[part 2]

Also, while I’m sure you could take Lojban and use it as a syntax for a more traditional formal system, idk what the purpose would be cuz we already have good systems for doing math on computers or whatever that use already familiar syntax. It would probably just be off-putting to both most Lojbanists (the few that remain at this point) and mathematicians :(

But anything more than that is kinda dreamy and vague. And nailing down the meanings of Lojban root words might be useful but it would also just constrain people entirely to pre-existing biased cultural conceptions of meaning. Maybe some kind of formal system that only defines the semantic meaning of the standard grammar but with optional and modular definitions of root words and other stuff that can be “imported” into a speaker’s personal formal conception of Lojban contingent on the speaker’s or the listener’s acceptance of those meanings could be constructed, idk.

Idk, the secret, forbidden desire inside every Marxist or at least inside me to do metaphysics :3

Or idk, maybe a formalization of dialectics is possible without ending up at metaphysics?

I am so far away from your reply now, let me try to get back to it lol

A paraconsistent system where where individuals can have different universes of discourse would have no analytic statements. Instead, I think you are looking for Jaskowski’s discursive logic, which formulated in modal logic.

Yeahh, I think I kinda misused the term “universe of discourse” lol. I was actually thinking along the lines of discursive logic, as in like some kind of shared frame or world or whatever where proposition P can be true but in other worlds P can be false or vice versa or something more complicated than that. The system is paraconsistent but has a concept of a local consistency I guess

I am VAGUELY (been aware of but didn’t have the context to begin to understand until recently) more familiar with da Costa’s various systems of “formal inconsistency” or whatever. Would def recommend looking into if you’re interested how inconsistency can even exist in a logic without reducing the whole thing to triviality

A final thing i would point out, is that there is a good reason sets aren’t the exact formulation of lojban: see russel’s paradox. This is a problem which intuitionistic logic “solves”, which sees usage in proof assistants like coq and lean.

Sets have a weird place in current Lojban cuz they do exist both explicitly and implicitly as the products of the set-specifying gadri (articles) le’i and lo’i, and the indefinite gadri le and lo, respectively. Yet they don’t really have any semantics beyond vibes rn

Sry, there is lots more to say but this is way too long and I’ve burned myself out for rn lol. If you ever get this far into reading this confused mess, thank you :3

I am doing metaphysics and I’m not doing metaphysics , repeat this sentence forever except this part past the comma including the comma

[part 1, see second reply]

Hii, ty for your reply, it has given me a lot to think about tbh. I actually hadn’t read Quine’s “Two Dogmas of Empiricism” or even heard of it before (showing my inexperience ofc) despite being vaguely aware that Quine’s thinking is kinda hugely relevant to this whole issue. I did end up reading it, very fun read tbh :3, although it’s definitely something I’m gonna have to digest for a while. Has made me think more about what exactly I even would out of a formalized Lojban (or in Quine’s words: “a language in the ordinary sense [PaX: we have this former part] plus a set a set of explicit semantical rules – the whole constituting, let us say, an ordered pair”, which is the same thing as an axiomatic system or formal system, which is what I/we want for whatever reason)

Idk, so I kinda ended up here (Lojban and formal systems) cuz for a few years I have been thinking, on and off, about (these may seem incompatible lol) what a formalization of dialectics would look like cuz I’ve been microwaving my brain with Marxist philosophy for like a decade at ever increasing power levels since my early teens lol, and so much of it is quite vague at this point (btw, if I seem fixated on paraconsistency, this is why lol). Am continually kinda baffled, yet not surprised??, by the wide variety of metaphysics a lot of mathematicians and analytical philosophers work themselves up into doing. I never got any formal (in colloquial meaning) education in abstract mathematics, only found myself interested recently, but my vibe from the outside is that most mathematicians don’t really care about the philosophical foundations and implications of the systems they work within, they just wanna grill do math. I legit was under the impression previously that we all agreed this was a like a thought game we were all playing with a tenuous connection to reality but now it all kinda makes sense lol. Likeee… Russell’s paradox is a great example of how baked-in metaphysics is to this whole thing, and how inescapable it is even if you just wanna do math (grill). Naive set theories are conceptually much simpler and more elegant and the math grillers (I am very online lol) were okay with it until the metaphysicians came in and showed that it leads to self-contradiction and it scared everyone so much, even the grillers, that the people trying to formalize mathematics confabulated ZFC set theory (which I get the impression no one particularly likes) to solve this and got everyone to use it (or agree to it being at the foundations of math at least) despite it being less useful. Idk, to me, the value of these thought-systems (this is how I think of math at least) is how practically useful they are and how easy they are to use to describe/model real life things that actually matter (literally matter even). Yet a lot of the people actually thinking about the basest logic that govern these systems don’t see it as a set of arbitrary axioms attached to this language of mathematics (really just a special type of conlang with high social status and usefulness hehe) that we can just change if we don’t like and if it becomes limiting but rather some unchanging fundamental rules of reality (or in a word: metaphysics lol). Which I guess is how you end up with people like Karl Popper who take these ideas to their natural political implications: “Marxism is wrong cuz it’s not falsifiable, and being falsifiable is when you accept my metaphysics and can write your hypothesis as a theorem in my logical system that can be contradicted [or something silly like that lol]”. And at the furthest extreme of that, you get people like Ayn Rand who say stuff like that Marxism is fundamentally wrong cuz it contradicts the laws of identity and non-contradiction lmao (it’s like the most ridiculous form of the human nature argument lol, “actually the very nature of reality itself isn’t compatible with communism” lmao). And ofc a lot of new physics is finding empirical evidence of phenomena which are hard to reconcile with the deterministic classical logic at the base of mathematics, at least without adding a whole bunch of new structures on top (I saw a physics meme in your post history, you probably know more than me lol) but I think people have also been cooking up “quantum” logics to deal with this too right? I guess that makes me some kind of intuitionist or something idk. Maybe everything I just said in this paragraph is wildly wrong (except this sentence ofc :3)

Ofc contradiction in the dialectical sense isn’t synonymous with contradiction in the traditional logical sense but I think they’re closer than it seems at first glance. Like it’s not that 2 contradictory terms, like the bourgeoisie and the proletariat can’t exist in the same universe at a given moment, but that the whole system eventually tends toward non-contradiction at some point in the future via some method which destroys the existence of one of the contradictory terms (or both if Marx’s “common ruin of the contending classes” nightmare becomes true) like Mao Zedong’s concept of the resolution of an “antagonistic” contradiction. This is obviously incompatible with the law of non-contradiction in some way but we also don’t want to drop the concept of consistency entirely cuz it’s useful to prevent the whole system from exploding entirely. Idk, there are lots of possible approaches to the problem and Soviet and Chinese philosophers were/are thinking about it not only cuz of its ideological aspects but cuz it maybe has the possibility of being more expressive

Anyway, that was kind of a long tangent but I feel like I need to get out into text why I think classical first-order logic is the wrong formalism for Lojban:

1. Paradoxes of material (bi)implication

The 2 connected bridi “la baljamna remoi cu se krinu le du’u le zu’adbo cu damba vo’a soi vo’a .ijo la lunra ca’a se marji le crino cirla” (World War 2 was caused by leftist infighting if, and only if, the moon is made of green cheese)

and

, for a more contrived example, the bridi “le du’u la’o sit. PaX .sit cmene mi ku goi ko’a cu nibli le du’u le du’u la lunra ca’a se marji le crino cirla cu nibli ko’a” (The predication that “my name is PaX” implies that the predication “the moon is made of green cheese” implies the predication that “my name is PaX”)

are true if we read classical formal logic into the vibes :3

Yet if a typical Lojban speaker heard you say either of these things, they would probably say: “na’i go’i” (metalinguistic negation of the last bridi) or in other words: , as in, there is something inappropriate about the entire bridi you just said lol. There is some kind of gap between the logical meaning of those bridi and what we really mean by those bridi (if we take the meanings of words I used as granted ofc). And most speakers, when they use these explicitly logical connectives, read the meanings of natural language connectives into them. Or basically, like there has to be an actual relationship between the antecedents and consequents in order for the speaker to judge the logical relationship as true. And ofc people have had an issue with this aspect of classical logic for a long time

2. Scalar negation

The bridi (sorry, this is just very funny to me, idk why lol) “le gerku cu na me la’o gy. woke gy.” (The dog is not woke) is interesting cuz all this bridi does is deny that a relationship, orrrr I guess a preposition really, exists. Or in other words, defined informally ofc, the dog not being woke doesn’t ONLY imply that the dog is based (assume reactionary definition of “based” where not woke = based).

If you want to say that, you would state the bridi “le gerku cu to’e me la’o gy. woke gy.” (The dog is the polar opposite of woke). If you want to say explicitly that the dog is something other than woke or based you would say “le gerku cu na’e me la’o gy. woke gy.”

Is interesting to me cuz the Lojban negation qualifiers seem to have meanings that would contradict the law of the excluded middle

3. There is lots more but this is getting long for a reply lol

There is a lot of other stuff like tenses or attitudinals (emotional indicators) or abstractors which would also seem to be incompatible with a classical formal definition or sometimes even any formal definition tbh

Like when I said the dog was woke or not woke like that, it might have have been more appropriate to say something like "le gerku cu ckaji le ka ce’u me la’o gy. woke gy. (The dog has the quality of wokeness) depending on what that word actually means ofc lol cuz “me” as a selbri (predicate word) really means “x1 is one of the referents of [sumti]” which when combined with “la’o” which means “the referent of” essentially means “x1 is one of the referents of the referent of the word ‘woke’” or, finally, “The dog is one of the woke ones”.

“Ka” is what Lojban calls an “abstractor” but I guess it’s also an attempt at something like an intensional logic to address the difference between “creature with a heart” and “creature with a kidney” (this example is from Two Dogmas) where they agree extensionally as in the sets or classes of things that satisfy the predicates “x1 has the body part of heart” and “x1 has the body part of kidney” may be the same thing (animals that have kidneys also have hearts) but their meaning is different. So, really, I’m saying something like “the dog or set of dogs I’m thinking of is a term that can satisfy the predicate ‘x1 is woke’”

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I guess I’m trying to figure out what I even want here. Or what is even possible. One thing I want to avoid is a massive (to me) gap between colloquial Lojban and a formal Lojban. Lojban is already a language where you can convey logic, but no one actually wants to convey logic when they’re speaking cuz it’s wordy and counterintuitive to our natural reasoning lol.