Logic 101: Category Error

They do it all the time.

You say something universal: "Women like floral patterns." They come back with: "Not all women like floral patterns, some of them quite like stripes." With the conclusion: "That's sexist!"

Conversely, you say something particular: "Lena Dunham has ugly tattoos." They say: "You hate all women. You hate tattoos." Followed quickly by: "That's misogynist!"

It does not matter that many women (myself included) quite like floral patterns. You have dared to make a generalization about women, thus suggesting that all women must have certain characteristics in order to be considered women.

It does not matter that you yourself have tattoos (I have four, three with floral patterns, all more beautiful than Dunham's). You have dared to judge any woman on aesthetic grounds, thus suggesting that the only thing that matters about a woman is her looks.

"All I meant to say," you sputter, "is that based on my experience most women quite like floral patterns. I didn't mean to suggest that they needed to like them in order to be women." Conversely, you rejoin: "I was only talking about her tattoos, which look ugly to me. Tattoos are a form of art; I was making an aesthetic judgment about the art she has chosen to wear on her skin."

But it's too late. For presuming to make a general statement about women, you have proven yourself incapable of seeing the differences between individual women, while for making a statement about an individual woman, you have illustrated the criteria by which you think all women should be judged.

Heads they win, tails you lose.

(My friends, I predict, will say I am exaggerating, but Milo fans will know that Milo gets this kind of pushback all the time, even from friendly interviewers like Joe Rogan. Milo says: "Women..." and Joe corrects him: "You mean 'most women'...")

You try again, thinking maybe this time to head off the accusations.

You say something more qualified: "Many women I know like floral patterns." They counter: "You cannot generalize from your own experience; just because the women you know like floral patterns doesn't mean other women do." (If this example doesn't seem charged enough, try substituting "Many black Americans I know..." and see how far you get before being called names.)

Conversely, you refine your particular: "The tattoo on her arm from The Story of Ferdinand is okay; I like the flowers." They don't care: "I find it really offensive that you would judge a woman for the art that she has on her own body."

By now, your head is spinning. What has just happened? How has a positive statement about what many women like (floral patterns, children, making sandwiches for their husbands) been turned into a prescription for what all women should be? Conversely, how has your response to a single woman's body art been turned into an attack on all women?

Answer: Logic. Or, rather, faulty logic disguised as reasoned argument, as every medieval schoolboy would have instantly recognized. ("That's sexist!" 'Cause, of course, reason is.)

Almost unknown today (contradict me, I dare you!), Logic is an ancient art, tricksy and dangerous for all those caught unawares, particularly those who do not understand her methods.

This, at least, is the way the fifth-century encyclopedist Martianus Capella described her in his Marriage of Philology and Mercury, in which Logic or Dialectic is one of the seven handmaidens whom Mercury, the god of eloquence, gives to his earth-born bride Philology as a wedding gift. (Note that the Arts are described as women, as is Philology or reason.)

In Martianus's telling, Dialectic's face is pale but she is keen-sighted, while her hair is "beautifully curled" and perfectly coifed (a clear sign that she is dangerous!). Grammar, who has been presented first, is afraid of her, particularly the snake that she carries in her left hand hidden under her cloak, while the god Bacchus claims she looks like a sorceress--or a charlatan. In her right hand, she holds a set of patterns (formulae) inscribed on wax tablets adorned with contrasting colors held on the inside with a hook. If, according to Martianus, anyone took a hold of one of the patterns, he would be caught by the hook and dragged toward the snake, who would bite him and capture him in its coils. (Milo fans, insert joke here.)

Dialectic is the one in the middle, with her snake.
Paris, Bibliothèque Sainte-Geneviève MS 1041, fols. 1v-2
Dangerous as she was, all of the other Arts depended upon her: "Without her," Dialectic insisted, "nothing follows, and likewise, nothing stands in opposition." It was through her that the other handmaidens learned the six canons on which they relied: terms, complete utterances, propositions, syllogisms, criticism, and style.

Dialectic was the one who taught them the five predicables (that is, things that can be predicated or said about a subject) on which all statements depend: genus, species, difference, accident, and property.

Dialectic was the one who taught them definitions, the relationship between the part and the whole, division and partition; the terms or instruments of predication; and the ten categories of predication: substance, quantity, relation, quality, action, emotion or passion, place, time, position, and state.

Dialectic was the one who taught them the difference between complete utterances (what we call sentences) and propositions or sentences that can be affirmed or denied.

And Dialectic was the one who taught them how to make syllogisms from propositions by which they might proceed from "two or more conceded positions to one not conceded"--with the caveat that both the propositions and the syllogism needed to be well-formed, otherwise a fallacy or fault of logic would ensue.

For example, the fallacy of equivocation, using the same term with two different meanings. Or the fallacy of begging the question, when the conclusion of the syllogism is assumed in the conceded premises. Or the fallacy of the undistributed middle, where the middle term in the premises of a categorical syllogism does not apply to all of the members of the categories to be linked.

Too technical? Here's a good test: if you feel like your head is spinning, you are more than likely in the presence of a fallacy, whereas if Dialectic's snake has captured you in its coils, logically speaking you will be powerless to resist. There is a difference.

The real problem, if you want to stay sane, is understanding which fallacies you are in the presence of.

Let's look at our examples. You say: "Women like floral patterns." They say: "That's sexist!" What just happened here? You have made a statement about "women" (substance) to which you have attributed a particular accident ("liking floral patterns"). They take the accident ("liking floral patterns") and conclude that you mean to apply it to "women" substantively, such that any women who do not like floral patterns may no longer be considered women. This is an error mistaking an accident for a substance, something said about a substance for the substance itself. Back in the dark ages, when I was in graduate school, this error was condemned as "essentialism": assuming that there were things that could be said about all women that would apply to them essentially, that is, substantively. Taken to extremes, it is a way of making generalizations about any members of a group (in technical terms, any species of a genus) impossible, because every statement about accidents belonging to some or most members of the group will be automatically inferred to apply to all members, whether the speaker intends it or not.

Conversely, you say: "Lena Dunham has ugly tattoos." They say: "That's misogynist!" Here, the fallacy is somewhat easier to detect. You have made a statement about an individual substance ("Lena Dunham") and its accidents ("tattoos") which has been taken as a statement about a species ("women").* If crying "essentialism" makes it impossible to make generalizations, this fallacy makes it impossible to make particular statements about any individuals whatsoever without their being taken as generalizations. For example, Milo's infamous last Tweet: "Rejected by yet another black dude," mocking Leslie Jones for her attempts to silence him and other critics of her movie, subsequently regularly taken as evidence that Milo hates all black people and all women. The fallacy here is the mirror image of "essentializing": assuming that every member of a group represents every other member of the group, such that a statement about one may be--must be--taken as a statement about all.

Both of these fallacies are species of a single genus: category error. The former, taking what is said about a species as a whole ("women") as being said about all of its parts (individual women), is a fallacy of division. The latter, taking what is said about an individual (Lena Dunham) as being said about the species as a whole ("women"), is a fallacy of composition. Note that it is the conclusions ("That's sexist!", "That's misogynist!") being drawn from the original premises ("Women like floral patterns," "Lena Dunham has ugly tattoos") that are the fallacies , not the original premises themselves. It may or may not be true that women like floral patterns or that Lena Dunham has ugly tattoos. These are statements of fact that may be tested empirically or aesthetically, by asking lots of women whether they like floral patterns or by looking at Lena Dunham's tattoos. The fallacy is in taking these statements of fact as proof of implied opinions held by the original speaker (you) either because you have dared to speak in generalizations or because you have offered a criticism of a particular individual.

"But," they may say, "you do this, too. You make statements about feminists being man-haters when not all feminists hate men. And you take what journalists say about Milo and assume that because they criticize him, they hate all conservatives or supporters of Trump." Again, however, these are statements that can be empirically tested: are there women who identify as feminists who do not say that they hate men? Are there journalists who dislike Milo who do not lump him together with all Trump supporters as members of the alt-Right? I, for one, am having a hard time thinking of examples, which is potentially another fallacy, that of anecdotal evidence. It would be a fallacy of division, however, for me to assume that because many feminists express things that could be taken as misandrist (#killallwhitemen), that means that in fact all feminists hate men. Likewise, it would be a fallacy of composition for me to assume that because a fellow academic writing an opinion piece argues that Milo's success arises from hate, it is because she sees hate everywhere in the GOP and among Trump's supporters--except when she says so. At which point, I am certain the fallacy is not mine, but hers.

*No, this does not mean women are a different biological species from men. "Species" here means they share enough common attributes to be called by the same noun.

[UPDATED January 3, 2017, with thanks to my Facebook friends for correcting the final syllogism.]

[UPDATED January 25, 2017: Proving that Milo's readers are the smartest, Andrés Silva has made the syllogism even better! Read on for his correction:

I am quite familiar with Artificial Intelligence (AI), databases and the use of formal logic, mostly in informatics, I am less familiar with dialectic and fallacies. In any case, in that post you mention the “division” fallacy, but I think that fallacy does not apply to the case of “women like floral patterns” or similar generalisations. The reason is that a woman (Lena, for instance) is not “part of” the set of women. It is a "member of" the set, which is a different relationship. I’ll try to explain.

In brief, usually in databases and the ontologies used in AI, there are two main ways to relate individuals to collectives.

- IS-A relationship. Relates individuals to the SETS they belong to. Is classificatory, about membership. Lena is a Woman. Milo is gay, etc. 

- PART-OF relationship. Relates parts to an AGGREGATE, that is, a whole made of connected parts. Not classificatory. Indicates possession, collaboration or interaction. The engine is part-of my car, the screen is par-of my iBook, my bed is part-of my bedroom, etc.

Note how “wrong” would sound something like "the engine is-a car", or “the engine is a member of a car". The correct sentence is “the engine is PART-OF a car”. Similarly, is not ok to say that Lena is part-of women: any particular woman is-a woman.  A car is not a set, is an aggregate, a composition. “American cars”, on the other hand, is a true set, like “women", a concept we use to classify things. I don’t know how scholastics named those two relationships, but I’m sure they dealt with them differently. 

What I think is wrong in your post is that the division fallacy is a fallacy that applies only to the PART-OF relationship, but in the post it is applied to the IS-A. A good and simple explanation of the fallacy is in http://www.fallacyfiles.org/division.html. The one you linked at ongoodmove.org, I’m afraid is not 100% correct on this. 

Your post says that individual women are parts-of women and I think this is not ok. The reason is that “women” is a set, not an aggregate. A woman like Lena, then, is not PART-OF the aggregate “women”. Lena IS-A woman. So if there is a fallacy at play here (and I believe there is), then is not the division one.

Regarding “stereotypes": they are a problem with the IS-A relationships only. Any IS-A relationship conveys inheritance of properties, something that PART-OF has not. So, if human are mortal, then all members of the set inherit the “mortal” property. However, if a brick wall is three meters high, the bricks are not three meters high (walls are aggregates of bricks, not sets of bricks).

This inheritance of properties is at the root of the problem with clichés and stereotypes. In formal logic, “Women like floral patterns” is something like 

   for_all(x): is-a-woman(x) —> likes-floral-patterns(x)

and that means that all members of the set like floral patterns. No exceptions!. If there is an exception, then the above sentence is not true !

So if there is a fallacy at place here it must be other (not the division one). In my opinion (but I am not sure about this) the fallacy is that generalisations apply to all members of a set ONLY when we are within the narrow contexts of mathematics and formal logics, but not in informal daily language. In everyday use of the language, a generalisation is always fuzzy, always implying that “most of” the individuals have a property. We don’t speak math ! 

Hence, if someone tries to falsify “women like floral patterns” (in plain language) then it's not enough to point to a single case. That the sentence is the same as “most women like floral patterns”, so the correct way to falsify it is by showing that the reverse is the case, that is: show that “most women do not like floral patterns” is true. That goes always beyond pointing out a single case. 

We have moved then, from an oversimplifying true-vs-false world to a more statistical world, and that’s where these discussion should be.]

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