FOM: Alice, Bob and Carol

[Martin Davis]

At 09:17 PM 4/8/2002 +0100, Dean Buckner wrote:
>5.  Using a very limited number of words, and without any stuff about
>properties of collections of objects, we can communicate an important fact
>about things, namely how many there are.
>
>And that, surely, is all we need to know about number.  Frege has this idea
>that something more is required.  Any collection of objects must have a
>property that defines them as a set. So Alice Bob and Carol have some
>property F3, that only applies to them, Alice and Bob are marked out by some
>F2, Alice by some F1, that uniquely applies to her.

Surely what is missing from this is the concept, idea, or (speaking 
extensionally) set of numbers. I believe Frege was trying to explicate this 
concept. I don't know whether Dean Bruckner is also trying to do this, but 
if so, I don't believe he has succeeded.

Martin Davis


                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
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