Re: A Modest Proposal

I have removed the responses to these various posts over to here,
where they seem more at home; and to avoid further polluting
the main thread with this worthless squabble.

|> There's no need for such a locution; "there exists an explicit..."
|> would be quite helpful to both sides.

This would be a handy phrase in some cases except that
it's already acquired a different and informal connotation
in classical mathematics,

It hardly seems all that different, but if you say so. OK then,
make it "there exists a specific..." . What does it matter?
As long as it's different, short and clear.

Given a continuous function f, where f(0)<0<f(1), the
smallest zero of f is an explicit example of a zero of f

Hmmmm. I would have not altogether said so. It's a *particular*
zero, but not really an *explicit* one, all that amount.
Explicit tends to mean "given in some sort of (semi-)closed
algebrao-calculus form. But this is now splitting hairs.

The point is, natural language is *full* of words that have as yet
no technically restricted meaning: let's make use of the facilities!
- and avoid avoidable confusion or misrepresentation.

|>I'm sure such brief and
|>simple expressions could be found in most cases.
|>I already mentioned "inhabited set".

What substitute for "real number" would you recommend?

What's wrong with "constructive number"?

However, getting back to something meatier than these word problems,
you have raised the point that it would be needlessly cumbersome for
const/intuitionists to keep using longer-winded terms, writing
for one another. This is a fair point, though as I've observed,
Brouwer does already sometimes, and Species, Spread and Bar are
good examples. (The whole matter is clearly not nearly as gross
and cumbersome as you are making out, a little mischievously!)

And in technical papers, which are only going to be read by others
who already know the subject, abbreviations to orthodox terms are
maybe quite acceptable. BUT:- in papers/articles/books/lectures
to orthodox mathies who are hoped to become more sympathetic to
the topic, it is quite needlessly confusing, if not actually
polemic in intent.

-- Wordly William
.

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