In Aristotle’s On Interpretation, the second book of the Organon, Aristotle presents four forms of proposition, four ways we say things are true or not: we say that things are positive and include all, such as All apples are round, positive and include some, such as Some apples are round, negative and exclude all, such as No apples are round, and negative and exclude some, such as Some apples are not round. This pair of pairs form what logicians called the Square of Opposition centuries ago, with two propositions positive, two negative, and overlapping with this, two universal, and two partial.
|Square of Opposition||All – Universal||Some – Particular|
|Positive||All apples are round.||Some apples are round.|
|Negative||No apples are round.||Some apples are not round.|
Aristotle did not systematize his ten categories to Kant or Boole’s liking, and his categories have been largely ignored by logicians since, but Aristotle’s four forms of proposition are the simple, systematic form central to the study of logic for Aristotle, Al Farabi, Avicenna, Averroes, Aquinas, Scotus, Ockham, Leibniz, Kant, Boole, De Morgan, Carroll and many others for centuries in an Abrahamic/Greco-Roman family of overlapping cultures of talking about debate and truth that led to modern formal logic and the Boolean algebra found in telegraph, telephone and computer systems.
Just as Carroll could have imagined Aristotle’s categories as a series of events and characters in his Wonderland to engage and exercise the minds of children, and followed the same series in the sequel, it is possible Carroll imagined Aristotle’s four forms of proposition as the four royal court characters that rule Alice’s dreams to engage children with Aristotle’s four forms of proposition, the four corners of the Square of Opposition, central to ancient Aristotelian logic, modern Boolean logic, and Carroll’s own work and lessons on logic.
In Wonderland, the White Rabbit is characterized as overly inclusive and particular, who worries about the needs of his superiors, and orders Alice into his house to look after his own things, the Duchess is overly exclusive and particular, ignoring the needs of her cook, punishing the cries of her baby, and moralizing about who and what is best or worst, the Queen of Hearts is overly exclusive and general, ordering the complete subtraction of anyone who displeases her in the slightest from her garden and existence, and the King of Hearts is overly inclusive and general, who includes all conflicting testimony and evidence in his court whether or not it matters or makes sense and hates to cross-examine anyone.
The two male royal characters, the Rabbit and King, are overly inclusive, the two female characters, the Duchess and Queen, are overly exclusive. The Rabbit and Duchess, each with their own particular house, the first two royal characters, are overly particular and partial, but not entirely, and the Queen and King of Hearts, the second two royal characters, are overly general and universal, without degree. None of the four are wise, as all four serve as excessive examples Alice finds foolish rejects in the end, waking from her dream. Alice makes her way from the overly particular in the first half of the book to overly general in the second half, and from overly inclusive in the beginning, to and through overly exclusive in the middle, to overly inclusive again in the end, fed up with the entire cast of characters and royal court.
|Aristotle’s Four Forms of Proposition||Wonderland||Looking Glass||Character|
|Positive & Universal – Includes All||King of Hearts||White Queen||Inclusive|
|Negative & Universal – Excludes All||Queen of Hearts||Red Queen||Exclusive|
|Positive & Particular – Includes Some||White Rabbit||White King||Inclusive|
|Negative & Particular – Excludes Some||Duchess||Red King||Exclusive|
Similarly, in the Looking Glass, the Red Queen is overly exclusive and universal, like the Queen of Hearts, who says all ways are hers, which implies none at all are Alice’s, contradicts Alice entirely, and shows Alice the distance she must travel, the Red King is overly exclusive and particular, including Alice in his dream, but silently without interacting with her as she dreams of him, such that neither is entirely real to the other, the White Queen is overly inclusive and general, remembering time both ways and impossible things before breakfast, accepting Alice’s help, turning into a sheep and dashing the full distance of the board, and the White King is overly inclusive and particular, including most but not all of his horses and men to help Humpty Dumpty and nervously encouraging both sides of the battle between the Lion and Unicorn. Again, none are wise, and Alice wakes from her dream frustrated.
If Carroll embodied Aristotle’s four forms of proposition as the royal characters who rule Wonderland and then repeated this in the sequel, much as I argue he did with Aristotle’s ten categories, he did not follow the same order chapter by chapter in both books as he seems to have done with the categories. In both books, each royal character gets their own chapter, and each chapter of a royal character almost always has at least one chapters between it and any other, with one exception, but the chapters do not line up together, and Alice does not encounter them in the same order. In the sequel, she does not work from particular to general and from inclusive through exclusive to inclusive again, but rather the opposite, from exclusive to inclusive, and from general to particular twice. Alice starts on the side of the board with the Red Queen and King, overly exclusive, works her way to the end of the other side of the board past the White Queen and King, to sit between the White and Red Queen at the end, a ruler and queen herself of her own court banquet.
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