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de'i li 2002-11-06 ti'u li 23:14:00 la'o zoi. John Cowan .zoi cusku di'e
>Please, please, people. I cannot follow you. I am a foolish fond old
>man -- or middle-aged, anyway. If I contradict myself, very well, I
>contradict myself; I am large; I contain multitudes. But cannot someone
>show me just how, in plain words of the English tongue?
>
>You know. The kind of explanation I would write myself, if I didn't
>happen to be entirely at the wrong end of the stick.
I think you're talking about the contradiction between 'ro broda cu
brode' having existential import and the use of DeMorgan's laws. If
so, I will attempt to explain.
Let us assume that "ro broda cu brode"/"All S are P" implies that
there exists some broda/S, as CLL states. So, the sentence
(1) All unicorns are white.
means
(1) There exists an x such that x is a unicorn, and For every y,
if y is a unicorn, then y is white.
This sentence is clearly false; there are no unicorns. Thus, its
negation must be true. Its negation is
(2) It is false that both there exists an x such that x is a
unicorn, and For every y, if y is a unicorn, then y is white.
This is indeed true; the first part of the conjunction "there
exists a unicorn" is false, and thus the whole conjunction is
false, which is what is claimed by the negation. Now if we consider
that (1) was a translation of
(1) ro pavyseljirna cu blabi
then its negation is
(2) naku ro pavyseljirna cu blabi
We have already determined that (1) is false and (2) is true. Now,
according to CLL, (16.11, p.405-407) we can move the negation
boundary in (2) past the universally quantified term, and switch
the universally quantified term to an existentially quantified
term, thus:
(3) su'o pavyseljirna naku blabi
Now, (3) can be rewritten as
(3) There exists an x, such that x is a unicorn and x is white.
This is clearly false; there are no unicorns, white or otherwise.
Thus, (2) is true and (3) is false, but CLL says that they are
equivalent, so there is a contradiction here.
mu'o mi'e .adam.