Aristotle’s Square of Opposition … in Lojban

Here it is: one obscure type of logic expressed in an even more obscure type of logic! You’re welcome!

xusra natfe
kampu ro da poi broda cu brode no da poi broda cu brode
steci da poi broda cu brode da poi broda cu na brode

I wasn’t sure whether to render the O categorical sentence (bottom-right) as {naku ro da poi broda cu brode} or {da poi broda cu na brode}. It has been left as an exercise for the reader to determine whether they are logically equivalent.

Lojban logical connectives illustrated with Venn diagrams

Truth functions for Lojban logical connectives
Truth functions for Lojban logical connectives

For my own reference, I have illustrated the 14 possible truth functions that can be expressed using the A, E, O and U connectives in Lojban, and annotated them with the most appropriate forethought connective to do the job.

In many cases, there are multiple ways to express a single truth function. For example, {gonai broda gi brode} is logically equivalent to {segonai broda gi brode} and {go broda ginai brode} and {sego broda ginai brode}, but despite the fact that they are well-formed Lojban there is literally no reason to ever use those constructions, and ones like {go … ginai …} kind of defeats the purpose of using a forethought connective in the first place. Mutatis mutandis with {ga … gi …} vs {sega … gi …}, etc.

Of course, since there’s 4 regions of the Venn diagram that could be shaded or not, that makes 24=16 possible truth functions. The topmost Venn diagram is the forethought-connected question, not an attempt at the truth function where all the regions are unshaded. So what happened to the remaining two functions? It is not possible, using the regular Lojban connectives, to make a Venn diagram that would be all white or all red. Fortunately, as the CLL says, these are “pretty useless anyway.”

Come to think of it, how would I render those into English? “A or B or both or not A or B?” and “Not A and Not B and not not A or B?” Gross.

For a more legible version, see the attached PDF: Truth functions

Short story prompt for Lojban enthusiasts: la cizra mensi

Short story prompt: la cizra mensi

The hero of your short story has found a way to summon the Weird Sisters of Macbeth fame to inquire after the future. Worried that the witches will try to trick your hero by giving a prophesy that can be favourably and plausibly read one way, but that also has an alternate, surprising and terrible interpretation that is consistent with the words of the prophesy, your hero finds a way to force the witches to speak in Lojban.

Unfortunately for the hero of your story, a witch’s prophesy can backfire in unexpected ways that still respect the letter of the prophesy itself, even if it’s delivered in a language that’s syntactically unambiguous.

Macbeth 1.3

In the spirit of this short story prompt, I have rendered the first part of Macbeth, act 1 scene 3 into Lojban for your enjoyment. Corrections and suggestions welcome. :)

termafyfe’i 1: [1] .i doi lo mensi do pu zvati ma

termafyfe’i 2 .i lo jai bu’u lo nu catra lo xarju

termafyfe’i 3 .i doi lo mensi do zvati ma

termafyfe’i 1 .i lo fetspe be lo blopre pu cpana be lo galtupcra ku ralte lo narge

[5] gi’e omnomo gi’e omnomo gi’e omnomo .i lu ko dunda fi mi li’u se cusku mi .i lu ko cliva doi lo termafyfe’i li’u lo zargu citka cagna cu se krixa .i lo nakspe be lo se go’i pu klama la .alepos. gi’e bloja’a la .tirxu. .i ku’i ne’i lo julne mi lo te go’i fankla

[10] .ije mi simsa be lo ratcu poi claxu lo rebla ku co’e gi’e co’e gi’e co’e

termafyfe’i 2: .i mi dunda do pa lo brife

termafyfe’i 1 .i do xendo

termafyfe’i 3 .i mi co’e pa lo drata

termafyfe’i 1: [15] .i mi ralte ro da poi drata .i je’a lo blotcana cu bifca’e ro da poi farna be fi lo makfartci pe lo blopre ku’o zi’e poi se djuno .i mi ba simsa be lo sudysrasu bei lo ka sudga ku rincygau

[20] .i lo nu sipna ku ba canai lo donri ku .a lo nicte ku dandu za’e lo galtu dinju canko gacri .i zo’e ba dapma renvi .i ba ca lo tatpi jeftu be li so pi’i so cu jdika lo ka stali .e lo ka pacna .e lo ka gleki

[25] .i zu’u lo bloti to’e pu’i se daspo .i zu’unai lo go’i vilti’a se renro .i ko viska lo se ralte be mi

termafyfe’i 2: .i ko jarco fi mi .i ko jarco fi mi

termafyfe’i 1 .i mi nau ralte lo tamji be fi lo blosazri

[30] poi ca lo nu zdani klama ku bloti janli morsi

[.i ne’i damri]

termafyfe’i 3: .i damri .i damri .ua .i la .makbet. je’a tolcliva

ro da poi termafyfe’i: .i lo cizra mensi noi xance jgari simxu zi’e noi klama be fo lo xamsi .e lo tumla be’o sutra

[35] cu klama fi’o tadji tu’a di’e .i ciroi klama lo tu’a do .i ciroi klama lo tu’a mi .i ciroi ji’a klama .iki’ubo krefu fi li so .i ko smaji .i lo makfa cu bredi

[.i nerkla fa la .makbet. .e la bankos.]

Four causes in Aristotle and in Lojban

Cause of parents' death? Got in my way.
Cause of parents’ death? Got in my way.

Reading through Lojban for Beginners on a Friday night (like everyone else who knows how to party—am I right?), I got to the chapter where causation and implication are discussed. In it, the authors explain that Lojban has 4 ways to say “because.”

The inventors of Lojban were not the first to preach a Doctrine of Four Causes. Aristotle also believed that when you asked Why?, you could be reasonably taken to be asking one of four different questions, which I have summed up below in Table 1. In Table 2, I summarise the four ways to say “because” in Lojban.

I made an attempt to see how well these things would match up by giving examples and rough equivalents. Unfortunately for Aristotle, they only seem to correspond decently well in two cases. But then I guess if I were trying to write a timeless philosophy, and someone told me that after ~ 2300 years, people would still be interested in half of the questions that I identified, I’d probably think that I did pretty well. Especially considering that Aristotle spoke Ancient Greek, which is pretty much the anti-Lojban if any language is.

For the other two of Aristotle’s causes, there are words in Lojban for the ideas expressed, but they aren’t really “causation” type words in the same way.

Table 1. Aristotle’s four causes

Cause Example Rough Lojban equivalent
Material cause The house is here because there were bricks, mortar and wood here previously. te zbasu (?)
Efficient cause The house is here because Bob built it. rinka
Formal cause The house is here because the materials have been arranged in a certain way. tarmi (?)
Final cause The house is here because Bob wanted to have dance-parties inside it. mukti

Table 2. Causes in Lojban

Cause “Because” word Root gismu Example Rough Aristotelean equivalent
Physically caused ri’a rinka la bab. morsi ri’a lonu mi darxi by
Bob is dead because I hit him.
Efficient cause
Motivated mu’i mukti la bab. morsi mu’i lonu mi na’e nelci by
Bob is dead because I didn’t like him.
Final cause
Justification ki’u krinu la bab. morsi ki’u lonu by djuno lo dukse
Bob is dead because he knew too much.
Logically entailed ni’i krinu la bab. morsi ni’i lonu ro lo remna mrodimna kei .e lonu by remna
Bob is dead because all humans are mortal and Bob is a human.

Here’s some materials for learning Lojban

Here are a few of the resources that I’ve been using to learn Lojban so far. I will very likely update and expand this list as time goes on.

Basics on Lojban

Good Lojban reference sites

Flash cards for learning Lojban

Anki (free and open source for Linux/Mac/Windows/Android/iOS)

  • Has a set of Lojban cards
  • Syncs between devices

So I started learning Lojban .ui

This Friday past, I started learning Lojban. For the non-initiate, Lojban is a constructed language based on predicate logic that is syntactically unambiguous. I’d known about it for years, probably hearing about it first on CBC, maybe 10 years ago. It’s the sort of thing that shows up in Dinosaur Comics or in XKCD periodically. Up until this weekend, the existence of Lojban had mostly been one of those “cocktail party facts,” but then I finally took the plunge. After 1 weekend of working on it, I’m about 35% of the way through Lojban for Beginners, having downloaded it to my Kobo for reference during the car ride to Stratford.

It’s often billed as being an ideal language for fields like law, science or philosophy, due to its unambiguous and culturally neutral nature. So I set out to find out certain specialised terms from my field, bioethics, and it turns out that they mostly don’t exist yet. This, of course, offers some exciting opportunities for a grad student. :)

I’ve convinced a few people in Montréal to learn Lojban with me, and even found a Montrealer who speaks Lojban on a IRC channel. (Yes, IRC still exists!) We may “ckafi pinxe kansa,” as they say in Lojban, apparently.

If you too want to get in on the ground floor of Lojban Montréal, let me know!