Are there objects or just patterns of activity?

On Mar 17, 10:59*pm, Immortalist wrote:
Heraclitus thought that the contents of things change, but their form
remains the same. He wondered under what conditions do objects persist
through time as one and the same object. In ancient times, this
problem came to be associated with the Ship of Theseus;

The ship wherein Theseus and the youth of Athens returned had thirty
oars, and was preserved by the Athenians down even to the time of
Demetrius Phalereus, for they took away the old planks as they
decayed, putting in new and stronger timber in their place, insomuch
that this ship became a standing example among the philosophers, for
the logical question of things that grow; one side holding that the
ship remained the same, and the other contending that it was not the
same. --Plutarch (c. 46- 127).

The original puzzle is this: over the years, the Athenians replaced
each plank in the original ship of Theseus as it decayed, thereby
keeping it in good repair. Eventually, there was not a single plank
left of the original ship. So, did the Athenians still have one and
the same ship that used to belong to Theseus?

http://en.wikipedia.org/wiki/Ship_of_Theseus

One possible answer; Leibniz's Law

The German philosopher, Gottfried Leibniz, came up with what is now
called Leibniz's law (see Identity of indiscernibles) that may have
some bearing on the question. Leibniz's law states:

X is the same as Y if, and only if, X and Y have all the same
properties and relations; thus, whatever is true of X is also true of
Y, and vice-versa.

Applying Leibniz's Law to the Ship of Theseus problem, S2 is the same
as S1 if, and only if, S2 and S1 have all the same properties and
relations. Does the ship now in the harbor have all the same
properties and relations as the ship that was in the harbor fifty
years ago? One might be tempted to say, "Clearly not! They have lots
of different properties. So they can't be the same ship." Does that
sound convincing? To answer this question, let us consider the
property, "contains mast #1". Mast #1 is one of the masts that the
original Ship of Theseus had. S1 definitely had this property, but S2
is not so equipped, but has mast #2, instead. It follows that S2 must
therefore be different from S1.

Many philosophers strongly oppose this view. For if this argument
works, then any property that has changed from the last time we looked
at a thing would mean that the thing does not exist anymore, and there
is a new thing in its place. Every little change in every little
property would mean the whole thing is destroyed. Suppose we look at
S1 just a couple of years after it was built. If just one plank has
been replaced, will we say that the ship is a different ship? Many
philosophers would say surely not, as would common sense. But the ship
that is floating on the ocean for a couple of years does have
different properties from the original. Leibniz's Law would have us
say that it is a different ship. One might see all this and conclude,
"Well, Leibniz's Law must not be a law at all, but a false claim! X
and Y do not need to have all the same properties to be the same
thing."

Leibniz's Law can be saved, by saying: Properties are to be described
as occurring at particular times, i.e. they are indexed to times. A
property that is described as at a particular time is said to be
"temporally-indexed". For example, we can say that S1 has mast #1 in
600 BC. If we say what time the ship has the mast, then we have
indexed the property of having the mast to that time. We say the ship
has the mast then, using the word, "has", tenselessly. That means we
do not say that it, at present, has the mast, but rather, we say it
"has" the mast in 600 BC. We are not claiming that the ship has the
mast at any other time; just at that time. But if it were a later
time, say 550 BC, that very same ship could "have" mast #1 in 600 BC,
considering that we are talking about a tenseless "have". That is, it
always has the same properties, but the properties are of the form P-
at-T. This gives us a way to save Leibniz's Law from the objection we
gave, but at the same time, brings up the issue of whether change
really occurs. After all, we defined "change" as something having one
property at one time, and not at some later time. By this solution
though, any given object always has all the properties throughout
time, and the properties are merely temporally-specific.

Putting this in plain English, S1 now has the property that it will
have mast #2; and S2 now has the property that it did have mast #1. We
can then say that S1 and S2 have all the same temporally-indexed
properties. According to Leibniz's Law, therefore, they would be the
same ship.

One might also say, through the same sorts of contortions that S1 and
S3 might have the same temporally-indexed properties. It then follows
from Leibniz's Law that they instead would be the same ship.

Can Leibniz's Law help us decide whether it is S2 or S3 that is the
same as the original Theseus? Perhaps not by itself. Leibniz's Law
says that some ships are the same, just in case, they have all the
same properties and relations — or, rather, the same temporally-
indexed properties and relations. How then is one to decide that they
have all the same temporally-indexed properties and relations?
Leibniz's Law seems to offer little or no help when it comes to that
decision.

http://en.wikipedia.org/wiki/Identity_and_change