Posts tagged with modal logic




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.

  • When deciding whether I want to read a book or not, I am acting on incomplete information—and not just random incomplete information, marketing and Ising-spin-ish hubbub. I have a hazy idea of what the book is going to be like.
  • As I read the book it is going to change me.
  • "Be very, very careful what you put into that head, because you will never, ever get it out." —Thomas Cardinal Wolsey (c.1475-1530)
  • I can’t unread the book and I can’t unthink or unknow whatever ideas it gives me.
  • So even before I know what it is I have already consented to be changed.

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.

 

So it’s a logical circular logic and a higher modal order than the standard model of choice—and it relates to two other themes I want to talk more about later:

  1. So many economic decisions are just like this. Beyond just knowing my edge, I need to decide whether quantitative finance is actually a thing (and not just the subject of a book by Emanuel Derman) before enrolling in an MFE. (There are various signals on the interwebs that suggest MFE’s are not a good idea. I wrote out my reasoning more fully when I was making this decision, google “DIY MFE”.) And say I spend half a decade training to be a lawyer or engineer or doctor. Then what if I don’t like it? Since young people don’t intern or work in hospitals / law firms / alongside engineers before choosing their course of study, their decision is based on folderol, disinformation, heresay, and outer appearances. If I would have loved a career in X I’ll never know it because I couldn’t possibly sample.

    On the hypothesis that most people don’t know what they want most of the time (nor do most corporations know what they’re doing or why it works, except by accident), I’d rather look at economic agents as operating at some higher order level, away from all the information. The most I feel I can do as a rational maximiser is try a lifestyle and sample how it makes me feel (although…again, I am changing both with time and changed by my own choices as I do this). Sampling from my own utility function rather than knowing it beforehand. (Or with a corp sampling from revenue & other responses.)
  2. "Dug like a river" / "Hebbian history". One of the famous models of brain development is “Neurons that fire together, wire together”. Yogis (need a link, sorry) draw the analogy to a river—as water flows from tributaries to deltas, the act of doing so cuts a deeper and deeper channel along the same course.

    These are the same idea and I think juxtaposing habit (in mathematical terms, bien sûr!) alongside personality, mood, preference, desire, intent, pleasure, happiness, goals, rank, and free will is going to lead somewhere interesting. I’ll write more about how I can exercise “second order” free will more easily than first-order.

    For example if I close this laptop and hide it from myself I will waste less time on the internet than if I leave it open and tempt myself. (On the other hand—back when I had much better time discipline from running my business I was quite better at focussing whilst at the computer. But from doing more computer stuff since then the “edges of the water” “eroded” the “sides of the channel”—and now my computer time management is spilled out like a floodplain. So very Hebbian in that story itself.) Some people pay a personal trainer so that they’re committed to work out (but couldn’t they have saved money and just worked out?). And a married man may stay away from strip clubs, red light districts, and too many drinks with attractive coworkers—and would we consider his desire to steer clear of temptation a form of infidelity?

    The jazz educator David Baker described the progression of jazz improvisational creativity this way: first you learn to copy long licks, scales, pre-formed patterns. Second you start playing with these, so that you have a coarse level of control (free will, in my “interpretation”)—splicing together the known parts. As you progress to higher levels of mastery, your control, focus, creativity become ever more atomic. A true improvisational master is present—deciding, thinking—in every millisecond of the notes, rests, articulation, and consciously chooses every aspect of what s/he’s doing and why.

    I’ve found this pattern to hold for me in areas besides jazz improv (and it even holds a lesson for maths explanations—to remember that your audience is probably not at such a fine-grained level) and I want to juxtapose as well whatever this view of personal development is pointing to, against the Lagrangian utility concept.




  • ❤ ❤ ❤ ❤ ❤ ❤ ❤ ❤
  • I think I think I love you.
  • I know I know my heart.
  • I think I know what love is.
  • I know I think you’re wonderful, but I also know my thoughts are fickle.
  • ☠☠☠☠☠☠☠☠☠☠☠☠
  • I hate those who hate.
  • I judge the judgmental.
  • I don’t tolerate the intolerant.
  • Mitt Romney is a bad person.

Oops, that last sentence wasn’t modal.

◻ ⋄          ∀ ∃          ⊢ (⊬¬)




Brought to you by into the continuum:

To paraphrase Boolos paraphrasing Gödel paraphrasing himself:

It is true that 2 plus 2 is 4. I hope you can at least believe that much. Of course, it can be proved ⊢ that 2 plus 2 is 4. It can also be proved that it can be proved ⊢⊢ that 2 plus 2 is 4.

Moreover, it can be proved that it can be proved that it can be proved ⊢⊢⊢ that 2 plus 2 is 4. We could continue in this seemingly trivial manner, but what we are hoping for is that 2 plus 2 is not 5. Fortunately, it can be proved ⊢ that 2 plus 2 is not 5, and that too can be proved ⊢⊢.

Now just to be on the safe side what we really should ask is if it can be proved that it can’t be proved ⊢⊬ that 2 plus 2 is 5…. It can’t! ⊬ ⊢⊬ In fact, no claim of the form “claim X can’t be proved” can be proved.∀X:(⊢⊬X)→⊥ or ∀X:⊬X

So thanks to Gödel … it can be proved that if it can be proved that it can’t be proved that 2 plus 2 is 5, then it can be proved that 2 plus 2 is 5. ⊢(⊢⊬X→⊢X) [Which is a contradiction.] I would rather take an incomplete theory over [an unquestionably wrong, self-]inconsistent one any day. Wouldn’t you?

… pretty tanpura drones in the pitches of C# and A, respectively (which I suggest listening to with eyes closed and nice headphones).

If on reading that you thought: “the ⊢⊬⊢⊢ symbols…could you do math with those operators?” then here’s some more at the SEP.




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.