BHA: Identity and change

[Louis Irwin <lirwin1@xxxxxxxxxxxxx>]

Tobin,

I think there are some issues about identity and change you are
overlooking.  First, understand a relational property to be a property a
thing has by virtue of being in relation to something else.  If R is a
relation and Rab, then a has the relational property Rxb, and b has the
relational property Rax.  Regarding the changes in the properties of a
thing, the following can occur:

1. Its essential properties can change.  This may result in the thing being
changed to something else, but not always, as in the case of a caterpillar
which changes into a butterfly but remains the same thing.

2. Its non-relational properties can change.  For example, it melts,
splits, it cries, it gains weight, it changes color, etc.

3. Its relational properties can change.

These are not mutually exclusive, since essential properties may also be
relational or non-relational.  But let's make them exclusive by restricting
2 and 3 to non-essential properties.

Now you and Colin want to say, it seems to me, that a thing changes only if
its essential properties or its non-relational properties change.  I, on
the other hand, want to say that a thing changes even if only its
relational properties change.  A lot of your irritation may have to do with
your inability to accept my use of "change" in saying that a thing changes.
 Maybe as an emprirical fact of language no one ever uses "change" in that
context in my sense, or maybe it's not  a very fruitful use, but you act as
if I had blasphemed the Great Lexicographer in the sky!

You can't stand the description that a rock in Cambridge has changed merely
because a rock in Arizona was moved, even though a relational property of
the former without question changed.  I agree that is not what most people
would say, and I think they would at least tacitly appeal to 1. and 2.:
neither an essential nor a non-relational property changed.

Now suppose that the rock in Cambridge is moved with no change in essential
properties and no change in non-relational properties.  The rock has
certainly changed location.  Would we say it did not change?  In the sense
of 1. and 2., no it did not.  But is sense 3. now so outrageous?  I don't
think so.  The rock did undergo change, albeit only in location.  You could
propose to make this slope less slippery by splitting 3. up as follows:

3a. Its relational properties can change due to a causal impact on it.

3b. Its relational properties can change due to a causal impact on other
things.

The Cambridge rock that is transported might then be said to have changed,
while the Arizona rock that is moved does not allow us to say that the
Cambridge rock has changed.  So you could allow 1,2 and 3a to define the
limits of the criteria for when we can say something has changed without
offending the Great Lexicographer.  The number 2 cannot be transported or
otherwise be subjected to causal impact, so 3a is not an option.

The issue is not over identity.  Take any entity x some of whose properties
change while x remains the same.  You and Colin appear ready to allow that
x has changed if the properties of x that have changed are essential or
non-relational, maybe even relational of type 3a, but you want to deny x
has changed if the only properties that have changed are relational of type
3b.  I am willing to say that x has changed even if only 3b non-relational
properties have changed.  This may not be natural, but then it's not
natural to define water as H2O (natural water has lots of other stuff).

>First, let me state what
>should be clear to everyone: pi is not some arbitrary number invented by
>mathematicians to keep us lowlifes amused.  It is not 22/7, or 3.14, or even
>3.141592653589793.  It is, *precisely*, the ratio of a circle's
>circumference to its diameter.  All those numbers just approximate the value
>of this relation.  When I speak of pi, I am referring to this relationship.

You are confusing the sense of an expression ("pi" in its mathematical
usage) with its referent, a number.  Its sense is given by the relation you
describe, but its referent is a number determined by that relation.  Your
distinguishing pi from several rational numbers which approximate it just
clouds the issue.  Pi is a real number distinct from any rational number;
you don't get it "precisely" by moving from a series of rational numbers to
its sense.  You get at it by moving from rational approximations to a real
number.

>I think Louis's argument that a change in the length of Pinocchio's nose
>somehow alters pi is not only specious, but silly.  Let's rephrase it: does
>a change in the length of Pinocchio's nose affect the ratio of a circle's
>circumference to its diameter?

Your argument here trades on the sense/referent confusion.  All I said was
that the relational properties of the number pi (the referent of "pi" in
standard math usage) changed.  I did not say that the sense of "pi"
changed, that is I did not say that the referent of "pi" is no longer
determined by the ratio of circumference to diameter.  I said merely that
some of the relational properties of pi changed, even though pi continues
to be determined by its essential property.  I am willing to say that pi
changes even though it is still identical with 3.141... .

>Does the fact that water failed to put out a
>fire somehow miraculously change the structure of water?

No, I'm glad I never suggested it did.  The properties of a thing can
change without its essential structure changing.  I said that already.  I
don't know how you missed it.

>I'm also not
>particularly worried by his distinction between "essential" and
>"inessential" changes (though I don't think his discussion of it is very
>good), because in making that distinction Louis concedes the point at hand:
>not everything changes.  Can pi enter into various and changeable relations
>with other things?  Yes, of course--but *that's not the question*.  The
>question is, can such changeable relations with other things alter what pi
>is, i.e. the ratio of a circle's circumference to its diameter?  If the
>answer is No, then at least one thing doesn't change.

Clearly you are using "change" to mean "essential change", which is what is
at issue.

Louis Irwin





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