I believe Lewis Carroll used the categories of Aristotle backwards, as if seen in a mirror, to plot out and order the events of Alice’s Adventures In Wonderland and Through The Looking Glass.  In Aristotle’s Categories, which Carroll knew well as the first of Aristotle’s works on logic, Aristotle lists the ten types of things we can say about things as substance, quantity, quality, relations, place, time, position, state, action and passion.  In Carroll’s mirror-image order, these are passion, action, state, position, time, place, relations, quality, quantity, and substance.

In Wonderland, the White Rabbit is passion, the Mouse is action, the Dodo and his Caucus Race are the state, the White Rabbit’s House is position, the Caterpillar is time, the Cheshire Cat is place, the Duchess is relations, the Mad Hatter’s Tea Party is quality, the Queen of Hearts is quantity, and the King of Hearts is substanceThrough the Looking Glass, corresponding exactly chapter by chapter with Wonderland, as if in a mirror, the Black Kitten is passion, the Red Queen is action, the Train is the state, Tweedle Dum and Dee are position, the White Queen is time, the Sheep is place, Humpty Dumpty is relations, the Lion and Unicorn are quality, the White Knight is quantity, and the Queens’ banquet is substance.

Some have said Wonderland and Through the Looking Glass are works of nonsense, meant to amuse more than educate.  Carroll designed both books to illustrate forms of logic with emotional and unreasonable characters, memorable illustrations and bad examples for Alice to learn and remember well.  I have used these to teach students Aristotle and logic, and they work for well. Carroll inverts many things between the two books, but he kept the order of the categories consistent.  The lesson of both books is also the overall lesson of Aristotle’s Ethics, balance, avoiding extremes on either side and learning with patience over time and by position between places to make good choices for ourselves and others.

There are many more lessons of Aristotle and others hidden in the works, but these are the overall structure and purpose.  As Carroll told Alice, we should not go anywhere or do anything without a proper porpoise.

The next logic lesson from Aristotle which can be found that is hidden but central to both of Alice’s adventures is royal characters of the court, the greater pieces of the game and plot, serve as Aristotle’s four types of assertions and corresponding perfect forms of the syllogism, fundamental to Aristotle’s Prior Analytics, well known by Carroll as the second book of Aristotle’s logic, and to many as the four corners of the Square of Opposition.

In Wonderland, the White Rabbit is positive and particular, Some A is B, the Duchess is negative and particular, Some A isn’t B, the Queen of Hearts is negative and universal, No A is B, and the King of Hearts is positive and universal, All A is BIn the Looking Glass, the Red Queen is negative and universal, No A is B, like the Queen of Hearts of Wonderland, the Red King is negative and particular, the White Queen is positive and universal, and the White King is positive and particular, like the White Knight, and like the White Rabbit, in the beginning of Wonderland.

The Looking Glass shows what Aristotle calls sub-alternation twice, with each particular king following his universal queen.  If we know No A is B, then we also know and later meet Some A isn’t B, the Red Queen leading to the Red King, and if we know All A is B, then we also know and later meet Some A is B, the White Queen leading to the White King, and later White Knight.

Syllogistically, in the Looking Glass, the White Queen, inclusively open like a child, is the universal positive (All, All, All), the Red Queen is the universal negative (All, None, None), the White King is the particular positive (Some, All, Some) and the Red King is the particular negative (Some, None, Some-Not).

In the end, Alice sits as an inclusive-exclusive OR between All and None, as the one who must decide for herself, with her powers of logic and reason, some and some not like an adult between the extremes, as Aristotle advises us in ethics. There are countless examples of syllogistic reasoning in both texts, but here are central examples that show each royal chess piece as an Aristotelian corner.  Aristotle starts with the Positive Universal, so Carroll starts with the opposite, not Negative Particular, but Negative Universal, the Red Queen, continuing much as if at the end of Wonderland, with the Queen of Hearts screaming for executions.

CELARENT, the Negative Universal Syllogism: If All A is B, and No B is C, then No A is C.  If All ways are mine, as the Red Queen says, and None of what’s mine is yours, as the Duchess moralizes, then none of these ways are yours, is what the Red Queen means but doesn’t say, which we understand and infer quite syllogistically from what is given in her words.  As a Venn diagram, if A is entirely B, and no B is C, then no A can be C.

FERIO, the Negative Particular Syllogism: If Some A is B, and No B is C, then Some A is not C.  If all things are dreams, as Tweedle Dum and Tweedle Dee tell Alice, and some dreams are untrue or not ours alone, then all things are somewhat untrue, and somewhat aren’t ours alone, which is what Tweedle Dum, Dee and the Red King dreaming silently imply, but don’t say.  As a Venn diagram, if some A is B and no B is C then some of A is C. As Aristotle says, if we have only some and no all or none, we can’t draw syllogistic judgements completely, leaving us with only a relative, somewhat satisfying conclusion, just as the Red King silently dreams and says nothing to Alice after she happily dances around hand in hand with both twin brothers.

BARBARA, the Positive Universal Syllogism:  If All A is B, and All B is C, then All A is C.  If all things are possible to think if you Shut your eyes and try very hard, as the White Queen suggests to Alice, and if all impossible things are things indeed, even if they, unicorns and we are all quite mental, then Alice can think six or more impossible things before breakfast if she shuts her eyes, imagines, and tries very hard, as the White Queen implies but doesn’t say directly, meaning what she doesn’t say syllogistically.  In Venn diagram form, if A is entirely B, and B is similarly C, then A must also be C.

DARII, the Positive Particular Syllogism:  If Some A is B, and All B is C, then Some A is C.  If the White King says he sent almost all his horses along with his men, but not two of them who are needed in the game later, and if Alice has met all the thousands that were sent, 4,207 precisely who pass Alice on her way, then Alice has met some but not all of the horses, namely the Red and White Knights who stand between Alice and the final square where she becomes a queen.  As a Venn diagram, if some A is B and all B is C then some A must be C.