Le vendredi 7 février 2014 06:22:09 UTC+9, xorxes a écrit :
On Thu, Feb 6, 2014 at 1:34 AM, guskant
<gusni...@gmail.com> wrote:
Although it will become out of topic, I have another suggestion related to the BPFK page of gadri.
"Any term without an explicit outer quantifier is a constant" should be changed to
"Any term without an explicit outer quantifier can be a constant",
because an usual predicate logic has an axiom on a constant c that "F(c) {inaja} there is at least one (individual) x such that F(x)";
That applies to singular constants, whereas unquantified terms need not be singular, but the version with plural quantifiers will still be valid.
Actually, there is no explicit plural qiantifier in Lojban, though implicitly there are.
Even Thomas McKay does not adopt plural constant. For individual constant c, there are two axioms:
- [for all Y: Y {me} c] c {me} Y ;
- F(c) {inaja} there is X such that F(X) .
Even in the plural logic, F(c) implies a quantifier.
If you use the term "constant" as of the version with plural quantifiers, you should mention it in the gadri page, and also you should explain how Lojban treats plural quantifiers. Otherwise I don't understand how a constant implies no implicit quantifier.
this means that the sentence "any term without an explicit outer quantifier is a constant" automatically implicates an outer quantifier {su'o},
It shouldn't implicate that. "F{c} -> Ex F(x)" does not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for "Ex ...x...". Similarly xorlo says that "lo broda" is not just shorthand for "su'o lo broda".
I did not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for "Ex ...x...".
When F(c) is said, it says implicitly that "Ex F(x)" is true.
and it contradicts to xorlo itself that there are no default quantifiers.
Not just no default quantifiers. No implicit hidden quantifiers at all, The point is that "lo broda" is not a quantification of the bridi it appears in, the way "su'o lo broda" is.
I agree to that point, and I consider that F(c) implies implicit hidden quantifiers, and conclude that it contradicts xorlo.