might be, then the proposition is not truly a brute fact.[4]

To develop propositions from brute facts that contradict known brute facts would be to engage in self-contradiction, which is not reasonable in interpretation nor in theorizing. It is especially unreasonable to develop propositions that contradict the very brute facts from which they were developed.[5]

Philosophers have a long history of exposing where propositions are reliant upon prior interpretation and assumption. Towards an extreme, we are asked how we know ourselves not to be brains in vats, fed stimuli corresponding to a virtual reälity. It's not my intention to labor this question, beyond noting that it may be asked, and that acts of interpretation are entailed in any belief about whether we are other than about 3 pounds of tissue, bobbing-about in Pyrex™ jars, with electrodes attached here-and-there, whether the belief (for or against) be knowledge or not.

I referred to this question about whether one is a brain-in-a-vat as towards an extreme, rather than at an extreme, because a case in which stimuli are purely engineered is not an extreme. The presence itself of stimuli is not a brute fact. We conjecture their existence in our explanation of the sensations or sense-perceptions or perceptions that appear in our minds. If those things appear in our minds ex nihilo, then there are no stimuli, engineered or otherwise. That the mind is associated with a brain (or something like it) is not a brute fact. We build a model of reality that includes a body for us, and decide that our minds are housed within that body (as an activity or as a substance) or otherwise associated with it.[6]

The formation of sense-perceptions and of perceptions would seem to involve acts of interpretation; perhaps one would want to claim that the formation even of sensations involves interpretation. However, the presences of such things in the mind are themselves brute facts, whatever may be the theorized or conjectured origins of those things.[7] If by inner we understand the kernel of our belief system, and by outer we understand that which is built around that kernel, and if we begin our notion of mind with the capacity for sensations and the system that interprets these, then we should reälize that rational empiricism begins with the inner agent that the behaviorists and others want to dismiss as fictitious, mystical, superstitious; and it is the outer that is hypothesized in our explanation of the evidence. Those who attempt to deny or otherwise to exclude the inner self are trying to turn science on its head. Rational empiricism starts with a mind, and works its way out. And science, whether we simply equate it with rational empiricism or instead see it as a specific variety thereof, is thus committed to the existence of a mind, which is present in its foundation.

I say a mind advisedly; because, when rational empiricism starts, it starts anew with each mind. Of course, some minds do a better job of the rational empiricism than do others. The mind may be relatively inert rather than interpretive, or its interpretation may be largely irrational from the earliest stages.

If the mind continues, then it may develop an elaborate theory of the world. My own mind has done just this. And one of the important features of this theory is the belief in other minds (implicit in some of what I've been writing). Now, if we set aside issues of rationality, then an elaborate theory of the world might be developed without a belief in other minds. But as I constructed my theory of the world, including a theory of my having a body, it seemed that some of the other things out there exhibited behaviors similar those of my own body, such that those behaviors of my own body were in part determined by my mind. Subsequently, my theory of minds in general, including my own, began to be informed by their behavior.[8] According to later features of the theory that I hold of these minds, some minds do a better job of developing a theory of other minds than do other minds. Some never develop such a theory; others develop theories that impute minds to things that have none; some assume that any mind must necessarily be almost identical to their own minds.

As communication developed between my mind and these other minds, my theories of things-more-generally began to be informed by what I was told of those other things. One of my problems from that point forward was ascertaining the reliability of what I was told. (It might here be noted that my aforementioned development of a theory of the world was of course in very large part a wholesale adoption of those claims that I considered reliable.) And that brings us to collaborative theorizing, of which what many people now think science to be a special case.

But science is not essentially social. It does not pause between acts of communication, nor do we require the resumption of conversation as such to learn whether our most recent attempts were or were not science (though what we learn in conversation may tell us whether our prior conclusions continue to be scientific).

Consider whether Robinson Crusoe can engage in science, even on the assumptions that Friday will never appear, that Mr Crusoe will never be rescued, and that there is no means for him to preserve his work for future consideration. He can certainly engage in rational empiricism. He can test his conclusions against different sets of observations. (He can even quantify many things, and develop arithmetic models!)

Or imagine that you think that you see Colonel Inchthwaite commit a murder, though you are the only witness. Further, whenever you confront the Colonel and he is sure that there are no other witnesses and no recording devices, he freely admits to the murder. Your hypothesis that he has committed murder is tested every time that you query him. The fact that only you witnessed the apparent murder doesn't make your experience mystical. Your theory is a reasoned conclusion from the empirical evidence available to you.

Of course, others cannot use Mr Crusoe's work. And I will readily grant that it might be unscientific for someone else to believe your theory of murder. (That someone else may have little reason to believe your testimony, may have no independent means to test the theory, may have a simpler explanation to fit the evidence available to him or to her.)

Which is all to say that there can be private science, but it is only when the science of one's position is shared that it may become science for others.[10] (And, even then, they may have other evidence that, brought to bear upon one's position, renders it unscientific.)

The notion of science as intrinsically collaborative proceeds in part from a presumption that science is what those widely recognized as scientist do,[11] and in part from identifying science with the subject of the sociology of those seen (by some researcher) as scientists. But much of what people take to be science is, rather, a set of requirements — or of conventions attempting to meet requirements — for social interaction amongst would-be scientists to be practicably applied in the scientific development of belief.

It might be asked whether the scientists manque who deny the mind plausibly can have no experience of it, and under what circumstances.

One theory might be that, indeed, some of these alleged scientists have no experience of consciousness; perhaps they are things that behave indistinguishably or almost indistinguishably from creatures with consciousness, yet do not themselves possess it. Perhaps there are natural machines amongst us, which behave like more, yet are just machines.[12] But I'm very disinclined to accept this theory, which would seem effectively to entail a reproductive process that failed to produce a creature of one sort then successfully produced mimicks thereöf, as if bees and bee-flies might have the same parents.

Another theory would be that some of these alleged scientists are autistic, having minds, but having trouble seeing them. There is actually a considerable amount of mind-blindness amongst those who attempt social science. An otherwise intelligent person without a natural propensity to understand people may involve him- or herself in the scientific study of human nature — or in an ostensibly scientific study thereöf — exactly as an outgrowth and continuation of attempts to understand it by unnatural means. These attempts may in fact be fruitful, as natural inclinations may be actively defective. The autistic can offer us an outsider perspective. But outsiders can be oblivious to things of vital importance, as would be the case here.[13]

(And one must always be alert to attempts by people who fail at the ordinary game of life to transform themselves into winners by hijacking the meta-game, rewriting the rules from positions of assumed expertise.)

A remaining theory would be that these are rather more ordinary folk, who encountered what appeared to them to be a profound, transformative theory, and over-committed to it. (There seems to be an awful lot of that sort of thing in the world.) Subsequently, little compels them to acknowledge consciousness. They aren't often competently challenged; they've constructed a framework that steers them away from the problem; and most people seem to be pretty good at not thinking about things.

While the behaviorists have run off the rails in their insistence that minds are a fiction, that does not mean that the study of human behavior with little or no reference to the mind of the subject is always necessarily a poor practice. As I stated earlier, some people assume that any mind must necessarily be almost identical to their own minds, and a great many people assume far too much similarity. I find people inferring that, because they have certain traits, I must also have these same traits, when I know that I do not; I find them presuming that others have traits that I am sure that those others do not, again based upon a presumed similarity. A study of pure behavior at least avoids this sort of error, and is in some contexts very much to be recommended.

[0] I began writing this entry shortly after seeing the articles, but allowed myself repeatedly to be distracted from completing it. I have quite a few other unfinished entries; this one was at the front of the queue.

[1] When behaviorists found other psychologists unreceptive to their approach, some of them decided to decamp, and identify that approach as a separate discipline, which they grotesquely named behaviorology, combining Germanic with Greek.

[1.50 (2015:06/10)] The comment of a friend impels me to write that, by measurement I intended to refer to the sort of description explored by Helmholtz in Zählen und Messen, by Suppes and Zinnes in Basic Measurement Theory, and by Suppes, Krantz, and Tversky in Foundations of Measurement. This notion is essentially that employed by Lord Kelvin in his famous remark on measurement and knowledge. Broader notions are possible (and we see such in, for example, Rand's Introduction to Objectivist Epistemology).

[2] Under a narrowed definition of science that entails such things as measurement, a reality in which quantification never applied would be one in which science were impossible. Many of those inclined to such narrow definitions, believing that this narrowed concept none-the-less has something approaching universal applicability, struggle to quantify things for which the laws of arithmetic are a poor or impossible fit.

[3] The term brute fact is often instead used for related but distinct notions of fact for which there can be no explanation or of fact for which there is no cause. Aside from a need to note a distinction, I am not here concerned with these notions.

[4] Propositions that are not truly brute fact are often called such, in acts of metaphor, of hyperbole, or of obliviousness.

[5] Even if one insisted on some other definition of science — which insistence would be unfortunate — the point would remain that propositions that contradict known brute fact are unreasonable.

[6] Famously or infamously, René Descartes insisted that the mind interfaced with the brain by way of the pineal gland.

[7] I am sadly sure that some will want to ask, albeït perhaps not baldly, how the mind is to know that its sensation of its sensation is correct, as if one never sensed sensations as such, but only sensations of sensations. And some people, confronted with the proposition put that baldly, will dig-in, and assert that this is indeed the case; but if no sensation can itself be sensed except by a sensation that is not itself, then no sensation can be sensed, as the logic would apply recursively.

[8] Take a moment now, to try to see the full horror of a mind whose first exposures to behavior determined by other minds are largely of neglectful or actively injurious behavior.

[9] If I impute less than certainty to some proposition then, while the proposition may be falsified, my proposition about that proposition — the plausibility that I imputed to it — is not necessarily falsified. None-the-less, it is easier to speak of being wrong about falsified propositions to which one imputed a high degree of plausibility.

[10] The confusion of transmittability with rationality is founded in stupidity. Even if one allowed science to be redefined as a collaborative activity, somehow definitionally requiring transmittability, private rationality would remain rational. But I promise you that some will adopt the madness of insisting that, indeed, any acceptance of private evidence by its holder is mystical.

[11] When would-be scientists imitate, without real understanding, the behavior of those whom they take to be scientists, the would-be scientists are behaving in a way analogous to a cargo cult.

[12] Some people are convinced that they are unique in possessing consciousness, and the rest of us are just robots who do a fair job of faking it. This is usually taken as madness, though there is rather wide acceptance of a certitude that all other sorts of animals are natural machines, and that anything that seems as if it proceeds from love by a dog or by a pig is just the machine performing well.

[13] The presence of consciousness is here a necessary truth, but the proper grounds of its necessity are not obvious to most who are aware of consciousness; thus it should be unsurprising that a markèdly autistic person could not see this truth in spite of its necessity.

### Oh, you can't help that.

Sunday, 24 February 2013

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.

### Voigt's Zahl und Mass

Thursday, 17 January 2013

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.

### Weighty Matters

Sunday, 26 September 2010

The metric system has some points of genuine superiority to those of the English (aka American) system, but that superiority tends to be exaggerated. For example, the every-day English measures for volume tend to be implicitly binary, allowing easy halving or doubling. (If base 10 were everywhere superior to base 2, then our computers would be designed differently.)

One of the things that I was told as a child was that the metric system were superior because it measured in terms of mass, rather than weight, with the former being invariant while the latter would change in the face of a gravitational field. Well, actually, the English system has a unit of mass; it's the slug, 1 lb·sec2/ft, which is about 14.6 kg.

Meanwhile, I observe that, in countries where the metric system ostensibly prevails, people typically use its names of units of mass (gram and kilogram) for units of weight; they even refer to what is measured as a weight. Now, the real metric system does have a unit for weight, because weight is a force; weight can be measured by the newton (or by the dyne, which is a hundred-thousandth of a newton). But people aren't doing that; they're using kilogram as if it means about 9.807 N.

Much as it may be claimed that America is the only industrialized nation not on the metric system, really nobody's on it.

I notice that the Beeb most often wants to speak and write of weight, rather than of mass, but in the most ghastly unit of all, the stone (pronounced /stɛun/, with at least one pinkie extended). The stone is 14 pounds (divisible by 2 and, uh, 7). When weights don't divide into integer multiples of 14 pounds, tradition is to represent weight in terms of a combination of stone and pounds, as in Me mum weighs 19 stone and 12. Of course, if the Beeb were using pounds at all, there'd be the two obvious questions of

Why aren't you just using pounds for the whole lot?
and
Wait, now that I think of it, what happened to that metric stuff?
So the Beeb feels compelled just to round everything up or down to an integral number of stone, and somebody's mum either gains two pounds or loses twelve.