T.Forster at dpmms.cam.ac.uk
Fri Jan 16 05:08:24 EST 2004
The reason for my asking this question is that - if you are
platonist - you must have an answer to it. And I would be quite
interested in the means used to arrive at that answer. I am not a
platonist, and I suspect that if I were I would have a very strong
inclination to say that they are clearly different things. But life
is full of surprises and it seems worth asking!
Thu, 15 Jan 2004, Alasdair Urquhart wrote:
> 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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