ericgerlach79

Wittgenstein’s Tractatus: The Board Game

Let us imagine a game played with pieces on a board, a logistical space for moving the pieces. What is on the board is true and certainly the present case. The pieces on the board and in the box beside the board contain all the pieces that can possibly be used, all the possibles and possibilities, such that if we see the pieces on the board and beside the board, we don’t know what pieces will be played but know all the pieces that could be played. A piece beside the board is false and dead, unless it gets onto the board, and then it is true and live in the game, and a piece on the board is false and dead if it is taken off the board. There are also things that are not in the game, the logical universe of discourse, the subject under discussion or consideration, and these are neither true nor false, as the are not in the cards, are not possibilities or pieces that can possibly enter the game or be negated to the side.

With this structure alone, we can exhaust all the connectives we use in formal Sentential Logic the way Wittgenstein envisioned it in his Tractatus and set it with truth tables. First, AND puts pieces on the board, including them together, but it could also, in combination with NOT, take sets of pieces off the board, adding them to the possibilities currently false rather than those currently true. NOT takes pieces off the board, or adds them if it is tied up with other NOTs. OR considers pieces, involved with whether or not pieces are moved on or off the board, completely indeterminate by itself, but determinate in combination with pieces added to or dropped from the board with ANDs and NOTs.

IF-THEN connects pieces possibly on the board together, such that one should lead to the other. Sluga argues that there are connections between things in the moment, such as speciation, with all men being mortal all at once or always, and connections between things over time, such as causation, with one thing leading to another. If the game changes with the possibilities over time, the first would be statements about the relationships between pieces at the same time, and the second different times. Bivalence, IF-AND-ONLY-IF, would simply state the relationship is reciprocal, working both ways, which would work with speciation and causation in a chicken-and-egg situation, where two things lead to each other circularly over time, again and again.

November 21, 2019 0

Turtles All The Way Down & Around

Ludwig Wittgenstein (1889 – 1951) is my favorite of the latest, greatest philosophers, and I learned his work from Hans Sluga and Barry Stroud at Berkeley, who taught me that Wittgenstein’s later thought experiments can lead to much more than he or we have worked out about truth and meaning. Wittgenstein’s thinking can answer many questions about thinking, not completely but more fruitfully, as Wittgenstein says, than other thinkers can.

The turn between Wittgenstein’s earlier and later thought is much like the Indian metaphor of turtles supporting the world and the question that arises from such an arrangement. Locke, Hume, Russell and other European philosophers have brought up the Indian debate about what the world sits on such that it is stable and continues. Some say that it sits on a turtle, an animal that symbolizes the cosmos in India and China, as it is flat on the bottom like the earth, and round on the top like the sky. Others ask what the turtle sits on if the world sits on it, and someone once said it’s turtles all the way down. Some have called this an infinite regress, an endless series that vanishes over the horizon, Buddha called it an unsolvable problem, Plato called it the greatest difficulty for philosophy, and today some call it the foundationalism debate, arguing whether or not knowledge or certainty sit on anything known or certain.

Philosophy is the love and study of wisdom, truth, meaning and thought. Thought interweaves several elements in our world. We sense, see, hear, touch, smell and taste things in our world. We also feel, feeling good, bad, tense and calm about the things we sense. We also remember, sense and feel things that are not in our world, but were. We also reason, building what we remember from sense and feeling into thoughts. In the middle of all this are words, things we hear and see from others that are interwoven with what we sense, feel, remember, and think.

Is sensing a thing without words, feelings or memories a thought? Is looking at an apple thinking? Is looking at it and feeling a feeling thinking? If I look at an apple and feel happy, is that a thought without words or images in mind? Some say yes, and others say no. Once we have several things interwoven, including the words we use to mean things, many call that thought. Some say thought is logical and rational, such that it follows rules, or follows rules when it is right and correct in judgement. Others say that this is the turtle problem yet again.

If things need thoughts to make sense of them, and if thoughts need thoughts, such as rules, or plans to make sense of them, is there thought that makes logical, self-aware, rational sense of thought itself? Are there words that make sense out of how we use words to mean things and know things? Some say yes, and it terminates in the rules and forms of logic, and others say no, and we simply continue to gather and divide things without an underlying logic that brings all of our wants and plans into common, coherent systems, visions or words. As Zhuangzi the Daoist asks, What do our ways or words rely on such that our words mean things?

What do turtles sit on? Some say other turtles. The Buddha in India and Wittgenstein in Britain answered the question with similar, simple metaphors that show us more than any system or logic in images or words can completely in itself. Thought and our world are interwoven, such that it isn’t turtles all the way down, but turtles all the way around. Much as Nicholas of Cusa and Hegel said about a circle, it is an infinite regress, but it is also complete in itself, and continues right in front of us. It isn’t that truth or rules rely or rest on any specific thing, but rather situations of sense, feeling, memory, reason and words mean things all together.

Situations shift, and these shifts show us how things mean things to us better than any specific words can. As Wittgenstein said, there is what can be said, but what can be said is only a part of what can be shown, which is best done not with complete, enclosed systems of words or images but by leading people through many open-ended situations of mind, stagings of thought, what Wittgenstein called thought experiments that involve many and any elements.

Much as Alice is frustrated with her sister’s text without pictures in the opening of Wonderland, words and rules without many interrelated examples of rich situations and the infinite variety found in them confuse us and lead us into considering words outside of actual, useful meaning. Carroll wrestled with Boole’s algebra much as Wittgenstein wrestled with Frege’s logic, and both came to the conclusion that words and systems can trap us like a fly in a bottle.

As Zhuangzi said, once we have the rabbit, we can forget the trap, and then we can involve the trap or not as we like, such that we can have words with others who have forgotten words, remembering and forgetting words and understandings freely as we please rather than sitting on particular words or systems as final, fixed foundations. Wittgenstein enjoyed reading Alice’s adventures to two sisters in Wales where he worked on his final thoughts, and he likely heard and felt Carroll’s deeper meaning, that it is good to use thought, rules and logic to show others how open-ended thought can be, beyond anyone’s particular logic, words, thought or feelings.

Buddha called the interweaving of everything codependent-arising, life as a tangle of many forms of life, as we see in Klimt’s painting Death and Life, which he began in Vienna 1908 and finished in 1915, the time Wittgenstein left Vienna to study logic, mathematics and philosophy with Russell at Cambridge. Klimt was not only one of the most influential painters of Wittgenstein’s Vienna, he painted a portrait of Wittgenstein’s sister, who was also psycho-analyzed by Sigmund Freud. As we might suspect, Wittgenstein’s family had some pull in Vienna, which in Klimt’s day was the city with the latest, greatest culture, replaced in the 1920s by Paris, the 40s by New York and the 60s by San Francisco. Wittgenstein said that life and thought are like an old city, with many forms of life inter-tangled for centuries.

Much as Buddha taught there is no essence or nature that completely defines or causes a thing because it arises out of the relationships it shares with other things outside of itself, Wittgenstein argued that life is like a thread without a single strand running through the entire length, and so we should always beware of the lure of the secret cellar, the proud idea that we have hit bedrock and completely revealed the truth rather than revealed yet another strong connection between different interwoven things. The cure for this proud ignorance, what Heraclitus called the human disease, is a rich variety of interwoven examples and elements that continue to show us more and more about the greater whole, endlessly.

November 19, 2019 0

Lewis Carroll’s De Morgan Fireplace

In the 1860s, Carroll had his most troubled and inspired years, producing both Alice books as he struggled with how to be a good person and great mathematician and logician, as well as his father’s death and the social isolation he felt at Oxford. Just after completing Alice in Wonderland, Carroll moved into a suite of rooms in 1868 with the money from his popular book and he lived there the rest of his life.

An excellent piece of evidence that Carroll was staging logical connectives as animal characters can be found in his personal fireplace. Carroll had the logician Augustus De Morgan’s son, William De Morgan, design tiles for his fireplace, most with animals, several with animals attacking each other, and several pairs of tiles with the same animals in opposite emotional states. When Carroll was later in charge of the common room in the building, he hired De Morgan’s son yet again to put similar tiles in the fireplace and other furnishings.

In Wonderland, many of the characters act as logical connectives, the sorts of nots, ands, and ors that Boole, De Morgan and Carroll worked on as logicians. There are many puns about oars, like ors, that involve choices, and Alice in the end of her adventures sits between the White and Red Queens much as Boole’s or sits between his inclusive and and exclusive not. The Caterpillar acts as a more inclusive but reclusive or, who gives Alice the power to change size and perspective.

The Cheshire Cat acts as an exclusive or, who sees and travels between exclusive perspectives opposed to each other, with dogs insane to cats and cats insane to dogs as he explains to Alice, which is why everyone is crazy to someone in Wonderland. This is why we don’t see him entirely, most of the time, because just like the elephant to the blind men from India, each perspective, such as Alice’s, only sees part, not the whole. This is how his head watches others argue about whether or not he can be beheaded, each side of the argument seeing a part of the truth, but not the whole situation, as he grins on them from above, seeing both sides fight.

The Caterpillar is like time, which includes more in our lives as it continues in series, but the Cat is like space, moves through it freely, and grins at the divisions it inevitably puts between people, even after the passage of time and experience. Carroll is himself from Cheshire, and missed his family there at Oxford. We can see De Morgan’s theorems at work in the plot and characters, and particularly in the moves from the Caterpillar to the Cheshire Cat to the Mad Tea Party, with De Morgan’s second law working one way and then the other back again.

November 19, 2019 0

Aristotle, Boole, Carroll & De Morgan

Lewis Carroll, the pen name and popular title of Charles Dodgson, mathematician and logician at Oxford, author of Alice and Wonderland and Through the Looking Glass, was well versed in the logical forms of Aristotle, Boole and De Morgan, and was working on his own understanding of how logical connectives, thoughts and emotions include and exclude members of sets before Frege, Russell and Wittgenstein set formal logic in its current form and founded analytic philosophy. Carroll was engaged with problems of German idealism and British empiricism found in the work of Locke, Hume, Mill, Boole and De Morgan in the late 1850s and early 1860s, the years that he planned and wrote both of Alice’s adventures.

A careful historical, social and psychological reading of both Wonderland and the Looking Glass show that Carroll used his fantastic characters to lead Alice through the forms of the central figures in the history of logic as he knew it, including Aristotle, De Morgan, Boole and Mill, using both stories to explore how inclusion and exclusion structure our thoughts, feelings, relationships and politics. The characters of both fantasy worlds engage Alice in gathering and dividing, such that through her experiences she assumes the roles and positions she wanders through, engaging with forms and the problems of philosophy and society that involve them.

The forms of Aristotle, Boole, and particularly De Morgan are structural to the characters and plots of both of Alice’s adventures. In Wonderland, Alice works her way from inclusive child to exclusive adult, from the White Rabbit, an absurdly inclusive conjunction, to the Queen of Hearts, who threatens others with total exclusion and negation. In the Looking Glass, Alice works her way from the exclusive Red Queen, much like the Queen of Hearts, and says all ways are hers and not one else’s, to the inclusive White Queen, who accepts impossible and absurd things many times before breakfast, to finally balance in the middle, with the White and Red Queens sitting on either side of her. Alice is a developed OR, having taken all sides, who must gather and divide empirically as she moves through the adult world between total inclusion and total exclusion.

Aristotle’s syllogisms, Boole’s logical connectives, and De Morgan’s theorems and notation are structural to the absurd humor of the work and reveal much of Carroll’s process as he invented the entertaining tales that are also instructive, both false and true, possibilities, fantasies and dreams, half-truths between non-being and being, between 0 and 1 for Boole. In the opening poem before the story, Carroll says, The dream-child (like the fantastic hybrid White Rabbit) moving through a land of wonders wild and new, In friendly chat with bird or beast- and half believe it true.” Aristotle’s syllogisms and the corresponding four corners of the square of opposition can be found in Wonderland in the glass table with the golden key, the reasoning of the pigeon,the Mad Tea Party and several key characters, and in the Looking Glass it is displayed in the Red and White queens and kings, with the queens standing for ALL, the kings for SOME, the white for inclusive positive and the red for exclusive negative. The syllogisms apply to the characters in complex and interesting ways, but simple enough to identify.

De Morgan’s theorems can be found in the structures of the stories as well. After Alice meets the Caterpillar, a very inclusive but reclusive Or who tells her little, questions her much and gives her the ability to grow or shrink in perspective and size, introducing Alice to transformations, she argues with a pigeon who fears for her egg, and then goes to the Duchess’ house, where the Duchess is beating her baby and the cook is hurling everything he can at her. The pigeon is negative to alice but conjoined with her egg, and then Alice wanders into an abusive exclusive OR from a conjunction that is also a mother-child relationship, moving along De Morgan’s first law, from ~(A ^ B), pigeon protecting Alice from egg, to ~A v ~B, with dueling Duchess and baby, as well as Duchess and cook, as Alice has moved into the house and inside the brackets, finding division within.

Immediately after this, the Cheshire Cat, who sits as a grinning exclusive OR inside the divided house, wise to how every position is opposed to another, tells Alice everyone is exclusively in their own dream and mad, opposed to anyone against them, so everyone is insane. The Cat tells Alice he takes the shortcut, just as De Morgan’s theorems are shortcuts for logic, and says you can go one way to the March Hare or the other way to the Mad Hatter, ~A v ~B, but when Alice goes one way she ends up going both ways and finds the two at a table, and they protest there is no room for her, excluding her, which reverses the course of De Morgan’s first law immediately after going the first direction, from ~A v ~B, the choice of one crazy person or another, opposed to Alice’s perspective either way, to ~(A ^ B), where the two are opposed to Alice at the table together, and say there is no room inside for her. The Tea Party resembles the absurdity of Boolean abstract logical algebra, where time doesn’t move unless you ask it to, and the Mad Hatter schools Alice on how IF-THEN works in syllogistic exercises.