Re: identity (was: names as predicates) (fwd)

[cowan (John Cowan)]

Forwarded message:

>From eric Fri Jun 14 13:22:08 1991
Message-Id: <m0joHqW-00030kC@snark.thyrsus.com>
From: eric (Eric S. Raymond)
Subject: Re: identity (was: names as predicates)
To: cowan  (John Cowan)
Date: Fri, 14 Jun 91 13:22:02 EDT
Cc: 
In-Reply-To: <m0joF5R-0002yyC@snark.thyrsus.com>; from "John Cowan" at Jun 14, 91 10:25 am
X-Mailer: ELM [version 2.2 PL13]

> I suppose it depends what you call an "abstraction".  To me, numbers and
> sets are as "concrete" as rocks and trees.

This isn't quite the issue I'm trying to address here, but it is a significant
one.  Historically, there was at one time a controversy among metamathematicians
(people who study the philosophy of mathematics; I used to be one) between
`Platonists' like you (who believe that mathematical entities have some sort
of `real' existence) and `Formalists' like me (people who regard mathematics
as a zero-content formal system, a game played with marks on paper).

Platonism seems `natural' to most people, but mathematicians have abandoned
it.  It starts to look naive when you realize that multiple, mutually
inconsistent axiom systems can all be modelled by entities as basic as what we
think of as "physical" numbers.  A related problem is that you can't really
reconcile Platonism with the existence of mathematical paradoxes.  And there
are some nasty ones out there.  Look up Bolzano's sometime.

In fact, when you identify a formal mathematical entity (a mark on the paper)
like `2' with a model such as a pair of apples, you are making a sophisticated
inductive leap.  You are generalizing from previous experiences in which the
behavior of marks on paper shadows the behavior of physical systems; that it
will continue to do so is a hypothesis subject to confirmation and
disconfirmation in the same way as any other.  There is no mystical connection
between the '2' and your pair that makes the `2' real; only the apples are
real.

Among mathematicians, Platonism has been dead for two generations -- though
there is a certain delicate irony all mathematicians are aware of here; though
we *reason* like Formalists, we *create* like Platonists; the process of
mathematical discovery feels like *discovery*, not invention.

What consequences does this have for lojban?  Well...we should be careful not
to build in Platonist prejudices.  The confusion of `formal' equality
with has-same-physical-referent would be one of these.  It's intuitively
appealing, it has a long history...and it's wrong.
-- 
							>>eric>>