I love logic. Logic enchants me.
I normally post about story but my love for logic and its power to enchant is something I’ve been meaning to write about for a while but have been putting off. The lecture I attended last night by Patrick Curry about enchantment spurred me to finally get this piece written.
I’m not talking about modern logic, though. George Boole was one of the first to work with binary logic – something I’ve covered briefly elsewhere. As far as I’m concerned, Boole, like others before and after him, introduced a cold, soulless calculating thought machine which he used to manipulate, knead, twist, and braid sophistic arguments into a thought tangle, in what Patrick Curry might call a glamour. No wonder Boole’s wife had to restore balance and write a book called Logic Taught by Love.
But logic enchants me.
I was late for the Temenos Academy lecture last night – the 6:30pm starts are tough for me to get to on time. Sneaking into the room with as little disturbance as possible, it didn’t take me long to ease into the flow of Patrick’s argument. When one loses oneself in a piece of art, when time seems to slow down, and space warps, when you feel you are both fully present in the here and now but also transported to a different dimension of space-time, you’ve been – according to Patrick’s rigorous definition – enchanted.
So how come logic enchants me?
I’m talking about classical Aristotelian categorical logic here. It’s the type of logic Sister Miriam Joseph covers in her book The Trivium and the type of logic I’ve shown can be worked so intuitively and beautifully using Spencer-Brown’s calculus.
As Sister Miriam Joseph describes it, logic is the art of thinking. And art has the potential to enchant, doesn’t it? She sees it, as I do, as part of a unified organon, or tool for thinking, called the Trivium, which is made up of logic, grammar, and rhetoric. Here’s the example she gives of how they work together to reveal our knowledge of being:
The discovery of the planet Pluto in 1930 illustrates the relationship between metaphysics and the language arts. The planet Pluto had been a real entity, traveling in its orbit about our sun, for centuries; its discovery in 1930 did not create it . By being discovered, however, it became in 1930 for the first time a logical entity. When it was named Pluto, it became a grammatical entity. When by its name knowledge of it was communicated to others through the spoken word and also through the written word, the planet Pluto became a rhetorical entity.
Logic is the art of thinking; grammar, the art of inventing symbols and combining them to express thought; and rhetoric, the art of communicating thought from one mind to another, the adaptation of language to circumstance.
Logic is concerned with the thing-as-it-is-known.
Grammar is concerned with the thing-as-it-is-symbolized.
Rhetoric is concerned with the thing-as-it-is-communicated.(reordered from The Trivium, pp 8–10, )
Patrick argued for the importance of metaphor in bringing about enchantment.
Achilles is a lion is a logical proposition in form, but in content, it slips away and becomes a liminal statement.
But that is not why logic enchants me.
I quizzed Patrick at the end of the lecture: What did he have against logic? He came up with three intriguing points, each related to the three Aristotelian laws of logic:
The law of identity: a is a or Whatever is, is.
The law of non-contradiction: Nothing can both be and not be at the same time.
The law of excluded middle: Everything must either be or not be.
“What exactly is Achilles? A man? A living man depends on the air he breathes, the food he eats. Where do we draw the line?” asked Patrick.
Nice one, but that’s a category mistake – a confusion of substance and attribute. Substance (Gk: ousia) is the essence of a thing. For Aristotle, this was the difference between Achilles, as a living being, and his corpse.
“And when we talk about Achilles being a lion, we know he isn’t a lion. But he isn’t entirely Achilles either. While he ceases to be just Achilles, he still remains totally himself, as if under an enchantment.”
These statements seemingly overthrow the rules of logic - but they commit further category mistakes, confusing being and seeming. As soon as we introduce a stative verb (a verb like ‘to seem’ which indicates a state of being, rather than an action, or the being of a substance), we exit the world of logic and enter the world of rhetoric. Where those mistakes become con-fused, we shift from rhetoric to poetics. We would not be able to do so at all were it not for logic.
Logical propositions depend on clearly defined terms joined by the verb ‘to be’ acting as a pure copula. The verb, used this way, performs a joining or bridging function – the same kind of bridging function that operates when we feel drawn to a painting, or are taken over by a piece of music. It links through time. It links through space. It links beyond existence, revealing something about the enchanted and enchanting nature of the unity of being
Logic is an art which enchants.
The only things we can talk about using logical propositions are represented by substantives (nouns or pronouns, standing for the substance or essence of something, eg the subject term ‘Achilles’, in our example.
We either link the logical subject to an adjective, eg ‘brave’, or ‘handsome’ or a substantive, eg ‘warrior’ or ‘lion’.
Logically speaking, ‘Achilles is brave’ or ‘Achilles is a warrior’ are true logical propositions.
I find those statements enchanting because they allow me to understand something about the ineffable quality of Achilles’ substance that I would not otherwise be able to understand. They lead me back to the mystery of substance.
‘The being that is Achilles’ is ‘a being that exists’ leads me straight to the nature of being – to ontology, to metaphysics, to the heart of the mystery of being. The inclusion of the substantive as part of the predicate term, which Carroll argued strongly for, reveals that common ground of essential being very clearly.
‘Achilles is a lion’ has metaphorical or poetic truth.
Knowing that Achilles exists depends on logic, not rhetoric.
The metaphor would not function effectively if it were not based on an overthrowing of the fundamental rules of logic, to enable us to transcend them and end up where we started, in the mystery of being, knowing that Achilles is.
And that is why I am enchanted by logic.
The title of Mary Everest Boole’s book on logic is ambiguous. Does ‘Logic Taught by Love’ mean that love (passive verb) actively taught logic something, or (past participle, acting as an adjective) is a means by which logic can be taught?
Her work may not be fashionable now, but her passion for logic shines through it. It is subtitled ‘rhythm in nature and education’.
Now, that, I find enchanting.