FOM: the standard model of PA
holmes at catseye.idbsu.edu
Mon Nov 6 16:12:19 EST 2000
Contrary to what seems obvious to certain other correspondents on the
list, I think that any child can understand what a standard model of
PA is like, and it takes a great deal of logical sophistication to be
talked out of this understanding.
This doesn't mean that any child can "see" any but the very simplest
properties of a standard model of PA easily, just that any child can
identify what kind of structure it is. But I don't think that being
acquainted with something is the same thing as knowing everything
about it, even in mathematics.
I'm also not saying that the child will be convinced that there is a
standard model of PA, just that the child will know what a standard
model of PA would be like if there was one (a sophisticated child may
tell you (in effect) that any sequence has to come to an end, and so
deny that there is any standard model of PA).
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