[FOM] Which is clearer, "integer" or "symbol"?

[Vaughan Pratt]

On 1/2/2011 4:57 PM, MELVYN NATHANSON wrote:
> Everyone, even infants, understands one, two, three,..., but what's a symbol?

But do they understand one, two, three before they understand their 
first dozen words?  According to
http://firstwords.fsu.edu/parentsReportMeasures.html
children have typically acquired 30 words by 21-22 months.

Yet according to
https://wesfiles.wesleyan.edu/home/ashusterman/web/pdf/Shusterman_Gibson_Finder_BUCLD2010_largefont.pdf
children do not understand the exact meaning of "two" until they are 
nearly three years old.  Before then they only know it as meaning "more 
than one."

It seems to me that these data make a compelling case for defining 
numbers in terms of words than vice versa.

 From a pedagogical standpoint it might be better to start with the 
letter O than I, so that one can write O, OO, and OOO, pronounced 
respectively Oh, Ooh, and Oooh.  The first two can go hand in hand with 
learning to read words like MOM and BOOK.  The downside is unlearning 
that version of tally notation when counting to ten in decimal or 
writing zero as a digit, but that should have happened by the time they 
can read the first few Arabic digits.

Vaughan Pratt