Of course not; it is a DEFINITION of what identity is.
> The notion "=" is only meaningful
> to the extent that expressions on either side
> of it appear DIFFERENT, such as "2+3 = 5."
Correct: two different EXPRESSIONS of the SAME underlying thing.
PLEASE give some attention to the distinction between the expression and
the thing underlying.
> So once again, two things are meaningfully
> related only to the degree that they DIFFER.
By "meaningfully" I guess you mean "nontrivially". Where the relation
is identity, no two things are related; a nontrivial identity is a
relation of two (or more) expressions or perceptions of the same thing.
> "2+3" and "5" are different expressions of
> the same thing.
Thanks. ;)
> This tells us absolutely
> nothing about what identity is.
What?! A few sentences ago, you seemed to say that "2+3=5" *is* a
meaningful example of identity. Now you seem to say it's not.
You challenged me to give a meaningful example of identity.
I return the challenge.
> >> 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.
>
> IAN: Identity is what a thing is;
You must be very brave to stand up in public and say that "A=A" is
meaningless while "the identity of A is A" is not.
> wether rock,
> symbol, or idea, all things have an identity.
What does it mean to "have" an identity?
Apparently you deny my statement "identity is a symbolic construct - you
can't go out and dig up rocks and find an `identity'". If I understand
you here, every thing is its own identity: this clock is the identity of
this clock, the Pachelbel Canon is the identity of the Pachelbel Canon.
This suggests that "identity" has no *general* meaning, only innumerable
*particular* meanings. Must be awfully hard to theorize about it.
Again: you confound the mathematical sense of identity (the relation of
a thing with itself) with the vernacular sense (the sum of a thing's
attributes?). In the mathematical sense, everything "has" the same
identity - that is, for every thing, "identity" has the same meaning (I
am identical to myself, and you are identical to yourself); in the
vernacular sense, "identity" is different for each thing (I'm Chevy
Chase and you're not).
> Simply saying that A is the same as A tells
> us nothing about what identity is.
Too bad, because that is the (mathematical) DEFINITION of identity.
Like it or not, the word _identity_ was coined from the Latin word
_idem_ meaning `same'. Sameness is the defining element of identity.
If you don't like it, coin another word, or use one of the many words
available, such as description, distinction, attributes, qualities.
All I ask of you, Ian, all I have ever asked of you in this dispute, is
that you refrain from stealing for your concept a word which others have
adopted for a very different well-defined concept. No, even less than
that: I don't care if you misuse a word for your purposes; I object only
to your insisting that others, who had it first, are wrong in their use
of the word.
<analogy>
The ancients used the word _planets_ to mean Sun, Moon, Mercury, Venus,
Mars, Jupiter and Saturn. We have since found it more useful to
subtract the Sun from that list and add Earth. But our new definition
does not make theirs wrong; they were using the word in a different
sense. It would be foolish to go through old writings and attach a
gloating correction to each passage where the Sun is called a "planet".
The Sun *is* a planet in the older sense: a bright body which appears to
move against the background of the distant stars. When the new usage
came along, it was specialized at first; it was wrong to use the word
_planet_ in the new sense without explaining that it was being used in a
special way. Centuries later, the context has changed: nobody but
astrologers now have any interest in "planets" in the old sense, and now
it is they who must explain their special usage.
</analogy>
If your theory has merit, eventually most of us will forget the
etymological meaning of _identity_. I concede the remote possibility --
but it is still arrogant of you to behave as if that has already
happened.
> >> >> "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.
>
> IAN: So (A=A) = (B=B), thus A=B.
I'm not sure what you mean by posting this (invalid) syllogism; is it
meant as a reductio ad absurdum, somehow, of my previous statement
(using your definition, A = A+~A = B+~B = B), or do you concede the
truth of my statement, and mean here to show that my definitions lead to
an equally silly result?
That your syllogism is invalid can be shown by Boolean truth-tables:
A B A=A B=B (A=A)=(B=B) A=B
F F T T T T
F T T T T F
T F T T T F
T T T T T T
(The next-to-last column is always true because "T=T" is true.)
With my definition of identity, "_=_" is sometimes true and sometimes
false, depending on what's in the blanks, so there's something special
about "A=A" which is always true.
With your definition(?) of identity, "_=_" is always true; so no use of
"=" can ever say anything distinctive, nonvacuous.
-- "How'd ya like to climb this high without no mountain?" --Porky Pine Anton Sherwood *\\* +1 415 267 0685