The purpose of a family is the enhancement of the individual pursuits of happiness … in the overall … preservation of the family as a whole.
—from Family Wealth
Is this a logical sentence, or not?
Posts tagged with logical circular logic
Perception is reality. Any beer drinker who is surprised that Guinness has a unique and excellent taste and PBR tastes exactly like Budweiser needs to switch to Guinness because your taste is objectively awful.
That’s why Guinness’ branding is a seal with a ball and Budweiser needs to use bikini babes.
There’s something much deeper going on here, though: a fundamental problem with utility theory and hence, with economic theory. Kahneman & Tversky pointed out that it’s wrong to think of preferences as being read off of a master list. But not only are they constructed in the elicitation process, they’re constructed before as well. You’re looking at experimental proof.
I tried to write about this before in the context of the famous Pepsi/Coke fMRI experiment, but it’s too hard. I want to tie in sardonic Don Draper quips, the invention of diamonds, and my own experiences of my desires and wants and dreams being formed by outside (and therefore, sinister?) forces rather than from truly “within me” — whatever that might mean. Why do I want what I (think I) want? Even Doug Hofstadter treads tenderly around the topics of free will and one’s own true desires and self-determination and such.
I have no idea what my subconscious wants— Cameron Guthire (@thiscameron)
Even though I feel that these things all belong together, I don’t understand it all well enough to put forward a thesis explaining the inchoatia. But even with just the few experimental examples we have, it’s clear that desires can be manufactured, and that there’s a lot of money to be made in doing so. So just with that basic knowledge the Lagrangian model of utility that underlies all of the Edgeworth boxes, welfare theorems, and so on is missing a crucial quality. Namely, &sym;1% of the global economy is spent on making people want things. That doesn’t bear on “utilitarian” products like oil, shipping, … but it definitely bears on aspiration and retail. I’m talking about circularity in the definition of value. If you can logic that one out, let us know.
Several years ago I sat (after yoga class) with some Zaa Zen practitioners. As I understood the practice from doing it once, Zaa Zen basically consists of sitting in good posture, staring at a blank wall, and clearing your mind.
It wasn’t my favourite meditation I’ve ever tried. (So far my favourite was something that into the continuum introduced me to: Vipassana meditation. The way I did it was to sit outdoors in nice weather and listen to the sounds and stop thinking about my own anxiety or problems. Something much like the John Cage lecture that until a single soliton survives posted. Being aware of the world around you and “listening” or “taking in” rather than “forcing” or “pushing out”.)
But I definitely remember the conversation I had with one of the practitioners (Tony) afterwards. Tony was maybe 20 or 30 years older than me but I felt we instantly connected on some mental level. He told me he had been a failure at pretty much everything he had tried in life. How he was a black sheep of his family; how he tried to be a biologist; there were a few other things he tried and he hadn’t been very good at any of them. But in some sense it didn’t matter (remember, this is the wisdom of years talking. According to economic research people tend to mellow, their aspirations and hopes drop to a realistic level, and they become intimately familiar with the passing of time—whatever you optimise, whatever you read, however much you drink, whatever you earn, however you train, however many relationships you destroy—that passing of time always clicks, click, click, tick, steady.) and he could always come back to his practice. A different meaning of “return to the breath”.
Anyway, we were talking about various I guess spiritual things. More like a mixture of the mental-ethereal and the sense-grounded. He was telling me how Zaa Zen was so great and I would really like it and I should read this book and so on. You know how people always do that—they’ve read a book and then they say you would love it. Well, no, I think just you liked it and I have my own stack of stuff that’s my to-read list already. So normally I would just keep that kind of thought to myself but since Tony and I had an unusual level of honesty and directness for perfect strangers who just met, I brought up what I see as the circular-logic problem of picking up any book.
This is why, I said, I won’t read the book you’re telling me I will like so well. From my outsider’s perspective I don’t trust enough in the Zaa Zen idea. Not to say that it is some hokey New Age crystals or whatever, but I don’t sense—from standing on the threshold—that this is a house I want to get comfortable in.
(This is also why I started reading so much mathematics. From an outsiders’ perspective it seemed like “This is where the truth is. Following Wolsey’s idea, with a hungry reification of Plato’s philosopher-kings, if I put in only veracity and earnest labour, the result should be something good.)
Tony told me this attitude was actually quite Buddhistic or Zen of me. So I felt very proud that in avoiding looking at the Zaa Zen I had apparently picked up something of it—and it’s a nice geometric shape now that I reflect on it.
Some say science & mathematics are reductive.
żfunction independently. (The speed the soccer ball falls downward off the cliff is unrelated to how much forward momentum you kicked it.)
The reductionistic approach to science has to pair with qualifiers and caveats that “The lab is not the real world” and “We’re just trying to model one phenomenon and understand one thing”: hopefully combining
B doesn’t introduce complexity in the sense that
A+B is more than the sum of its parts — in statistical modelling language, that the interaction terms don’t overwhelm the separable, monic terms.
But is it really true that mathematics is reductionistic? I can think of both separable mathematical objects and not-separable ones. You could argue, for example, that a manifold can be decomposed into flat planes—but then again, if it has a nontrivial genus, or if the planes warp and twist in some interesting way, wouldn’t you be nullifying what’s interesting, notable, and unique about the manifold by splitting it up into “just a bunch of planes”?
Or with set theory: you could certainly say that sets are composed of atomic urelemente, but then again you could have a topological space which is non-decomposable such as an annulus or network or 1-skeleton of cells, or a non-wellfounded set (cyclic graph) which at some point contains a thing that contains it.
How about a sort-of famous mathematical object in the theory of links & knots: the Borromean rings.
The Borromean rings are famous for the fact that they cannot be decomposed into a simpler atom, whilst retaining their Borromean nature. In other words the smallest atom you can find is the 3 rings themselves. If any one or more rings were removed then they would not be linked together.
So not only is it an interesting case for causality (is
ring 1 binding up
ring 3? No. Is
ring 2 binding up
ring 3? No. In a way none of the rings is locking up any other ring, and yet they are locked by each other.
It takes the interaction term
[ring 1 ∩ ring 2] — only together do they bind up
ring 3, but together they do bind it completely. (Did something like this come up in Lord of the Rings or some other fantasy or myth? Like the weakest link or that square battle arrangement with spears, or having a ton of archers in Warcraft 2, but not like Captain Planet, if any member of a group breaks then its entire strength is lost (super convexity) but together they’re nearly undefeatable.)
I don’t know if historically the Borromean rings were a symbol of holism, although one would think so given this picture from the Public Encyclopedia:
Even if it hasn’t been, we certainly could use the Borromean rings now as a symbol of holism, complexity, integratedness, un-separability, irreducibility, and convolution.
Life is meaningless, unless you believe otherwise.
The theory of universal algebras was well-developed in the twentieth century. [It] provides a basis for model theory, and [provides] an abstract understanding of familiar principles of induction, recursion, and freeness.
The theory of coalgebras is considerably [less] developed. Coalgebras arise naturally, as Kripke models for modal logic, as automata and objects for object oriented programming languages in computer science, and more.
Paul Finsler believed that sets could be viewed as generalised numbers. Generalised numbers, like numbers, have finitely many predecessors. Numbers having the same predecessors are identical.
We can obtain a directed graph for each generalised number by taking the generalised numbers as points and directing an edge from a generalised number toward each of its immediate predecessors.
It has been shown that these generalised numbers can be “added” and “multiplied” in a natural way by combining the associated graphs. The sum a+b is obtained by “hanging” the diagram of b onto that of a so the bottom point of a coincides with the top point of b. The product a·b is obtained by replacing each edge of the graph of a with the graph of b where the graphs are similarly oriented.