# Re: ATOMISM: Crackpot Theory

Anton Sherwood (dasher@netcom.com)
Mon, 16 Mar 1998 00:54:42 -0700

> >Ian Goddard wrote:
> >> Since the popular definition of identity is
> >> atomist and states "A=A," which is to say
> >> that the identity of A is exclusive to A,
> >> that A is what it is due exclusively to A,

> Anton Sherwood (dasher@netcom.com) wrote:
> >Rubbish. The statement "Ian=Ian" is not a denial that other entities
> >had causal influence on Ian's nature.

Ian Goddard wrote:
> IAN: The statement A=A tells us nothing.
> It is meaningless, it is no more meaning-
> ful than saying "A."

Not meaningless, but it is a trivial truth. Have you ever tried to
prove a mathematical theorem? A proof often amounts to fiddling with
both sides of an equation, replacing terms with equivalent expressions,
until you're left with something like "u + ax = u + ax" - something
which is utterly boring in itself, but which implies the truth of the
proposition.

Deny the value of such trivial truths, and you deny the foundation of
all logical proof.

> The philosopher Ludwig
> Josef Johann Wittgenstein was absolutely right
> to observe that "to say of one thing that it is
> identical with itself is to say nothing at all."
>
> The statement "A=A" is purported to tell us about
> the nature of identity, and yet it fails by 100%.
>
> >> it cannot be said to be a
> >> true identity theory,
> >
> >A definition is not a theory.
>
> IAN: A defintion of A tells us what
> A is,

Not exactly. We may define _star_ as "one of those shiny things in the
night sky," and this definition is sufficient to distinguish stars from
non-stars; but this does not tell us much about what a star is. Every
human language has a word for _star_, and everyone with good eyesight
agrees on the definition of the word (with an exception that I'll come
to later); but until recently there was no agreement on a theory as to
what stars are.

A definition of a mathematical or logical construct, on the other hand,
"tells us what A is" because such a construct - an integral, for example
- has no existence apart from its (manmade) definition, unlike a star.

> and a theory of identity
> tells us what identity is.

But that's circular. Since identity is a symbolic construct - you can't
go out and dig up rocks and find an "identity" - identity can only be
what it is defined to be; a theory follows from the definitions.

You've decided that the conventional definition of identity is boring,
and you've invented another definition (which appears to be "identity =
description"). That's okay; science does this from time to time. The
Greeks did not regard zero and one as numbers, so their theorems
sometimes needed to treat zero and one as special cases; later
mathematicians found it more convenient to redefine "number" to include
1 and 0 and -1 and -4+i. The ancients thought of Mars, but not the Sun,
as a star; we have adopted a more useful definition of _star_ that
excludes Mars and includes the Sun. And we've removed the Sun from the
classical list of "planets", and added the Earth.

These changes in the uses of words do not require us to reject all
writings of the Greeks that made special cases of zero and one, or old
astronomical records that call Mars a star. Nor does your new construct
which you call "identity" entitle you to say that everything that uses
the conventional definition of "identity" is wrong.

> The statement "A=A" does not
> tell us what identity is.

Identity is defined as the relation which each entity has with itself
and with no other entity. Maybe that's our problem: I see identity as a
relation, you see it as a property.

> >> and logic therefore
> >> dictates that it must be a false theory,
> >> particularly when the identity theory,
> >> "A=A+~A," is never shown to be false.
> >
> >Because it is vacuous.
>
> IAN: But the statement "A=A" is not??!!

Nope. "A=A" distinguishes A from that which is not A. "A=A+~A" does
not: since A+~A is the whole universe, A+~A = B+~B for any B, thus A=B
for any A,B; any two things are equal to each other. Thus, as you say,
this relation can never be false.

I hope you'll give this new kind of "identity" a new name. It does have
a slight similarity to conventional identity: both are equivalence
relations (reflexive, transitive and symmetric).

> >"A=A" is *useful*. "A = the whole universe" may be interesting in some
> >contexts but where does it get us?!
>
> IAN: To the truth.

Let me know when you have a theorem more interesting than
"everything=everything".

```--
"How'd ya like to climb this high without no mountain?" --Porky Pine
Anton Sherwood   *\\*   +1 415 267 0685
!! visiting New Mexico, end of March !!
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