urquhart at cs.toronto.edu
Thu Jan 15 10:32:09 EST 2004
A finite cardinal is an answer to the question: "How many?"
and a finite ordinal is an answer to the question:
"At what place in the sequence is this object?"
The questions are different, but does this mean that
the objects are different? Perhaps, but the question
seems to me not to make sense without a context.
For example, consider the question:
"Is the empty set the same as the empty sequence?"
In some contexts, the answer would be "yes." But in
a strongly typed programming language, you might want
the answer to be "no." Hence, I don't believe that
such questions can be answered a priori -- the context
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