On 03/10/2011 14:10, Andrew Welch wrote:
It's a common misunderstanding about universal quantification. The
proposition
every S satisfies P
is always true when S is empty, regardless of P.
For example, the statement "every hotel on St Kilda is fully booked" is
true, as is the statement "every hotel on St Kilda has vacancies" (there are
no hotels on St Kilda).
Heh, nice. So:
every hotel on St Kilda is fully booked, yet some hotel on St Kila
isn't fully booked.
Um no. Another surprise is that (every $x in X satisfies P) doesn't
imply (some $x in X satisfies P). If X is empty, then the first
proposition is inevitably true, while the second is inevitably false.
Logic is full of pitfalls.
Michael Kay
Saxonica
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