- Such systems that are complete are also inconsistent (Godel's first theorem)
- Such systems that are consistent cannot be complete as such a system cannot prove its own consistency (Godel's second theorem).
Predicate logic, how pretty delicate thou art
Natural language is not a formal system. Partially due to this reason, ambiguities arise which renders natural language somewhat inadequate for formal expression, but rather appropriate for planting memes in the impressionable. Ask Roman Polanski.
In an attempt to rid ourselves of the ambiguities of language, projects arose to establish language based on the principles of first order logic. That is, these projects aimed at formalising natural language by injecting a set of formal rules into a mixture of natural languages. Two of these projects are:
- Loglan, which is one of the first of its kind and copyrighted.
- Lojban, which is similar to the open source nemesis of Loglan because what good is a language if you can't speak it with anyone?
In my previous post on nerd bands, I lamented the fact that I couldn't find any bands who sang in Lojban. I went through a few Lojban lessons and noticed the following:
Lojban nouns
In Lojban, there is a class of word called cmene. Cmene is the Lojban term for name. This is similar to the existential quantifier in predicate logic. In other words, without the jargon or the batty symbols:
There exists one something with one particular name. The name for this name is cmene
All cmene follow the format of CCVCV, or five letters consisting of Consonant Consonant Vowel Consonant Vowel. Even cmene, so that's pretty sweet as this barber shaves himself.
Edit: this is incorrect. All gismu (root words) follow the format of CCVCV or CCVCV. Cmene is the gismu that refers to proper nouns in Lojban. All cmene that are first names are preceded by a full-stop if they start with a vowel and end in a consonant.
Lojban verbs, or what functions as verbs
Words that function as verbs in Lojban are called selbri. In the lesson on selbri, the authors explain that a selbri and a verb are not the same thing, as a selbri merely functions like a verb does. A selbri is usually a root word from a class called gismu. Gismu is a type of word that indicates a root word in a similar way that verbs have roots, though a gismu is not necessarily a selbri, or vica versa.
All gismu have one of two forms: CVCCV or CCVCV. This means that all cmene are gismu, or that all names are root words. Right?
Edit: Since I was mistaken and cmene do not have the form of CVCCV or CCVCV if they are first names, all cmene are not gismu.
What is the hax?
Cmene (name) is a gismu (root word) because cmene is a root word that indicates a name for a group of words that indicates names.
Gismu (root word) is the cmene (name) for root words in Lojban. It has the form CVCCV. Yet all cmene are meant to have the form CCVCV. This barber does not shave himself. Maybe it's a bit of a long shot as all cmene are gismu but all gismu don't have to be cmene? Fine.
Edit: I was wrong here so the above hacks does not apply.
Selbri (connective that acts like a verb) is the cmene (name) that refers to a group of words that function like verbs in Lojban. Thus, selbri is a cmene that has more than five letters. Selbri also breaks the rule that all cmene have the format CCVCV, as it has the format CVCCCV. This barber does not shave himself either. Hello, Russel's paradox.
Edit: Selbri is not a cmene in the first name sense, but a cmene for connectives that act like verbs. This means the only cmene rule for selbri is that it has to end on a vowel, which it does.
Is Katie the cmene of Katie Price or Katherine Jenkins?
Well, this is not so much a paradox as a set on its own. A couple of nice sets within the set, though.
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Katie Price Jordan. I wish she'd make up her mind about her cmene.
Katherine Jenkins. Too classy for this blog.
I can just imagine the kind of selbri you have in mind for these two ladies, but please let me imagine it's an empty set, thank you.
9 comments:
You don't seem to actually know what you're talking about. Let's address each of your points in order.
1. cmene is not a class of anything. It's a word that means "name". You probably mean "cmevla" (name words), which do not have to obey any rule except that they must end in a consonant.
2. All gismu are selbri, all selbri are not gismu. You have that one wrong. gismu is a morphological class, selbri is a grammatical class. This has nothing to do with cmene/cmevla, which are a completely different grammatical/morphological class.
3. Again, wrong. All gismu must have either a CCVCV or CVCCV morphology. cmene/cmevla I've already explained. So again, no.
4. Once again you're wrong. The word "selbri" is a lujvo, a different morphological class formed by combining two or more "short forms" of gismu whilst obeying certain rules of the morphology. It's formed from the cmavo {se} and the gismu {bridi}.
Also, we usually use the name of the class, but we don't say everything is a name for something, we usually say they are words meaning something (the gismu {valsi} is what you want for that).
So no, it isn't whatever's paradox, you just poorly researched your topic.
By the way, I'm a musician/audio engineer and have written at least one song in Lojban, with more to come once some other community projects are out of the way.
If you're interested in learning Lojban, we do free lessons on IRC.
irc://irc.freenode.net/lojban
Maybe you can stop by for a free lesson and then make a blog post with the correct information about Lojban's grammatical and morphological classes. You seem like you would learn very quickly.
Thank you for the comment.
1. According to entry on cmene on this Wiktionary, cmene is a term used to indicate proper nouns. There is also a list of the indexes used on that Wiktionary, that includes cmene as proper nouns. Thus, cmene is the name for a class of words that functions like proper nouns function in other languages. Or it's just a word for names, in which case names for other things (other than proper nouns) have to follow the format of cmene to avoid paradoxes.
2. I never claimed that all selbri (predicates) are gismu (root words). I claimed that all cmene (names) are gismu. I claimed this because cmene follow the CCVCV format and gismu follow both CCVCV (same as cmene) and CVCCV (different from cmene) formats. But I never claimed that all selbri are gismu. In fact, I claimed that selbri and gismu are not necessarily the same.
3. I'm not sure what you are referring to with 3. Please clarify your statement (in a natural language :-)).
4. I understand that cmene is a name for a name and selbri is a name for a predicate. This is exactly where the paradox comes in. Selbri is a cmene but it doesn't follow the format of cmene. Unless of course cmene were a class of words, like proper nouns, of which a word like selbri would not form a member.
The purpose of my post was not to highlight my ignorance of Lojban (which I readily admit), but to point out that if a language is based on predicate logic, it ought to inherit the inherent paradoxes.
It depends on how you interpret the term cmene - as a name for any name (which would include the names of classes of words, thus the barber shaves himself and thus selbri would have to follow the same format, which it doesn't), or just the name of proper nouns (which would not include names like selbri, thus the barber does not shave himself, thus selbri can't be a name for something, including predicates in Lojban).
The fact that I cannot determine from my sources (to which I've linked to, so please verify that they are reliable and that I've used them correctly) whether the barber shaves himself or not, is the paradox.
Thank you, I'd love to learn some Lojban and I'd love to hear some Lojban singing.
Lojban took inspiration from predicate logic. However, it need not inherit any paradoxes. Lojban is not a formal logic, it is a language.
We might describe formal logics and theories in Lojban, and we might even write the axioms of our theories in grammatically correct Lojban, but the language these formal sentences are written in will not really be Lojban (it will need to be restricted if we are to have any hope of proving our logics complete), and the provability relation in these logics will have little to do with Lojban.
It is certainly possible to express paradoxes in Lojban, of course. {.i la'e dei jitfa}, for example, means something like "this sentence is false." Paradoxes like this don't make Lojban itself in any way inconsistent or incomplete.
.i .a'o lo nu cilre la .lojban. cu pluka je se snada do
>1.
We don't have nouns, proper or otherwise.
>There is also a list of...
Again, we don't have nouns.
>Thus, cmene is the name for a class of words that functions...
Again, that doesn't mean anything. "cmene" is literally a name, nothing more, nothing less. It isn't a morphological or grammatical class. "cmevla" is a morphological class of words which are names and only names.
>2.
This is also wrong. All cmevla are not gismu, and in fact, they cannot be as they are two different morphological classes. All cmevla must end in a consonant, all gismu must obey CVCCV or CCVCV morphology. There is no contradiction because they are two completely different morphological classes.
>I claimed this because cmene follow...
Again, wrong. See above comment.
>But I never claimed that...
They are necessarily the same. -ALL- gismu are selbri.
>3.
Should be clear by now.
(more to come)
>4.
No, it isn't. "cmene" is a word that means "name". It doesn't mean anything else. The actual word "selbri" is a valsi (word), morphologically it is a "lujvo" (compound word), and grammatically it is in of itself a selbri. Your logic is circular in that case. "Duck" is the name of ducks, selbri is the name of selbri. I'm not sure what you're getting at.
>Selbri is a cmene
Semantically, yes.
>but it doesn't follow the format of cmene.
Assuming you meant "cmevla" then yes, you're correct, because it's morphologically a lujvo and grammatically a selbri.
>Unless of course cmene were a class of words...
Correct. "cmevla" look like this: "lindar". It ends in a consonant, and doesn't have to obey any other rules (perhaps other than obeying rules regarding valid consonant clusters). cmevla have no meaning in of themselves.
>The purpose of my post...
You have, as of yet, failed to point out any paradoxes that actually exist in the language.
>It depends on how you interpret the term cmene
No, it doesn't. Literally "cmene" is defined as "x1 is the name of x2 as used by x3". I don't know where you get this idea. To call "selbri" a cmene/cmevla is plainly redundant. How would you phrase that? "selbri" is the name of "selbri"? No, it's a valsi "x1 is a word meaning/conveying x2 in language x3" if anything.
> - as a name for any name...
Okay, if you want to say it, {.i zo selbri cmene lo valsi}, which is literally, "The word 'selbri' is the name of selbri.". There is no morphological, syntactic, grammatical, or any other kind of paradox present in this except in your own logic. Whatever resource you used is incorrect, and is not using the correct names for things, or is giving out confusing information.
>The fact that I cannot determine from my sources...
I don't know what you mean by a barber, but if you're saying that 'selbri' is the cmene (name) for selbri, sure, that's correct, but the word 'selbri' is not a -CMEVLA-, which is an important distinction, as CMEVLA is a morphological class of words which must obey rules regarding phonological pairings just like every morphological class in the language, but otherwise simply must end in a consonant to satisfy the rules of morphology. 'selbri' is not a cmevla, but if you like, it is the "cmene" for the grammatical class 'selbri'. The name of its morphological class, as I had said earlier, is "lujvo". Not only that, but you missed something. The word "cmene" itself is, obviously, the cmene for cmene. (lol, zo cmene cmene la'e lo cmene) However, grammatically it is a selbri, and morphologically it is a gismu. You need to distinguish between semantics, morphology, and grammar.
There is no logic flaw, you just don't seem to understand how our grammar system words because there are so many different names for things.
Also, at a cursory glance, your source of information is correct, which makes me wonder how you managed to get so confused in the first place.
>Thank you....
You're welcome.
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