Re: Epistemology 201: The Science of Science

From: Dave Rusin (rusin_at_vesuvius.math.niu.edu)
Date: 03/23/05 

Date: 23 Mar 2005 01:03:26 GMT

In article <Bz20e.14998$Fy.6022@okepread04>,
Albert Wagner <albertwagner@cox.net> wrote:

>So, the pickpocket who works
>in gloves is innocent of theft?

A person who wears gloves but does not steal is innocent of theft.
But let's not belabour the cute turn of phrase (see below). You mean
something more precise, namely:

>The mathematiker who never explicitly mentions 'infinity' doesn't
>need a definition of infinity

That is correct. If I don't use a word, I don't need a definition.

>as long as he uses some other form of the word e.g.
>'infinite sets'.

If I thought they were synonyms, I would say that they were synonyms
(and then that would be a definition of "infinity", assuming that
"infinite sets" had already been defined). But did you hear me say
that they were synonyms? Or did you rather read that I explicitly
disavowed any claim that "infinity" meant the same as "infinite sets"
(or anything else for that matter)? I do not use "infinity" and I
take no ownership of any ideas you may ascribe to that word. I
do refer to infinite sets, and I am responsible for saying what they are.

You want to ask a question about "infinite sets"? I'll be delighted to
take your questions. Again, that means they are "sets" and they are
"not finite". I can describe in more detail what each of those things
means. (Turns out it's not all that easy!)

You want to ask a question about "infinity"? You'll have to tell ME
what that means, because I don't know.

You want to ask a question about "infinity" with the understanding
that "infinity" is a synonym for "infinite sets"? Well, um, OK, sure.
Boy, that makes the grammar funny. "Infinity" are things then, are they?
How do I form the singular, that is, what form of the word "infinity"
do you want me to use when I want to talk about just one infinite set?

>You have just made the only point that I have ever really been
>concerned about in this thread.

Which is?

>The emperor has no clothes.

Analogies are nice; they set a general image. But they fail to fix
details. I can't imagine what you mean with this cute phrase.
By the way, mathematics is traditionally not an "emperor", she is
a "queen". Ask Gauss.

dave

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