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

[A. Mani]

MELVYN NATHANSON <MELVYN.NATHANSON at lehman.cuny.edu>
> Tim,
> 
> You wrote, "So to recap my question...is it just me, or has there really 
been a sociological shift over the past several decades?"
> 
> I think it's just you.  Everyone, even infants, understands one, two, 
three,..., but what's a symbol?

Infants and preschool children can do mathematical reasoning without integers 
and they may not understand integers well. They seem to develop their own 
deviant symbolism that may or may not confirm to classroom practice.
See for e.g  relevant survey articles in Handbook of International Research in 
Mathematics Education, LEA, London , Eds: English, L., and others, 2002

The meaning of 'symbols' does depend on one's philosophical viewpoint and 
develops over time. Only those who use logic, will try to clearly understand 
the importance of atomicity and theory of substitution that may be associated.    

The ontological commitment associated with interpreting integers in a domain 
is much more than that of PA and that again is much more than that associated 
with interpreting symbols. The relationship is not independent of domains.

There has been no sociological shift apparently ... concrete intuitive 
examples are needed by everybody at their level of understanding. "Can you do 
with more-abstract examples in your field?" in the context of the people 
mentioned should be understood better to answer questions about sociological 
shifts in their attitude.   


Best

A. Mani


-- 
A. Mani
ASL, CLC, AMS, CMS
http://www.logicamani.co.cc