[YG Conlang Archives] > [jboske group] > messages [Date Index] [Thread Index] >
This is a precis of what I think jboskologists think about logic in Lojban,
or at least what I think that I think. :-)
The four Aristotelian functions are expressed by Q da poi S cu P, where
S is the subject term, P is the predicate term, and Q is a quantifier.
Any quantifier is meaningful, but the standard A, E, I, and O functions
are expressed by the Qs "ro", "no", "su'o", and "me'iro".
These can be translated "every", "no", "some", and "not every".
(The formulation "Some S is not P" is apparently a mistranslation by
Boethius of Aristotle's original "Not every S is P".
Existential import is required by quantifiers which do not allow 0 as a
possible value: specifically, "ro" and "su'o" have import, "no" and "me'iro"
do not. Existential import means that if the S term doesn't apply to
anything, the statement is false.
The standard Aristotelian relationships apply: A and O are contradictories,
E and I are contradictories, A and E can't be both true (contraries),
I and O can't be both false (subcontraries), A implies I, E implies O,
some S is P implies some P is S, no S is P implies no P is S.
Frege-style logic does not have "da poi" constructions, and there are
only quantified variables and predicate terms joined by logical operators.
The standard rewriting of A, E, I, and O as (x) S(x) -> P(x),
(x) S(x) -> ~P(x), (Ex) S(x) & P(x), (Ex) S(x) & ~P(x) apply.
--
John Cowan jcowan@hidden.email
"You need a change: try Canada" "You need a change: try China"
--fortune cookies opened by a couple that I know