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Topic: Matheology § 258
Replies: 29   Last Post: Apr 27, 2013 7:43 PM

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FredJeffries@gmail.com

Posts: 1,013
Registered: 11/29/07
Re: Matheology § 258
Posted: Apr 24, 2013 6:18 PM
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On Apr 23, 1:01 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> God made all the integers and Man made all the rest

Get out of the 19th century (or 17th)

by C. R. Gallistel, Rochel Gelman and Sara Cordes, "The Cultural and
Evolutionary History of the Real Numbers" in S. Levinson, & P. Jaisson
(Eds.) "Culture and evolution"

http://hum.uchicago.edu/ck0/kennedy/classes/s09/experimentalsemantics/gallistel-etal05.pdf

<abstract>
The cultural history of the real numbers began with the positive
integers. Kronecker is
often quoted as saying, "God made the integers; all else is the work
of man," by which he
meant that the system of real numbers had been erected by
mathematicians on the
intuitively obvious foundation provided by the integers. Taken as a
statement about the
cultural history of mathematics, this is beyond dispute. But if this
is taken as a claim
about the psychological foundations of arithmetic reasoning, then we
suggest that here, as
in many other areas of psychology, introspection and intuition are
poor guides to the
inner workings of the mind.

We suggest that it is the system of real numbers that is the
psychologically
primitive system, both in the phylogenetic and the ontogenetic sense.
We review evidence
that a system for arithmetic reasoning with real numbers evolved
before language evolved.
When language evolved, it picked out from the real numbers only the
integers, thereby
making the integers the foundation of the cultural history of the
number. Secondly, we
suggest that this ancestral non-verbal real number system becomes
operative in the
prelinguistic child and makes possible the acquisition of language-
mediated counting and
language-mediated arithmetic reasoning. It is the foundation on which
an individual?s
language-mediated understanding of what numbers are and what may be
done with them
rests.
</abstract>



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