Greetings Economists,
On Oct 20, 2006, at 12:28 PM, Carrol Cox wrote:
I'm inclined to see algebra as the opposite of metaphor. 1/2 and 2/4
are exactly the same quantity, just as the equals sign states.
Nothing metaphorical about it, to my mind.
Exactly correct.
An identity is NOT a comparison. Of course mathematics, like any other
realm of human knowledge or fancy can be used metaphorically, but then
it ceases to be mathematical. Most general statements of probability
are
not mathematical but uses of mathematics for metaphorical purposes.
Doyle;
Well Carrol since you state this as fact, are you then willing to
defend this statement in a scientific sense? George Lakoff in his book
takes a look at a variety of branches of mathematics, and in the case
of algebra he starts out by saying the basic metaphor is essence in
which there three fundamental metaphorics:
Where Mathematics Comes From, Lakoff and Nunez, Basic Books, printing
2000, page 108 (the chapter on algebra and metaphor)
Essences are Substances
Essences are forms
Essences are patterns of change
Doyle;
Now one remembers in the history of mathematics that algebra was
preceded by more visual sorts of numerical expressions and that algebra
over the last three hundred years gradually separated out from
geometric thought to it's own field. When I say something is
something. That is an equation. 1+2=3 you could say it's an
identity. But what's an identity? 1+2 is a mapping of quantities into
a whole of three and that's basic metaphorical methodology.
The principle behind this approach is to embody mathematics so that
mystifications about it's other worldly qualities can understood as
what they are myths. Functionally math is simply brain work. It's not
an ideal form. It's not out side history. And one has to accept if
one is a materialist that math itself is produced by human minds. So
that the 'root' of math is really forms of brainwork, of which a
primary form is neural networks mapping to and performing operations on
information, from net to net.
Now if you will please explain how mathematics as an identity is not a
metaphor? Of course this theory is controversial. Let's not take this
as a settled issue, but we certainly want to not accept as definite
your point about algebra.
thanks,
Doyle
