Pat C, Matthew, Phil M, and Jon A,

Basic issue:  How do we determine whether two things that we
experience on different occasions (or that we describe in
different ways) are "the same"?

For example, suppose we describe something as a vase, and somebody
else describes it as a lump of clay.  Are they referring to the
"same thing"?

Or suppose we meet John Doe on one occasion and his "identical" twin
Jimmy Doe at a later date.  Even if Jimmy tells us that he's not
"the same" as John, we can't observe the earlier stages.  His words
are our basis for talking, reasoning, or acting about the difference.
Even if we get more records or testimony from independent sources,
they are just words or photos.  We can't observe the continuity.

And Pat raises an even more complex example:

PC
one can refer to  a “quantity of a substance” as a “PhysicalObject”
(mass, location, composition).  In the (very common) case where one
has a quantity of some mixture of substances (a 14-K gold ring, e.g.)
there is a quantity of “gold” and a quantity of “copper”.  There is
no reason I can think of not to be able to refer to the gold in
that ring as an object separate from the copper – that is logically
coherent.  As long as the ring exists, those two quantities of
substance will have the same spatio-temporal location.

You can only answer this question with a question:  Why do you ask?

As a somewhat simpler case, suppose you go to IKEA and buy a box of
parts for a table.  Those parts were spatially very close from the
moment they were packed in Sweden, shipped to the store, brought
to your garage, and taken out of the box.  For a while, they were
separated by a short distance, mixed with yourself and some tools,
and finally assembled as a table.  What are the identity conditions
for that "thing"?

MW
if you find two objects with the same spatio-temporal extent, then
they are the same thing. Essentially that means that if (and only if)
they occupy the same space over the whole of their life, they are the
same thing.

But what do you mean by "the whole of their life"?  Are the parts in
the box a different "thing" or are they part of the life of the table?

PM
the 4-D model for objects seems at odds with how humans actually
experience and understand the things, beings, and processes around
them, regardless of changes in state and changes in characteristics
over the course of their existence.

Yes.  Although I have a strong sympathy for the 4D view, it isn't
sufficient by itself.  Intentions are critical to explain our ways of
talking, thinking, and acting.  You might say that the table wasn't
"born" as a table until the parts were assembled in your garage.  But
then you might discover that getting the table from the garage to your
basement, up a flight of stairs to the kitchen, and then to the dining
room was a challenge.

At that point, you wouldn't disassemble the whole table.  You could
just remove the four legs, ask a friend to help, carry the table top
to the dining room, go back for the legs, and attach them where you
want the table.

While the legs were in the garage and the top was being moved,
the parts were separated by a greater distance than they had been
since they were packed in the box in Sweden.  How can we describe
the various stages of the table (or the vase or the gold ring) in
a systematic way that is faithful to the way we talk and the way
we translate our talk to some version of logic?

PC
Does the notion of “identity” as implying “identical spatio-temporal
location” require that we do the impossible, of tracing an object
back to the origin of the universe?  How does one preserve that
notion of identity and deal with the problem of co-location, within
some meaningful and accessible time interval?

The 4D definition requires a "God's eye" view of the universe.  You
could say, along with Heraclitus and my namesake John the Evangelist,
"In the beginning was the Logos, all things (panta) that came to be
(gignomai) came to be through (dia) or according to (kata) that Logos."

St. John added "the Logos is God".  Spinoza was more faithful to
Heraclitus by identifying God and Nature (i.e., pantheism).  But that
answer got him in trouble at the local synagogue.

But whether you prefer theism, pantheism, or atheism, you can talk
about a system of laws (Logos) as explanations of how all things
(including people) behave and interact.

The laws are a compact statements.  They include the precisely
formulated laws of science and engineering and the more complex
intentions of people and other living things.

Most laws of science are simpler when stated in a 4D coordinate
system.  But ordinary language is usually simpler with a system
of 3D plus time.  But any observations (data) stated in one
language or notation can be translated to and from any other.

Richard Coyne, as cited by Jon Awbrey
Architecture is a practical and pragmatic discipline, and a study of
Peirce emphasises architecture as a practice, and a practice grounded
in the materiality of the world.

Unlike other thinkers headlined in the Routledge book series Thinkers
for Architecture (my book is number 15 in the series), there is no
“Peircean architecture” as such, and no particular movement, style or
body of work that demonstrates allegiance to him. But in so far as
any practitioner, educator or critic claims to be pragmatic, they owe
a debt, however indirectly, to Peirce’s thinking...

Peirce speaks to mathematicians, logicians, those systems theorists
who seek orderly methods for solving the world’s problems, and those
of the Design Methods Movement who seek orderly, mathematical and
logical procedures for designing buildings.

Peirce’s influence extends to digital practitioners and programmers
in architecture, and more recently those interested in big data, and
responsive architecture that copies biological processes and forms
(biomimesis).

That is Coyne's own summary of his book.  For more, see
https://richardcoyne.com/2019/03/30/architectures-pragmatic-turn/

For a brief (12 page) intro to Peirce's theory of signs and its
application to ontology, see http://jfsowa.com/pubs/signs.pdf

My answer to the original question:  Any statement in any language
or logic is always intended for some purpose in some context.  That
is just as true for the most abstract theories of philosophy and
science as it is for ordinary life.

The only way to answer a question about the Ship of Theseus or Pat's
golden ring is to respond with another question:  Why do you ask?

The way the US army answered the question about rifles is the only
general principle that can end the chain:  Assert some officially
specified identity conditions:  Two rifles are "the same" if and
only if they have the same serial number on their stock.

This is one of many reasons why I keep saying that Part I of the
proposed ISO standard is worthless as a guideline for specifying
or evaluating ontologies.

Any ontology that is not designed for some purpose or intention
has no purpose.

John
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