
respose to read
vance@MAPLE.CIRCA.UFL.EDU
Sun, 23 Jan 1994 13:35:29 EDT
Read inquires of Foss's definition of culture (to wit)
" To understand myself, I return to
the definition of Culture as "the mental life of society and the
material products wherein it is objectified."
Since the mental life in question must be shared in order to
exist at all, and presupposes a material life whereby the
biological organisms which share it may continue to live at all,"
Is such a definition more a definition of what culture is not, as
"culture is that which is not objectified" and then provides an
example from mathematics (to wit)
Read:
In the axiomitization of the number system there is no definition
of a number. Rather, one positis the existence of the number 1
(with no definition of what is meant by "the number 1") and one
posits that if n is a number then there is a successor number,
call it n' (with no definiton of what is menat by "a successor
number"). Those two primitives, plus what is referred to as the
induction axiom, suffice to generate what we call the number
system. That is, one proves that in any system in which the two
primitives are valid and the axiom of induction holds, then the
whole set of theorems that constitute the number system must be
valid, regardless of what the primitive "1" is thought to
represent. Now in the oridary usage of the number system, we
take the symbol "1" to mean the quantity "one" (which is
definable without recourse to numbers so there is no circularity
here). So what the abstract construction establishes is that if
the symbol "1" shall be interpreted as the quantity "one", then
the system of quantities encompasses the structure we know of as
the number system.
Comment:
What I understand D. Read to be saying here is that if there is
agreement as to "primitives" in essence a mutual expectation that
"1" apple, say, corresponds to a physical entity of which there
can be "1" i.e. a single apple in the hand then n can symbolize
any quantity of apples, say, such that quantity less "1" apple
will be n' if the induction axiom holds. The induction axiom
must be agreement, common expectations, that it is possible to
have any number of, say, apples, which if counted by those who
agree on what n will be, will be n. And that if this quantity of
apples is less "1" apple it will be n'.
Read again:
The other kind of definition does not have this vagueness and is
very precise. E.g., one can define an "integer" to be a solution
to an equation of the form a = b + x, where a and b are counting
numbers (1,2,3,...). From the definition of an integer one then
derives properties that the integers must have.
Comment:
The important point here is "counting numbers" which must
correspond to a common expectation of what "1", "2", "3" and so
on is,, say in terms of how many physical apples is associated
with "3" and "4" and so on.
Read:
Here we arrive at the point I am trying to make. The definitions
(such as that of an integer) that mathematicians also enable the
development of a theory, or (in the case of primitives) serve as
the foundaiton for everything else.
Comment:
The "primitives" must be derived from common expectations about
the behavior of other people when presented with the same
"symbols" i.e. mathematical concepts such that people can produce
responses that are "knowable" to one another as common behaviors,
say spoken responses indicative of similar mental processes as in
"1" + "1" = "2" which we will now call "n" such that "n"  "1"
= "1".
D. Read again:
For example, Foss's definition, and others like it, place first
priority on mental activity. We might begin by asking a question
such as: When we consider culture to refere to mental products,
are these mental products structured and if so in what manner?
Comment:
These mental products are structured as expectations or
predictions of events.
D. Read:
Can we account for how such mental products can be generated or
produced (at the level of mental activity)? Or we might focus
more on the second part of his definition where there is implicit
recognition that the "mental life" is abstract and eventually has
material representation or interpretation. We might ask: What is
the process by which this representation takes place?
(Obviously, both of these approaches have already been explored
in anthropology  I am not suggesting something new, only, I
think, a different way to think about what a scientific
anthropology should have as its goals).
Comment:
A scientific anthropology should focus on culture as the
expectations that people have of events, especially the behavior
of other people toward the goal of identifying what expectations
are intrinsic to a group of people and are different from the
expectations of other groups of people such that a group can be
identified as a "culture" an entity consisting of a group of
people with common expectations of events.
vance@ufcc.ufl.edu
