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Re: Lojban is *NOT* broken! Stop saying that! (was Re: [lojban] Re: Vote for the Future Global Language)
Robert LeChevalier, On 06/01/2011 15:00:
Ivo Doko wrote:
Wow, you guys need to learn your logic. Let's do it properly:
A = "lojban is fully defined."
B = "lojban is complete."
C = "lojban is a functioning language."
"lojban is not a fully defined, complete and functioning language" can be written as:
Not it can't. Your summary sentence is NOT
¬(A ∧ B ∧ C)
The closest English can come to that is
"It is not the case that lojban is fully defined, and that lojban is complete, and that lojban is a functioning language." and even that is potentially ambiguous in several ways, because the words themselves are ambiguous given differing contexts. (for example, "Lojban is complete" and "Lojban is a complete language" are not necessarily identical in meaning.)
Your summary sentence uses "not" as a contrary rather than contradictory negation, and combines the three independent logical terms into a single complex modifier of the word "language". It thus is NOT the same as the three separate sentences, logically ANDes and the whole negated.
Lojban makes the differences extremely clear. English obviously does not.
In English, logical scope tends to be ambiguous, at least within the same clause. So English "not A, B and C" can mean "It is not the case that each of A,B,C is the case" or "For each x, where x is one of A,B,C, it is not the case that x is the case".
Unless it has been fixed by recent BPFK action, Lojban has *exactly the same ambiguity* with regard to logical scope between elements that are not explicitly prenexed. (At least Lojban has the option of prenexing to eradicate ambiguity, but it is an option almost never used and that if often used would be received with opprobrium as stylistically objectionable.)
--And.
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