We could try something similar even without Lojban, just in written English. We could include the 'evidentials' in text using some agreed upon notation. I guess it would be inconvenient at first, but later it could become more easy.

I just cannot imagine that I would seriously estimate the probability of every sentence I write. That would make my writing too slow, or I would just assign some arbitrary probabilities -- like 80% or 95% -- to most things.

Well, here's a first stab. We only need to cover 50-100% since English gives us negations: "unlikely" versus "likely", "unprobable" versus "probable". (If we can express 60% and we want to express 40%, we can just negate whatever we say for 60%.) Going by the above scheme, the 50-100% range requires 13 modifiers. If I replace the >99% for 99%, which I don't think is very useful, I need 13 or so. For infinity or 100%, I think it's better to signal a discontinuity by using a pair like "certain"/"impos... (Read more)(Click to expand thread. ⌘F to Expand All)Cmd/Ctrl F to expand all comments on this post

3DataPacRat8y Evidentials in Lojban are optional, not mandatory; and most of the point of this exercise, for me, is to see if I can improve the probability I assign to sentences from being simply arbitrary. I know that as I started this, many of the probabilities I assigned have been laughably inaccurate - and I haven't been able to think of a way to improve my estimation any faster than by constantly practicing my estimations.
3[anonymous]8y Using probabilities is assuming too much information you don't actually know. Probabilities depends on calibration, good math, understanding the massive difference between 98%+1% and 50%+1%, and so on. I'd use more qualitative measures that could be mapped to quantities if need be. Tautology, strong disbelief, disbelief, weak disbelief, etc.

Thinking Bayesianically, with Lojban

by DataPacRat 8y24th Jan 20121 min read66 comments

11


"Do not walk to the truth, but dance. On each and every step of that dance your foot comes down in exactly the right spot. Each piece of evidence shifts your beliefs by exactly the right amount, neither more nor less. What is exactly the right amount? To calculate this you must study probability theory. Even if you cannot do the math, knowing that the math exists tells you that the dance step is precise and has no room in it for your whims." -- from "Twelve Virtues of Rationality", by Eliezer Yudkowsky


One of the more useful mental tools I've found is the language Lojban ( http://www.lojban.org/tiki/Learning ), which makes explicit many of the implicit assumptions in languages. (There's also a sub-language based on Lojban, called Cniglic ( http://www.datapacrat.com/cniglic/ ), which can be added to most existing languages to offer some additional functionality.)

One of the things Lojban (and Cniglic) has are 'evidentials', words which can be used to tag other words and sentences to explain how the speaker knows them: "ja'o", meaning "I conclude", "za'a" meaning "I observe", "pe'i" meaning "It's my opinion", and more. However, there hasn't been any easy and explicit way to use this system to express Bayesian reasoning...

... until today.

Lojban not only allows for, but encourages, "experimental" words of certain sorts; and using that system, I have now created the word "bei'e" (pronounced BAY-heh), which allows a speaker to tag a word or sentence with how confident they are, in the Bayesian sense, of its truth. Taking an idea from the foundational text by E.T. Jaynes, "bei'e" is measured in decibels of logarithmic probability. This sounds complicated, but in many cases, is actually much easier to use than simple odds or probability; adding 10 decibels multiplies the odds by a factor of 10.

The current reftext for "bei'e" is at http://www.lojban.org/tiki/bei%27e , which basically amounts to adding Lojbannic digits to the front of the word:


ni'uci'ibei'e -oo 0% 1:oo complete disbelief, paradox
ni'upabei'e -1 44.3% 4:5
ni'ubei'e <0 <50% <1:1 less than even odds, less likely than so
nobei'e 0 50% 1:1 neither belief nor disbelief, agnosticism
ma'ubei'e >0 >50% >1:1 greater than even odds, more likely than not
pabei'e 1 55.7% 5:4 preponderance of the evidence
rebei'e 2 61.3% 3:2
cibei'e 3 66.6% 2:1 clear and convincing evidence
vobei'e 4 71.5% 5:2
mubei'e 5 76.0% 3:1 beyond a reasonable doubt
xabei'e 6 80.0% 4:1
zebei'e 7 83.3% 5:1
bibei'e 8 86.3% 6:1
sobei'e 9 88.8% 8:1
panobei'e 10 90.9% 10:1
pacibei'e 13 95.2% 20:1
xarebei'e 62 99.99994% 1,500,000:1 5 standard deviations
ci'ibei'e oo 100% oo:1 complete belief, tautology
xobei'e ? ?% ?:? question, asking listener their level of belief



By having this explicit mental tool, even if I don't use it aloud, I'm finding it much easier to remember to gauge how confident I am in any given proposition. If anyone else finds use in this idea, so much the better; and if anyone can come up with an even better mental tool after seeing this one, that would be better still.



.uo .ua .uisai .oinairo'e

11