The existence of firemen imply the existence of ________.
Categorical Implications, or How to Turn y Into χ
"Dr. Pepper implies the existence of Dr. Salt.”
"George Bush implies the existence of George Tree."
"Coke Zero implies the existence of Coke One, Coke Two, Coke Three..."“If x + element of set A, then x + another element of set A.”
Commutativity applies.
"Casual sex implies the existence of ranked sex."
"Townhouses imply the existence of farmhouses."“If element of set A + x, then another set of element A + x.”
The good folks over at knowyourmeme call this “Antonymic Misinterpretation”,
or, “x implies the existence of y.”
The latter is too vague in describing the form, the former, too restrictive, that is to say, the misinterpretations of this form which may be determined as antonymic are all misinterpretations of this form, but not all misinterpretations of this form are antonymic.
Antonymic forms are qualified by the substitute being an antonym i.e. the opposite of the original.
Here is an example of a strictly antonymic form:
"The existence of criminal blacks imply the existence of criminal whites."
Of the examples above, only the fourth and sixth are antonymic. The first is not, as pepper is not strictly the opposite of salt, but both merely belong to the same set which we may define as “seasonings”. Compare also Dr. Cumin, Dr. Paprika, etc.
It’s quite fun trying to come up with a few yourself, and some examples may be philosophically and/or spiritually enlightening.
But we can go further. Perhaps you already have. In the algebraizing of the linguistic form, as:
“If element of set A + x , then another element of set A + x”
we notice that the first “x” may be replaced “by element of set B”,
and the second “x” likewise, “another element of set B.”
“if the element of set A + element of set B,
then another element of set A + another element of set B”
We shall define the transformations as y and x respectively.
In transformation y, Dr. Pepper and Dr. Salt/Cumin/Paprika. In transformation x, Dr. Pepper and Mr. Salt/Cumin/Paprika.
where set A is the title and set B is the seasoning.1
In form y we only switched the second variable, whereas in set x, we switched both.
Compare werewolves, werebears, and werepigs with Batman and Catwoman.
Doesn’t it seem like we’re missing something though?
What about when we only switch the first variable?
For that we have to turn to another form, which we may define as form λ.
In transformation λ, Mr. Pepper,
and technically, transformation x, fully expanded, (that is to say, transformation χ,) is
Dr./Mr./Mrs. Salt/Cumin/Paprika
But wait Vlad, I can already hear you asking. Is not transformation λ just the same as transformation y, like in the commutativity part you mentioned earlier?
Two responses:
Number One (1): the overlap of y and λ make a convenient x, or χ, so we’re sticking with it.
Number Two (2): Distinguishing between transformation y and λ is helpful not only in that it distinguishes which variable we’re transforming, but also, and more importantly, the order in which we do the transformations.
Consider the title of this article.
“The existence of firemen imply the existence of ________.”
And I know for a fucking fact that you did not automatically fill that blank-in with “watermen”.
You went with “firewomen” the y transformation, where “watermen” would be the λ transformation.2
But wait Vlad, I’ve already heard you asking. Is this not a λ transformation, as it is the second variable that we are changing and not the first?
Jokes on you kid, that’s what you get for assuming.
y transformations occur prior to λ transformations not because the first variable is prior to the second variable, but rather because y transformations are whichever variable is naturally transformed first in the order of transformations.
But isn’t that arbitrary? Couldn’t you have transformed either variable first? I’ve heard you ask so long ago. Luckily enough I remember the answers.
Of course, you could have. But you didn’t. That’s my point. My stake, if you will.
The beauty of the separation between y and λ transformations is that it gives us clues as to which of the sets are more malleable to begin with, or in other words, more volatile to change, which, we might as well formalize right now.
In cases where the volatility of the sets are about even, the first transformation, i.e. the y transformation, has about even odds in occurring within either set e.g. a butterfly flaps its wings and someone makes a Mr. Pepper tweet before a Dr. Salt tweet, probably having to do with who Pepper was before he became a Dr.3
It takes hell of a lot more flaps of a butterfly to get from Firewoman to Waterman. In fact, it went to Firefighter first before it got to waterman. It probably got to firefighter before it even got to firewoman and I bet this sequence of transformations even map with how such name changes occurred in the social sphere as well:
First it was Profession+Man, then Profession+Woman OR Profession+Neutral Term, then whichever one it wasn’t prior.
In the former case, (probably older in my estimate) the inclusion of woman was meant to be a spotlight of a woman in the profession. Then once women were to be included, that is to say, the situation changing from “a woman in a male-dominated industry” to “hey we can’t call this a male-dominated industry when half of you guys are girls” then the gender was neutralized. In the latter case, it was much more likely that the gender balancing happened on an industries (rather than an industry) level as a whole, in which case the situation changed from “male-dominated industry” to “still male-dominated but we can’t say that anymore, but don’t worry, it’s a guy pulling you out of the fire”, and then some fireman’s daughter who he brought to work often as she was growing up really really wanted to become a firefighter despite knowing the challenges associated with pulling people out of burning buildings, and she became one because hey, why not, there’s only one of her, and we need someone to stay and watch the phone in case it rings which she’s totally fine with doing because she knows the risks of pulling people out of burning buildings and besides, we all love it when she wears the hat. Also the fireman calendar surprisingly works better with one girl in it, who knew?
And she’s a firewoman.
But I digress, ‘cause we’ve gotta take a step back and look at a transformation we missed. The v transformation, otherwise known as the neutered transformation.
Such is when the changed variable becomes all inclusive of every possible permutation of the second variable, such as with firefighter, or with everyone’s least favourite v transformation, flight attendant. Often this transformation occurs when the set is gender specific and becomes person as opposed to man or woman, as in Doorperson, Mailperson, Chairperson etc.
There are such cases where there exists the possibility of future collapse (of categories that is,) such as in the case where non-human entities may receive a specialized title, such as police dog, which may further be collapsed into policebeings due to the meddling and counter meddling of furries. (But then we get into robot police, and…robot dog police…)
V transformations are of course a favourite with Vlad, who, though being a shapeshifter and therefore qualified to perform all manners of transformations, nonetheless enjoys the inescapability of the v transformation, in that, like in the words of Qui-Gon-Jinn, there’s always a bigger set, as in the example of the police.4
And just as there is a λ for y, is there corollary for v? Of course, it is the Λ transformation, which may be defined as a y transformation in which there exists no corresponding λ transformation, the signature example being a werewolf.
“Wolf” in this instance may be switched out with anything; as mentioned above, examples include werebears and werepigs, and I believe there is such a thing as a wererabbit.
But if one were to attempt a λ transformation as with the other examples one would find it impossible.
____wolf, ____bear, ____pig cannot be completed, at which point all y transformations automatically become uppercased and Greekified into a Λ.
To close off, we might attempt bringing an immovable object against an unstoppable force: What happens when we try v transformations on a subject which only produces Λ transformations?
Werewolf→Wereanimal—>Werecreature—>Werething…
And what is a Werething? Why, follow the algebra. If a Werewolf is a man who turns into a wolf, a werething is a man who turns into a thing.
And we might just simplify that into a ‘tool’.
And that might as well be equivalent to a phallus.
Of course, Vlad has other tricks up his sleeve, but that is far too complicated at this point to get into.5
If we wanted to be technical about it, or at least, more technical than we already are, we can say that set B is the intersection of two other sets, one being surnames and the other being seasonings, or Surname ∩ Seasoning, but as Surnames are a near universal set, this is, for the most part, superfluous.
Which, by the way, should totally be the female equivalent of fireman. And also we should go back to saying firemen, cause firewomen are just as rare as werewolves.
My personal Pepper canon is that first he was a boy Pepper, then he grew up to be a Mr. Pepper, then joined the army where he became a Sgt. Pepper, and used the GI funding to pay for med school, at which point he became, Dr. Pepper.
Fun fact! According to the taxonomy laid out by Socrates via Plato, even with the Diogenes stipulation, Vlad is a man! But then again, so are women.
Your homework, if you’d like, would be to try and define a set in which thing is an element, but not the only element.