FOM: Maths Barbie (Frege hath said it)

[Dean Buckner]

Extraordinary that 400 years after the reverence for Aristotle "by which
men's understanding was strangled in early years" was finally overthrown, it
is still enough to say "Aristotle hath said it".  As for Frege: "what is
long established has great power over the minds of men".  The beauty of
Frege, though, is that he rarely seeks the authority of earlier writers, he
relies on his own arguments of great power and simplicity.

I don't see any arguments in these e-mails.  Heck's paper contains some
ingenious insight and above all some powerful arguments about how we can
learn from the way very young children understand the world.  No one seems
concerned to address these.  They cite Aristotle or Frege instead.

Some arguments.  Heck's argument, as I understand it, is with concepts.  If
very young children have concepts (or seem to) that involve number, but
cannot grasp HP, that is important, isn't it?

Another argument.  Young children quickly grasp the identity of characters
in a story.  That there was a dog with small eyes different from one with
large eyes, and that there is a dog different from those others.  I could
say "different from those first two", but they don't understand "first" or
"two".  Haven't they nonetheless grasped, in understanding that there is an
A, another B, and another C different from B and from A, how many dogs there
are? In an adult, that would be a necessary and sufficient condition of
understanding there were three dogs.  Don't the children grasped that?  They
just haven't learned how to use the word "three".

Give me an argument to show I'm wrong, without quoting Aristotle or Frege or
anyone!

DB

PS Thank you by the way to the people who sent the interesting arguments
directly to me.