Aristotle’s Categories & The Hunting of the Snark

I have been developing my theory that Aristotle’s categories fits the order of characters and events of Wonderland and The Looking-Glass.  In the process, I realized that The Hunting of the Snark has ten characters with no individual names but whose jobs start with B, and that each could fit with Aristotle’s ten categories, types of being, as well.  If Carroll used Aristotle’s categories to plot out Alice’s adventures, it is not unlikely that the Snark works like a logic puzzle.  In his Game of Logic, Carroll similarly listed buns, babies, beetles and battledores (an early badminton racket) as examples of things, also known as beings.  In Carroll’s introduction he says his work shows he is incapable of nonsense, and this brief but instructive poem includes precise arithmetic truth and natural history, both which apply to Aristotle’s categories.

Edward Guiliano pointed out that the Bellman looks like Father Time and carries a school bell for lessons.  The best candidates for each  of Aristotle’s categories are: the Bellman is time, the Boots is place, the Maker of Bonnets and Hoods is position, birth and death, the Barrister who dreams of the pig’s trial is relations, the Broker who values the goods is quality, the Billiard-Maker who chalks his own nose is action, the Banker is state, the Beaver who knits lace is passion, the Butcher who carves things up, dresses formally for the fight and teaches the Beaver addition is quantity, and the Baker who leaves everything on the beach, wears many layers, bakes brides cake, doesn’t lie, forgets his specific name and fades away, vanishing without a trace in the end is substance.

Pascal & the Drift of the World

Blaise_Pascal“(We are) incapable of certain knowledge or absolute ignorance.  We are floating in a medium of vast extent, always drifting uncertainly, blown to and fro.  Whenever we think we have a fixed point to which we can cling and make fast, it shifts and leaves us behind.  If we follow it, it eludes our grasp, slips away, and flees eternally before us.  Nothing stands still for us.  This is our natural state and yet the state most contrary to our inclinations.  We burn with desire to find a firm footing, an ultimate, lasting base on which to build a tower rising up to infinity, but our whole foundation cracks.”

-Pascal, Pensées

The Truth of One Plus One Equals Two

Postcard Grand Central Station New York NYIf I wander into a crowded train station and scream “One plus one equals two!” at the top of my lungs, or mutter it to myself, and there is no apparent pair I am gathering together, are my words true?  Are they true even if they do not connect with anything or do anything for anyone?  If we say they are true in the abstract, is that true in a particular context, or in all contexts?

Principia_Mathematica_proof that one plus one equals twoIf Bertrand Russell and Alfred North Whitehead spent over 350 pages in the Principia Mathematica (1910) to prove, with absolute certainty via logic, that one and one make two, was it just as true as it was before?  Is it now more certain?  How certain are children, compared to Russell’s readers?

Preferring Certainty

Arabic AristotleOne of the many strange things encountered in studying Aristotle’s work on logic is the ability to derive the truth of a particular statement (some or some not) from a universal statement (all or none).  If we know that all cows have horns, we also know that some cows have horns, and if we know that no cows play the accordion, we also know that some cows do not play the accordion.

While we know that this is technically true, many a student of logic becomes lost here, as it sounds odd to make a statement only about some when we could make a statement about all.  If I know that cows never play the accordion, it almost sounds like a deliberate misrepresentation to say that some cows do not.

Black Swan

However, if we are strictly empirical, and investigating things with the idea that there can always be counter examples we have yet to encounter, we can only say that some cows, those we have encountered, cannot play the accordion.  Aristotle himself believed that all swans are white and all crows are black, and used these as examples of universal statements, but he was wrong, as both black swans and white crows existed at the time in Australia.

White CrowWhy, then, do we feel more comfortable making the universal claim then the particular one?  The particular statement, only about some, is more cautious than the universal statement, about all.  When we make universal claims, we are stating with confidence that there are, effectively, no counter examples, much as one could say, in Aristotle’s world, there effectively were no black swans or white crows, as Aristotle’s world did not include Australia.  When we are skeptical and doubt we are cautious, only feeling safe making particular claims, but when we are dogmatic and believe we are confident, feeling safe in making universal claims.  This is why making a cautious particular claim about some sounds odd when we have already assumed the universal claim about all to be true.