So I’m working on a new thing that I’m calling Reductive Reasoning. To my surprise, such a thing doesn’t already exist, and any searches regarding “reduction” and “reasoning” lead to reductio ad absurdum, which is certainly a type of Reductive Reasoning, but not the only type. I’m so intrigued by this idea, in fact, that I began a new book last night on the subject. I think I’ll provide this one for free, and the first draft will be finished around mid-April. Following a three month period of leaving it alone, I’ll begin the editing in mid-July, and should produce the finished version around the end of August. I’ve dropped other writing projects to pursue this one, because I think I’m onto something here.
Reductive Reasoning is all about sets and set theory, but, thankfully, doesn’t have to dive into the mathematics. In fact, it’s almost completely a logical exercise designed to separate fictitious sets from real items. There are countless ways in which this can be applied, and the book is going to spend most of its time providing these examples and explaining how it works. The interesting thing about this is that earlier I received an email from a colleague who was sharing with me an anti-transgender article from The Federalist, where I found myself immediately dissecting the assumptions and sets in my reply. The colleague wasn’t condoning the article; he just sent it as a point of interest.
Then, when I was working on this article about video games and RPGs, I found myself using it again, though only briefly. I mentioned that the definition of RPG must necessarily be a defining element–an element that is unique to the genre and ubiquitous in all games that are RPGs. If the element is not unique to the genre, or if the element is not present in all games that are RPGs, then we know that our definition isn’t adequate.
I’ve Got a Cat
Suppose I say “A cat is an animal that has fur and sharp teeth.” Here, obviously, my definition of “cat” is “an animal that has fur and sharp teeth,” because… that’s what “is” means.
We can immediately see that my definition is wrong. A dog has fur and sharp teeth. According to my definition, a dog is a cat. Similarly, hamsters have fur and sharp teeth, so, according to my definition, a hamster is a cat. Since we know that a dog is not a cat–because the entire meaning of “species” precludes the possibility that one species is another species, just as “is” has its own meaning–we also know that my definition is wrong.
For the most part, it’s irrelevant that my definition is wrong. However, suppose that I said “All cats know how to use a litter box.” It suddenly becomes very important to know what my definition of “cat” is. As I’ve provided my definition that “A cat is an animal that has fur and sharp teeth,” my statement is actually “All animals that have fur and sharp teeth know how to use a litter box.”
This statement is obviously false. Not only is a typical hamster incapable of using what we understand as a litter box, but you’ll go insane trying to teach a dog how to use one. My statement that “All cats know how to use the litter box” is built on the definition of what a cat is. It’s equally built on the assumption of what a litter box is, and what it means to use one. For the sake of keeping things simple–though I’ll probably delve into this in the book–“litter box” can be defined as “any small container filled with some sort of sand or gravel with the express purpose of being a repository for animal waste” and “using a litter box” means “releasing waste into the small container filled with some sort of sand or gravel.”
When attempting to determine whether my statement about cats using litter boxes is true, we must reduce it into its components:
- What is a cat?
- What is a litter box?
- What does it mean to use a litter box?
These three things are assumed by my statement, and must be individually demonstrated and defined before the statement can be decreed as true or false. We’ve already defined “litter box” and “using a litter box” satisfactorily enough–there may be some problems with those definitions, but, for the sake of the argument, let’s just go with “common knowledge” here. The remaining question is, “What is a cat?”
My definition that a cat is any animal with fur and sharp teeth yields a statement that is obviously false–hamsters and dogs both meet that criteria. In fact, whether my statement is true or false depends entirely on what the nouns and verbs conjured even mean. Even using the scientific definition of a cat–a felis catus–won’t result in a true statement. “Any animal that is a member of the felis catus genus and species knows how to use a litter box” is still a false statement, or, at best, unfalsifiable. For whatever reason, not all cats will use a litter box, and so whether or not they even know how cannot be determined.
Recently I pointed out on Facebook that “The United States” doesn’t share a border with Mexico. This is because “The United States” is a set, and sets aren’t real things. They’re imaginary human constructs that are often treated as real things, but aren’t. This is important, because the statement “The United States has every right to determine who can enter its borders” is just as open to reduction as the statement about cats. Does the United States even have borders? No. It’s a set of other states, and some of those other states have borders. California, New Mexico, Arizona, and Texas share a border with Mexican provinces.
So the United States can’t have the “right” to determine who can and can’t enter its borders, because the United States doesn’t actually have borders in the first place. Instead, we would have to say that California, New Mexico, Arizona, and Texas have the right to determine who can enter their borders.
Except we immediately have the same problem there, don’t we? These states are also sets without real existences. We treat them as real, but they aren’t. So the statement “California, New Mexico, Arizona, and Texas have the right to determine who can enter their borders” has to be reduced. And there’s no such thing as “California” or “Texas.” There are only sections of land with populations that we’ve artificially divided into different groups and that we treat as though they are real divisions. In reality, there’s just a large section of land, some of which is owned by individuals, and some of which isn’t owned by anyone but which is claimed to be own by the fictitious set called “the government.”
Well, “the government” isn’t a real thing, and so it can’t own property. It would be like if I gave my lighter to Casper the Friendly Ghost, and then everyone began acting as though Casper was the rightful owner of my lighter. In practice, I would contend that it constitutes a form of insanity to treat imaginary things as though they’re real; the only difference is that Casper is an imagined individual while “the government” is an imagined set. Who really owns my lighter, if I have given it to an imaginary entity?
Anyone who wanted to could take the lighter and then say that Casper gave it to them, and they would be just as correct to say that as I was to say that it belonged to Casper in the first place. We can attribute literally anything to a fictitious entity. “Casper hates black people,” I could say. “Casper doesn’t hate black people,” you could reply, “and actually worked in the Civil Rights Movement.” We’d have no problem recognizing any two people having a conversation about whether Casper worked in the Civil Rights Movement as being batshit crazy. And “government” is just as imaginary and fictitious as Casper. The only differences are that “the government” is a set and that a lot of us are batshit crazy enough to treat “the government” as though it’s a real thing.
When we get down to it, we find ourselves saying that “An individual who owns land has the right to determine who can enter that land.” This, too, is open to reduction and a discussion of the nature of property rights and ownership. That’s not my subject here; I only bring it up to point out that I know even this seemingly obvious statement is open to reduction–however, this statement also stands up to reduction if it is assumed that force, violence, and coercion are morally wrong.
So does the United States have the right to determine who can enter its borders? Obviously not. The United States doesn’t have borders, because it isn’t a real thing, and so it can’t have any characteristics. Do California, Texas, et al. have the right to determine who can enter their borders? Obviously not. These states don’t have borders because they aren’t real things, and so they can’t have any characteristics. Does an individual have the right to determine who can enter their property? Briefly, I will say “Yes,” though I’m aware that I have not, in this article, attempted to demonstrate that. Instead, I’m going to rely on common knowledge again so that I can move on to something else. In the grand scheme, yes, even “common knowledge” must be reduced, but I want to get to the next subject because I have shit to do.
Sex & Transgenderism
At one point in the Federalist article I linked above, the author says something like “This is a boy pretending to be a girl.”
Relying on “common knowledge” isn’t helpful here, because there is too much disagreement there. Here, whether one agrees with the statement or not merely depends upon their bias and what they believe to be common knowledge. However, we’re going to reduce it.
- What is a boy?
- What is a girl?
The quick-thinking person might say, “A boy is someone born with a penis. Duh. And a girl is obviously someone not born with one.” And they might roll their eyes in exasperation at how they were being asked to define something that they consider “common knowledge” or “common sense.” But not only is this not pedantic to ask, it is critical. The statement’s status as true or false depend entirely on these definitions; they are hardly inconsequential. Whether or not his person is a boy pretending to be a girl depends completely on what a boy is and what a girl is.
Well, that definition clearly doesn’t hold up to scrutiny. There exists a medical condition where boys can be born without penises and/or without testicles. The statement “This is a boy pretending to be a girl” becomes “This is a <person born with a penis and testicles> pretending to be <someone who was not born with a penis and testicles>.” But this statement is obviously not true, per the link I just provided.
If the person has any intellectual integrity at all, they’ll sigh in exasperation, admit that they’re previous definition doesn’t hold up, and might say, “Then a girl is someone born with a vagina, and a boy is someone who wasn’t born with a vagina.”
Again, though, this definition doesn’t hold up. It’s a bit rarer, but there have been born girls without vaginas. By the latest definition, this woman born without a vagina is actually a boy.
Frustrated and probably getting angry, the person might turn to what they learned in 8th grade Biology: “A boy is someone born with XY chromosomes, and a girl is someone born with XX Chromosomes.”
Until recently, I would have accepted that definition tentatively, because I lacked the knowledge to dispute it, but in fact human sexuality isn’t anywhere near that simple. It turns out that every single cell in a person’s body has its own sex. This means that, far from having “all XY chromosomes,” a boy can have anywhere from 0% and 100% of their cells having XY chromosomes. So no one is born “with XY or XX chromosomes,” because everyone is born with some combination of cells featuring both XX and XY chromosomes in virtually any conceivable ratio. So the statement “This is a person born with XY chromosomes pretending to be a person born with XX chromosomes” is similarly false–the statement isn’t scientifically valid and isn’t applicable to anyone.
What we find, as we continue reducing and continue digging, is that the entire argument is built upon the assumption that there is such a thing as “a boy” and “a girl,” and that these things are clearly defined along some delineating characteristic. Basically, “boy” is a set and “girl” is another set, but the person–any person–making the claim will be unable to provide any definition that doesn’t either apply to “boys” that the definer himself would dispute as being boys, or would not apply to boys that the definer himself would call “boys.” A hermaphrodite, for example, born with both a penis and a vagina, would count as a “boy” per the person’s first definition, but the person would adamantly deny that a hermaphrodite counts as a boy, even though his own definition means the hermaphrodite counts as a boy. Similarly, a male born without a penis would not count as a boy per the person’s first definition, though the person would adamantly insist that such a person counts as a boy, even though his own definition means the penis-less baby doesn’t count.
Any definition given for a set must include all members of that set and must exclude entities that aren’t members of that set. Otherwise, the definition is wrong and the set is improperly defined. Since the set itself isn’t defined properly in the first place, any statement made about that set must be either false or unprovable. As an example, any definition for “boy” must include all members of that set, at the very least according to the person defining it, and the definition must exclude all girls. The person must be able to delineate the set about which they are making a truth statement. Before it can be said that “This is a boy pretending to be a girl,” both “boy” and “girl” must be unambiguously and all-inclusively defined into their different, non-overlapping sets. Not only did the writer of that article fail to do that, but everyone would fail to do that, because it can’t be done.