[FOM] Finite Set Theory

[Stephen Pollard]

On Sat, 18 Feb 2006 Harvey Friedman wrote:

>I have had several occasions to explain what set theory is to "ordinary
>people" of a variety of age groups.

It sounds like Prof. Friedman has hit upon an effective way of introducing
the mathematical concept of set to a variety of audiences. (I speak from
experience: I've been teaching the rudiments of set theory for a couple of
decades.) One quiets the fears of the math-phobic by assuring them that you
are talking about something quite familiar: "bunching things together," for
example. One then introduces the mathematical concept of set without
necessarily pausing to note all the points where one passes from the
familiar to the unfamiliar. This can involve a bit of hoodwinking, but that
doesn't make it bad pedagogy nor does it mean that the mathematical concept
is unclear or illegitimate.

Prof. Friedman: Has any smart-aleck ever made the following point. "You're
saying that if x is a thing and A is a bunch of things, then we can bunch
together x and A. You're saying we can do this even when x is one of the
very things already bunched together in A. But that's crazy! How do you
bunch a bunch of grapes together with a grape that's already in the bunch?"
The answer, of course, is that you don't -- at least not in any naive,
familiar sense of "bunching together." It's lucky for us set theory
teachers that students almost never notice this sort of thing until after
they have acquired the mathematical concept and no longer need to be
hoodwinked.

In a later post, Prof. Friedman suggests that set theory teachers might
make good use of our commonsense notion of "list." I can report good
success with that approach. For what it's worth, my 12 year old daughter
strongly endorses it. One can carry it through with little or no
hoodwinking.

Stephen Pollard
Professor of Philosophy

Division of Social Science
Truman State University
Kirksville, MO 63501

(660) 785-4653