The axiom of Generalized Decomposition from Formal Qualitative Probability may be refactored to This refactoring is mathematically trivial, exploiting two automorphisms, but exhibits the principle more elegantly.

The axiom of Disjunctive Presumption in Formal Qualitative Probability may be more simply stated as

Measures — quantities to which some arithmetic can be meaningfully applied — can be fitted to some human attributes, even if not to others. When attempting to compare some populations to others, an assumption is made that the properties of the individuals within these populations are subject to quantification of some sort, and that the quantities are commensurable across populations. But usually these assumptions are implicit and unrecognized, and even those who have some awareness that they are dealing with quantities very often don't have a proper grasp of elementary issues.

Very often, people try to understand distinct populations in terms of some notion of averages. If each and every member of every population were exactly average in every regard, then averages would be perfect measures of the populations as such. More generally, if for any two populations the share of that population deviating from average by some specific amount were the same, averages would be sufficient for any comparison of the attributes of populations, except for population sizes. But if the overall variance from average in one population is different from that in another, then thinking in terms of averages can go very, very wrong.

Here are hypothetic distributions for some attribute within two populations, each population having the same number of members:[1] For both Population A and Population B, the median[2] of the attribute is the same, but Population B has more variance from the arithmetic mean than does Population A. Even though each of these two populations have the same median, more members of the population of greater variance are below some some measure, and more members of that same population are above some measure. Population B₂ has the same variance as Population B, but the same arithmetic mean (rather than median) as Population A. Again, even though the center is, by some measure, the same for both populations, more members of the population of greater variance are below some some measure, and more members of that same population are above some measure.

Even if a population has a higher center than Population A, if it has a greater variance then it will dominate the lower range of measures below some measure. And even if a population has a lower center than Population A, if it has a greater variance then it will dominate the higher range of measures beyond some measure.

If a measurable attribute correlates positively with social success, then ceteris paribus, a population of higher variance is going to dominate both social winners beyond some level and social losers below some level. If a population generally has greater variance amongst its attributes, then — discarding the assumption of ceteris paribus — that population is going to dominate both social winners beyond some level and social losers below some level; even if it has the same median or same mean or even a lower center than another populations.

In fact, though I cannot readily graph the cases in which attributes are only partially ordered and not measurable, the reader should see that the underlying point does not depend upon the measurability of the attributes, but only upon one population having greater propensity for variance than another.

But

• If one is only looking at the losers and thoughtlessly assuming that their numbers are explained by averages, then one is going inappropriately to infer that the population is generically inferior.
• If one is only looking at the losers, while thoughtlessly assuming that the averages are the same and that nothing else about the population itself can explain the difference in outcomes, then one is going inappropriately to infer that the population are victims of systemic bias.
• If one is only looking at the winners and thoughtlessly assuming that their numbers are explained by averages, then one is going inappropriately to infer that the population is generically superior.
• If one is only looking at the winners, while thoughtlessly assuming that the averages are the same and that nothing else about the population itself can explain the difference in outcomes, then one is going inappropriately to infer that any rival population are victims of systemic bias.

In each case, if we look at the other end of the distribution, the thoughtless conclusion falls apart.

When the last of these errors is made, an attempt may be undertaken to offset illusory bias, by putting an institutional thumb on the scales to shift Population A generally forward, until the the number of social winners at every level is at least the same. But notice what is then really happening as the relative outcomes for most members of the population of greater variance fall increasingly below those of the population of less variance — at previously targetted levels the population of lower variance comes to enjoy greater social success than does the population of greater variance. And notice that the population of greater variance necessarily still dominates above some value, albeït that the value increases as the institutional thumb comes down ever harder in a misguided attempt to match the upper tails of the distribution.

Only actual systemic bias can bring the number of social winners across populations into equality above any given level of social success beyond the center; and, the larger the population, the greater the required bias for such an outcome, and the more that most of the population of greater variance are victimized.

If the two populations are not equal in size, then the foregoing analysis would simply need to entail talk of proportionality. But one might as well speak and write of two populations of the same size, because the real-world application involves two populations that are very close to the same size in most first-world nations. The greater variance of one of those two populations is a consequence of the greater chaos in the formation of one of that population's chromosomes and of a lack of redunancy for another.

Unfortunately, most of the attempts to analyze what has been happening has entailed ham-fisted theorizing about differing averages.

[1] A population with finite membership cannot perfectly conform to a continuous distribution function; but, the larger the population, the less the necessary non-conformance.

[2] The median for each population is the point such that as many members of the population are above it as are below it.

Imagining all of a society's various generation and allocation of goods and services as if the creation and distribution of one big pie is very much analogous to imagining all of the sexual interactions of that society as one enormous orgy.

For many years, every manga that I had ever encountered was simply lousy. I came to have little expectation that any were not, but I was aware of Sturgeon's Revelation,[1] and so I would still occasionally look at manga. Eventually, I found some that were quite good, and even a few that were brilliant. I'd like to mention two that I find very interesting as works of philosophy.

Philosophy in general is sometimes characterized as consideration of the True, of the Good, and of the Beautiful. I don't know of a manga to which I'd point as a worthwhile meditation on the Beautiful, but I can point to one manga that has interesting ideas about the True, and another that is a wonderful meditation on the Good.

The official English-language title of the light novel 紫色のクオリア [Murasakiiro no Qualia], by Ueo Hisamitsu, and of its manga adaptation (by Ueo with illustrations by Tsunashima Shirou) is Qualia the Purple, but a better rendering would be Purple's Qualia or The Qualia of Purple. The story is marketted as yuri (work with a theme of romantic love or sexual attraction between females), and it has some elements of that theme, but most readers primarily seeking that theme are going to be generally frustrated.

The actual primary theme of the story is the uniqueness of the epistemics of each person. In response to the same stimuli, we have different sensations, and construct models that are very different not only in these building blocks but in subsequent structure. In the best cases, our models of the external world correspond very well to reality, and thus indirectly the models of one person correspond well to the models of another. But the maps are not the territories, and my maps are not your maps.

In Murasakiiro no Qualia, the character Yukari does not model animals and machines as fundamentally different. However, unlike a couple of other characters, Yukari does not think any less of living creatures for being machines; she treats machines with genuine affection and sometimes love. Moreover, within the framework of the story, Yukari's model works. (I deliberately refrain here from providing examples.) Another character, Alice Foyle, produces what appear to be child-like drawings but contain solutions to challenging mathematic problems.

Ueo doesn't simply write of characters with special abilities flowing from looking at the world differently. Ueo proposes the idea that personal identity itself is located exactly in our respective internal differences of sensation and of all that we build from sensation.

The story also involves elements of speculative science fiction, to which I impute no value except as plot devices. I'm rather more interested in how the protagonist, Gakku, obsessively fights Fate, much as does Homura in Mahou Shoujo Madoka Magika.

The official English-language title of 葬送のフリーレン [Sousou no Frieren], by Yamada Kanehito with excellent illustrations by Abe Tsukasa, is Frieren: Beyond Journey's End, though the pirate translations began with the closer translation Frieren at the Funeral; either of these titles is appropriate. (A more literal translation would be Frieren of the Funeral.) This series has become a huge critical and commercial success, and its anime adaptation has likewise become a huge critical and commercial success. (At this time, I've watched only clips of the anime.) Frieren begins with the return of a party of four adventurers after they have saved the world from a Demon King, a quest that they accepted a decade earlier.

The eponymous Frieren is an Elven maga, who had lived a quiet, meandering life for more than a millennium before joining the party, and who can expect to live many millennia more. During the celebration, Frieren casually makes plans to meet the other members of the party, in another fifty years. The significance to human beings of half a century does not begin to register with her until she returns, and finds Himmel, the once youthful leader of the party, to be an old man. And, when not much later Himmel dies, Frieren struggles to understand both how someone with whom she had spent only ten years could have come to mean so much to her, and how she could have failed to recognize that she had only another fifty or so years which she could have spent with him and did not.

Thereafter, Frieren is the story of the further adventures of this Elf, with occasional flashbacks to her time with the party who defeated the Demon King. What's really being delivered is both a bitter-sweet love story — as Frieren comes over decades to recognize that Himmel was the great love of her life — and an extended meditation on the importance of relationships, on the meaning of life, and on the nature of ethics. (The other commentary that I've encountered has missed both the point that Frieren loved and loves Himmel, and the consideration of ethics.)

As to ethics, I'll note that Himmel implicitly rejected the Utilitarian calculus and anything like it, and within the story the ethics that he instead embodied have, since the time of the quest, been propagating. Humans and Dwarves explain their acts of local goodness by saying That's what Himmel would have done. The world of Frieren continues to grow more humane, because of Himmel, long after his death.

Sousou no Frieren is a story that has more than once made me laugh aloud, not because of any jest, but because the author has made some excellent choice, often in having a character do something very right, but sometimes the author's choice involves other things. At least twice, his choice has concerned the rôle of Fate — once to challenge a character, and at another time to treat two of the characters with love.

[1] Ninety percent of everything is crud. Sturgeon did not claim that 10% of everything is not crud; the ninety percent is merely a lower bound. (And a metaphoric one at that, though I encountered one fool who tried to argue as if the legitimacy of Sturgeon's Revelation hung upon a literal interpretation of ninety percent.)

In the case of what has been called long COVID, two opposing camps are lost in a confusion of name with description.

The idea that SarsCoV-2 would have peculiar long-term effects upon health was immediately popular in some circles for appalling reasons, and thus viewed in other circles with strong inclination to disbelief.

Eventually, a cluster of persistent symptoms came to be widely associated with SarsCoV-2. Some of these symptoms are clearly present in some people, and not psychosomatic. But a very reasonable question is that of whether these symptoms are actually caused by SarsCoV-2, or have some other cause or causes. For some months now, the evidence has strongly indicated that, no, these are, variously, not effects of SarsCoV-2, or are common to respiratory or viral illness more generally. As a description, long COVID has been falsified, but it has lingered as a name.

I continue to encounter recent articles in prestigious, allegedly scientific journals that simply treat as given that these symptoms are caused by SarsCoV-2. An established name is treated as if it were a description. Now some institutions are beginning to insist reasonably that the name long COVID be abandoned, as inapt. But I'm encountering journalists and pundits who thence infer and claim that long COVID does not exists.

That inference doesn't follow if by long COVID is meant a cluster of symptoms, which symptoms are exactly what have been investigated under the name. Only if long COVID is taken to be defined as these symptoms resulting from SarsCoV-2 could we say that nothing fits the concept corresponding to the name.

I doubt that any Briton defined the French disease as especially French. In any case, telling a typical Briton that what he called the French disease did not exist would be tantamount to telling him that syphilis did not exist. What he should instead have been told was that syphilis were not particularly French, and ought to be called something else.

Likewise, the declarations should not be that long COVID does not exist.

Most people who claim that argument from authority is fallacious would, perversely, argue for that claim by reference to the authority of common knowledge or of what were often taught. A fallacy is actually shown by demonstrating a conflict with a principle of logic or by an empirical counter-example. A case in which an authority proved to be wrong might be taken as the latter, but matters are not so simple.

When one normally makes a formal study of logic, that study is usually of assertoric logic, the logic in which every proposition is treated as if knowable to be true or knowable to be false, even if sometimes the study itself deliberately treats a propostion as false that is true or a proposition as true that is false. In the context of assertoric logic, an argument from authority is indeed fallacious.

But most of the propositions with which we deal are not known or knowable to be true or false; rather, we find that some propositions are relatively more plausible than others. Our everyday logic must be the logic of that ordering. Within that logic, showing that a proposition has one position in the ordering given some information does not show that it did not have a different position without that information. So we cannot show that arguments from authority are fallacious in the logic of plausibility simply by showing that what some particular authority claimed to be likely or even certainly true was later shown to be almost certainly false or simply false.

Arguments from authority, though often not recognized as such, are essential to our everyday reasoning. For example, most of us rely heavily upon the authority of others as to what they have experienced; we even rely heavily upon the authority of n-th-hand reports and distillations of reports of the experiences of others. And none of us has fully explored the theoretic structure of the scientific theories that the vast majority of us accept; instead, we rely upon the authority of those transmitting sketches, gists, or conclusions. Some of those authorities have failed us; some of those authorities will fail us in the future; those failures have not and will not make every such reliance upon authorities fallacious.

However, genuine fallacy would lie in over-reliance upon authorities — putting some authoritative claims higher in the plausibility ordering than any authoritative claims should be, or failing to account for factors that should lower the places in the plausibity ordering associated with authorities of various sorts, such as those with poor histories or with conflicts of interest.

By the way, I have occasionally been accused of arguing from authority when I've done no such thing, but instead have pointed to someone who was in some way important in development or useful in presentation of an argument that I wish to invoke.

Everyday discussions of epistemics don't require us to discuss foundational epistemology explicitly. Were someone asked how she knew that Johnny and Judy are dating, it would typically be sufficient for that someone to say that Judy were wearing his ring. We don't usually need to ask whether the witness had a false memory or hallucination, mistook someone else for Judy, &c. But it is important always to understand that no one just knows any complex proposition. The only things of which we have perfect knowledge are the things immediately before the mind — such as a feeling of coldness — and then we don't perfectly know their sources. Perhaps some of us are utterly reasonable in constructing models of the world to explain things such as our occasional sensations of coldness; certainly nearly all of us are so convinced of these models that we refer to a major share of their propositions as knowledge. But none of us just knows that Johnny and Judy are dating, that it is cold outside, that his or her eyes are blue, &c. Any reasonable belief in these things is an inference ultimately resting upon primitive experience.

I don't just know how it feels to be a man. I know how it feels to be me; I have memories, which I presume to be reliable, of how it felt to be me; and part of my model of the world (constructed to explain my experience) contains adult male bodies, one of which is my body. And, to that extent, I know how it feels to be a man. When someone else tells me something at odds with my experience of being a man, I don't think Oh, maybe I'm not a man after all! I just infer that the other person is either a man over-generalizing from his own experience or from reports, or is someone who is not a man but engaged in incompetent conjecture. I don't know how it feels to be woman. I don't even know how I would feel if I woke and found that my mind were operating in the body of a woman (which I presume would be different from how I would feel if my mind had for its whole existence operated in a female body). I simply cannot know without the experience. I could, in theory, know that I were unhappy being a man. I could, in theory, know that I wished to have a female body. But I cannot know how it feels to be a woman, and thus in no sense could I know that I somehow had a female mind in a male body. It is impossible for me to know that I am a woman. It is impossible for those who have never had a female body to know that they are girls or women. It is impossible for any of them to just know that they are girls or women. But they can certainly know their unhappiness or know their wishes. And the complement is true of those who never had the experience of being in a male body. They cannot know that they have male minds. It is impossible for those who have never had a male body to know that they are boys or men. It is impossible for any of them to just know that they are boys or men. But they can certainly know their unhappiness or know their wishes.

Hormone treatments are available to make a brain that was supposedly already female be more like an actual female brain and more as if in a female body, or a brain that was supposedly already male be more like an actual male brain and more as if in a male body. But this treatment would be actively absurd if the mind of the subject were already that of the opposite sex. I am not somehow really more a man than my levels of androgen or of testosterone or of estrogen have ever allowed me to be; likewise, I am not somehow really more a woman than my hormones have ever allowed; nor is anyone else. Those receiving such hormone treatments are not of the opposite sex; they are seeking to become more as if of the opposite sex.

If a male body could be made of a female body and vice versa, then it wouldn't matter that the female body had previously been a male body or vice versa. But present technology allows no such thing. A body that has undergone the most extensive reässignment surgery is ruined for purposes of return to its original sexual configuration. What alteration is available is primarily cosmetic, and highly destructive. Testes don't somehow become ovaries or ovaries testes; they are discarded. Breast implants may later be removed, but mammary glands become tissue to be sold or incinerated. The rest of the reproductive system is savaged.

And, if a male body could be made into a female body, or vice versa, then the change would always be something of a leap in the dark. Quite plausibly a great many people would be happy with where they landed, but others would be depressed, shocked, or horrified. With the procedures presently available — with an ultimately irreversible leap — many are indeed depressed, shocked, or horrified, without even the genuine experience of a body with a new sex. I've had at least one friend kill himself because of what he'd had done in trying to be remade into a woman. In the case of children, we are not so much considering leaping in the dark as being picked-up and thrown into the darkness. In ten, twenty, and thirty years, most of those who had been cheering the throwing will speak and write as if society were at fault in the case of those children who discovered that they'd crashed in a terrible place.

Our response to those who have come to desire interaction as if of the opposite sex should not be founded in mystical nonsense; but neither should it be characterized by condemnation or by intolerance. People should not be prohibitted from doing as they will so long as only consenting adults are involved. I think that radical treatments to change an adult's appearance to resemble that of the opposite sex are plausibly the best way for some people to alleviate very great unhappiness. I think that accommodation of such people, treating them as if they are of the opposite sex, is often quite appropriate. However, no one has a right to be treated as something that he or she is not. And, in some cases, very good reasons underlie sexual distinctions and subverting those distinctions is less humane than respecting them.

Much of the discussion of transsexualism has involved confusion — often deliberately fostered — between sex and other definitions of gender. The use of gender to mean sex actually dates to about the same time as it was introduced to refer to the somewhat related but distinct grammatic classification; but, for a time, use of gender in the sexual sense fell away. It began to be repopularized for purposes of euphemism, and continues as a euphemism into the present. The grammatic sense was related to the sexual sense in that things that were male were usually named with words that had the masculine grammatic gender and things that were female were usually named with words that had the feminine grammatic gender; but many things that did not have any sex were named with words having a masculine or feminine grammatic gender even when a neuter grammatic gender was a feature of the language, and some things that had sexes were assigned names with the neuter grammatic gender. Grammatic gender was an often odd social construct.. Grammatic gender and notions of rôles appropriate to each sex each influenced the other. At some time around 1980, the idea began to catch-on of using the term gender not in reference to sex nor in reference to grammatic gender, but to socially or personally constructed notions of those sexual rôles. The scientific and philosophic study of social or personal constructions of sexual rôles is itself very worthwhile; and the analogic appeal of extending gender to refer to such constructions is evident. However, the pre-existing and repopularized use of gender to refer to sex facilitated a hijacking of discourse, which confused sex with a social or personal construct of social rôle, under which hijacking it has been pretended that persons who are masculine are ipso facto male, that persons who are feminine are ipso facto female, that some males are neither male nor female, that some females are neither female nor male, and that any otherwise legitimate distinctions by sex must be replaced with distinctions by personal constructions of sexual rôle.

Of course, more than just grammatic gender or our notions of sexual rôles are here social constructs. Our language and every other language is a social construct, and the taxonomies of biology and of every other science are social constructs. More generally all taxonomies are personal or social constructs. But that does not make propositions subject to falsification by a device of recategorizing things, of exchanging labels amongst categories, or of applying new labels to categories. Rather, with a change of language a proposition is expressed differently; with a relevant change of taxonomy, a proposition involves more or fewer categories. If we adopted the convention of using Earth to mean only the Western Hemisphere, both that and the Eastern Hemisphere would continue as they would under the old taxonomy, rather than the underlying geophysics changing. Propositions about a sex do not become false or true by the device of insisting upon a new definition of man, of woman, of sex, or of gender.

As is often noted, the map is not the territory.[1] But what is usually missed is that, when we attempt to think of how they differ, we most often slip into specifics such that what we really compare is not the map with the territory, but the thing first recognized to be a map with a mental map of the territory.

Our efforts to think about how models differ from reality are usually likewise characterized by comparisons between some model and some other model not recognized to be a model. When we abandon specifics, and attempt to think of reality in the abstract, we almost always think of what amounts not to reality but to a hypothetical, unknown, perfect model of reality.

[1] with Alfred Habdank Skarbek Korzybski being the first to put it just that way

When Oliver Cromwell wrote, on 3 August 1650 to the General Assembly of the Church of Scotland,

I beseech you, in the bowels of Christ, think it possible that you may be mistaken.

he was in fact paraphrasing Richard Hooker,

Think ye are Men, deem it not impoſſible for you to err; ſift unpartially your own hearts, whether it be force of Reaſon, or vehemency of Affection, which hath bred and ſtill doth feed theſe Opinions in you.

Preface [1594] § 9
Of the Lawes of Ecclesiastical Politie

(Underscore mine.) In Cromwell's time, and indeed for many years to follow, Hooker's work was widely known and widely respected, and Cromwell had every expectation that his allusion would be recognized for what it were.