la djan cusku di'e
In this mapping, S and P stand for sets when on the right side of a colon.I will write SP for S intersect P, /= for inequality, and 0 for the null set.All S is P (A): SP = S Some S is P (I): SP /= 0 No S is P (E): SP = 0 Some S is not P (O): SP /= S Then existential import is simply the assertion that S /= 0, and we can understand I- as asserting that S, which may be null, has a non-null intersection with P. But plainly no set P can have a non-null intersection with 0, and so from SP /= 0 we can deduce that S /= 0. Therefore I- is false if S = 0, and to assert anything useful we need I+.
The same reasoning applies to O-: Plainly no set P can have
an intersection with 0 that is different from 0, so we can
deduce that S /= 0 and to assert anything useful we need O+.
(I don't buy this argument, it is possible to give information
both with I- and with O-, it is just that this presentation
with sets already requires I+ and O+, and the same happens
in Lojban when {su'o} is defined as "at least one".)
mu'o mi'e xorxes
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