Binarists Vs. Spectrumists

Shoot-outs at the Not-So-O.K. Corral ...

That “debate” is, sadly, shaping up to be the century’s shoot-out at the O.K. Corral or on the streets of High Noon, although more honest or sardonic observers might call it a new Lilliputian civil war or Rape of the Lock, Part Deux. It has drawn fire from all quarters, particularly the spectrumist camp which has included, also quite sadly, Nature, “Scientific” American, the egregiously misnamed Science-Based Medicine, and Michael Shermer in a post @ the

Skeptic

.

But, somewhat in passing, of particular note from the latter is this passage which at least helpfully broaches the somewhat useful philosophical concept of family resemblances which leads into the more scientifically tractable and useful concepts of polythetic and monothetic categories, more of which later:

The reason is that the family resemblance fuzzy set representing “female” or “woman” contains far more than breasts and a vagina. Look under the hood and you’ll find hundreds, if not thousands, of differences with men, from anatomical and physiological to cognitive and emotional.

The question is, or will be, which of those “thousands” of differences will be deemed essential to qualify for membership in the sex categories, male and female?

However, several other Substackers have recently drawn some welcome and useful attention to several important principles, notably the aforementioned types of categories, and to various misperceptions, both of which bear some discussion & elaboration that may help to resolve the issue.

First off is a post by

Carolina Valencia

which provides a more or less clear but still quite useful distinction between the “colloquial definitions” for the sexes versus the strict biological definitions. Although her colloquial definition is still basically the spectrum — even if a somewhat usefully circumscribed one — that was “promulgated” by “biologists” Heather Heying (@

Natural Selections

), Emma Hilton (@

BeetleBomb

), & Colin Wright (@

Reality's Last Stand

) in the letter section of the UK Times. While that is a decent newspaper, it is hardly a peer-reviewed biological journal whereas the actual biological definitions are those that have, in fact, been published in such journals, those of Theoretical Biology, Molecular Human Reproduction, and the Encyclopedia of Evolutionary Psychological Science for examples. Which Carolina has usefully tweeted a link to so she at least knows of that fairly explicit though rather problematic dichotomy.

But secondly is Matt Osborne’s post at

The Distance

where he’s upping his prize from $1 million to $10 million for “proof of a third human gamete” which is, somewhat unfortunately, attended by his quite unscientific insistence that sex is, in his unevidenced opinion, an exhaustive binary that encompasses every last one of us. However, where he and far too many others — Andy Lewis, for example — are going off the rails is in “thinking” that sex itself has “evolved”:

But what has actually “evolved”, and what actually characterizes literally millions of anisogamous species, is the existence of those members who produce large gametes, and those who produce small gametes, each of which is, you know …, thereby able to reproduce. Which are the two main, though not exhaustive groups defined for ALL of those millions of species on the basis of reproductive function that humans — coming along several hundred million years after those two types first evolved — have given the NAMES “females” and “males”, respectively. Which illustrates a rather profound and quite problematic misunderstanding of the difference between the map – i.e., human creations – and the territory – i.e., God’s creation, however you conceive of Him, Her, or It to be …

But that naming is kind of the kicker: there are NO intrinsic meanings to the words we use, to “female” and “male” in particular. Moses didn’t bring the first dictionary down from Mt. Sinai on tablets A through Z so there are NO definitions that qualify as gospel truth, none that carry the imprimatur or signature of Jehovah — Himself. Despite the many who clearly think the latter is the case — and who get quite “peeved” when one attempts to point out the obvious.

Consequently, it would seem to help a great deal to recognize that the definitions for the categories “male” and “female” — for such are they — are somewhat arbitrary, are context dependent, depend on exactly what objectives we have in mind. Which then tends to determine the criteria for category membership — for instance, if we’re talking about male and female plumbing and electrical connectors then the criteria are external or internal threads, or convex and concave mating surfaces, respectively:

Though one might be amused — or depressed as the case may be — at Wikipedia’s ideologically-driven inability to use the traditionally more common and industry standard “sex”. Who knew that connectors had personalities? 🙄 Prudery — and/or Lysenkoism — as far as the eye can see …

In any case, that then raises the question of “necessary and sufficient conditions” for category membership, on which Carolina has provided a decent introduction, and which serves as a lead-in to some of the broader and more solid principles related to those methods of categorization:

In a definition, necessary traits are the characteristics or qualities that must be present for an object, concept, or entity to be considered an example of the defined term. …. In contrast, sufficient traits are those characteristics that, if present, are enough to classify something as an example of the defined term.

Wikipedia’s article on extensional and intensional definitions underlines the utility of the concept, as well as providing a clear case where a single condition is both necessary and sufficient:

An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term.

For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because any unmarried man is a bachelor.

Along the same line, an article at Law & Liberty likewise underlines the utility of the concept, this time in the context of resolving that other thorny problem, i.e., “What is a woman?”:

In analytic philosophy, a gold-standard definition gives necessary and sufficient conditions for being the thing defined. Definitions of this sort may not always cut to the heart of a thing’s true nature, but they offer a good starting place for dispelling serious confusion. Can we specify necessary and sufficient conditions for being a woman?

However, where I think both Carolina, and Emma Hilton and Company go off the rails is in not realizing that the latter’s definition basically specifies three distinct sufficient conditions for sex category membership, only one of which is necessary. Conditions which one might reasonably argue are mutually exclusive — past, present, and future clearly qualifying as such:

These systems are classified into two categories, based on the type and function of gametes produced and delivered, regardless of their past, present or future functionality.

But those three exclusive sufficient conditions for sex category membership basically turn those definitions into spectra of 3 discrete “colours”, into a matter of family resemblances, into polythetic categories — i.e., those with multiple sufficient conditions, only one of which is necessary for category membership. In notable, and profoundly antithetical contradistinction to the biological definitions which are explicitly monothetic, those with single necessary and sufficient conditions for category membership. From the Glossary of article in the Journal of Molecular Human Reproduction:

Absolutely nothing there about past or future functionality; it’s all about present functionality, i.e., “produces gametes” — right now, present tense indefinite.

While we can certainly create such definitions as we wish — pay the words extra as Humpty-Dumpty put it — it does seem rather a case of the pot and kettle for Hilton and Company to be throwing stones at more “liberal” spectrumists when they’re promoting a “spectrum-lite” version. In addition to which, apart from the questionable scientific and logical rationale for including potentialities into the criteria for membership in any category, one might reasonably ask how exactly will we determine past or future functionality. Which stages of “developed anatomies” — that may or may not have been present in the past or that may or may not be present in the future — are sufficient to qualify individuals, of all anisogamous species, as male or female?

So the questions are then, a single necessary and sufficient condition? Multiple sufficient conditions, only one of which is necessary? Which ones in the second case? The three of Hilton’s definition? Or the tens to thousands of Nature, Scientific American, and Michael Shermer? Hilton’s definition is somewhat more tractable and useful, and more or less comports with the “folk-biology” or “colloquial” definitions. But those of Hilton and Nature and Company both seriously conflict with the monothetic definitions of standard biology, and they both intrinsically exclude actual abilities to reproduce as any necessary condition. Which, one might reasonably argue, suggest their proponents are rather unclear on the basic concept:

Clearly, the more credible and authoritative portions of mainstream biology have put their money on the monothetic categories in which actual “reproductive function” is THE necessary and sufficient condition: no tickee, no washee. However, while there may be some marginal utility in Hilton’s definitions — at least in a nominal or proxy sense — those of Nature and Company are so profoundly unscientific if not entirely useless, worse than useless, that it might be useful to elaborate a bit on the differences between monothetic and polythetic categories, and how the usefulness of the latter rapidly decreases as the number of sufficient conditions increases.

The primary source for that elaboration is a paper by Belgium virologist, Marc Van Regenmortel, the Figure 1 of which provides a nice summary and illustration of the differences between monothetic categories and polythetic categories:

FIGURE 1. Distinction between polythetic and monothetic classes in the case of 8 individuals (1–8) and 8 properties (A–H). The possession of a property is indicated by a plus sign. Individuals 1–4 constitute a polythetic class, each member possessing 3 out of 4 properties with no common property being present in all the members. Individuals 5–6, 7–8 and 5–6–7–8 form three monothetic classes with respectively 3, 3 and 2 properties present in all the members (Van Rijsbergen 1979; see also: http://www.iva.dk/bh/lifeboat_ko/CONCEPTS/monothetic.htm).

Which, of course corresponds to, in the right half, the monothetic categories of mainstream biology as exemplified by the Molecular Human Reproduction article, and, in the left half, the polythetic categories of Hilton and Nature.

But somewhat more illustrative is this variation of Regenmortel’s table which creates two polythetic categories — Sally’s “family”, and Mike’s “family” — each of which might correspond to a sex:

In the foregoing table, consider Sally’s family — composed of her, her daughter, her brother, and her nephew — and Mike’s family — composed of him, his daughter, his sister, and his nephew. Each member of each family is characterized by a unique combination of 3 and only 3 properties or traits — the possession of which is marked by the presence of a plus sign — that are drawn from different sets of four for each family (A-D for Sally’s family, and E-H for Mike’s family). Each of those combinations — A and B and C, and not-D, or E and F and not-G and H constitute unique “sufficient” conditions for membership in the corresponding categories.

That uniqueness is underlined by the distinct binary representations of the properties possessed by each individual just to the left of each member’s description. Although it might be emphasized that, for example, the representation for Sally’s daughter could have 4 zeroes appended to the right of it — i.e., 1110,0000 — while that for Mike’s daughter could have 4 zeroes appended to the left of it — i.e., 0000,1110 — if we want a more precise and commensurable comparison of both families. But such a comparison would emphasize that the two families are entirely distinct and separate — Sally’s came over to North America on the Mayflower, Mike’s (Mike Lee’s) has been in China since the first millennium: absolutely no properties in common.

But that distinctness between the two halves might reasonably correspond to Hilton’s definitions for male and female. There are NO properties shared by any members so at least we have a binary, even if each half is a spectrum by itself.

However, when we come to the dog’s breakfast entailed by the spectra of Nature and Company then all bets are off: which of the myriads of combinations of “sufficient” conditions or properties are unique to one side or the other? Is there any way at all of ordering them into two distinct halves? Something that says any particular combination is, for example, more male than any other one? There is no longer anything at all that uniquely differentiates one individual from any other one — the whole concept of the sexes then becomes useless. Which, one might reasonably suggest, is the primary objective of many of those peddling that rather unscientific schlock.

As both Regenmortel and Needham — the author of the other paper — suggest or argue, there are often justifications for polythetic categories — Regenmortel in the case of viruses, and Needham in the case of anthropological studies. However, they also emphasize that they often entail unnecessary and cumbersome complications. Which stick out like proverbial sore thumbs in the case of the spectra of Nature and Company, and only marginally less so for those of Hilton and company. Somewhat apropos of the latter, while those definitions may work, in a pinch, for many species, they come a cropper when applied to many others where past and future functionalities aren’t so easily discerned or conflict with current states.

But beyond the question of the mechanics, logic, and coverage of monothetic and polythetic categories is the somewhat thorny though seriously problematic question of the rather egregious motivated reasoning behind the reluctance to endorse the standard monothetic definitions of mainstream biology. Bit of a murky topic, but some reason to argue — as I and more than a few others have done — that far too many people have turned the sexes into “immutable identities” based on some “mythic essences”. They’ve turned “male” and “female” — particularly the latter — into no more than badges of tribal membership, into self-imposed “yellow stars” that consign them to ghettos, and worse, of their own devising:

Though not really sure it’s just a case of “pretending” or just a “bun-fight” …