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Posted by Harvey on August 27, 2001 18:20:23 UTC

Hi Paul,

You were formally a platonist as I remember. Did your constructivism with infinities get the better of you? In any case, it is much more consistent of a view at least in rejecting one of them (sorry it had to be platonism, though).

>>>The formal mathematical system of arithmetic did not arise, at least in the literature, until many centuries after the usage of that system was widespread. Arithmetic has turned out to be very useful to people at the intermediate scale of humans in size and time. At our scale, there are many things whose noticeable identity persists long enough for us to count them.>Such counting, and the arithmetic operations performed on the resulting numbers, has been instrumental to human success, such as it is. It is that usefulness that answers your quoted queston.>It was only after the fact, and only relatively recently, that the system of arithmetic was formalized. Of course there is not such a gap between formalization and use of other mathematical systems, but on the other hand, those other systems find a much smaller number of users.

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