- 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:
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.
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.