The logic of the null set isn't quite that paradoxical.
But it is true that
it can look difficult if one doesn't
analyze it properly.
Did
google copy the empty set. Well yes because each element
of this empty set was
copied. Also no because each element
of the empty set was not
copied.
You are positing two different definitions for copying
a
set.
-
Your first definition appears to be that a set was copied
if
"each element of [the] set was copied"; that does indeed
lead to the
conclusion that the empty set was copied.
-
You reach the opposite
conclusion by using a different
definition: a set was not copied if "each
element of [the]
set was not copied". And indeed, that leads to the
conclusion that the empty set was not copied.
The confusion
comes from assuming that the two definitions
are equivalent. They are
not.
Consider the set S = {WarAndPeace,EndersGame}. Let's say I
copy
EndersGame but not WarAndPeace. Have I copied S?
By your first
definition, the answer is clearly negative.
WarAndPeace was not copied,
therefore S was not copied.
Now consider your second definition. S is
not copied if
each element of S is not copied. But I have copied
EndersGame;
therefore it is not true that I have not copied
S. Put more simply: S was
copied.
The logical rule that explains this is the following: if you
move a negation over a quantifier (either "each" or
"some"), the quantifier
changes to its opposite ("each"
becomes "some" and vice versa). Thus the
negation of your
first definition is that a set is not copied if some element
in it is copied". Some is not the same as each :-)
I rather
think the second definition is correct for the
purposes of this trial. After
all, there would not be any
sense in asking about de minimis if
infringement
could only happen if you copied
everything...
Antti-Juhani Kaijanaho [ Reply to This | Parent | # ]
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