The frying pan I just used was very hot, but now it is becoming cooler, and soon, it will be cold again. But it is the very same frying pan. And, if I were on the Moon, I would way much less, but it would still be me. How should we explain, persistence through change? What does it mean for something to be the same, even when it has changed? Aristotle gave one answer. He made a division between essential and accidental properties, and said that as long as the thing retains its essential properties, it is the same thing. But, unless we understand how to distinguish between accidental and essential properties, that is not helpful. So, what does "same thing" mean?

All poodles are dogs, but not all dogs are poodles. I suppose it would also depend upon how broadly or narrowly we want do define the characteristics of a frying pan or breakfast special or ourselves. Furthermore, I suppose those definitions may vary depending upon the time, place, and the object being defined.

I would suppose that a distinction needs to be made between "the same thing" and "identical."

Example:

I am at a restaurant and a sign at the door reads, "Breakfast Special: 2 eggs any style, hashbrowns, bacon and your choice of juice - $3.99"

I choose the breakfast special with scrambled eggs and orange juice.
My friend chooses the breakfast special with eggs over easy and tomato juice.

I would say that we have ordered the same thing - the Breakfast Special.
However, our orders were not identical.

The essential property of the Breakfast Special would be that it includes some form of eggs, bacon, hashbrowns, and some form of juice, and the price of $3.99.

The accidental properties of the Breakfast Special are the manner in which the eggs are prepared, and the type of juice chosen.

The essential property of the frying pan is circular shape, raised sides, handle, made of metal of some type. These are the properties we normally associate with frying pans.

The accidental properties of the frying pan would the changes the metal undergoes (and I don't know enough about thermodynamics to describe this process in detail) during the heating and cooling process, and any residue that might be left on it from whatever you cooked.

I would from this argument conclude that "the same thing" means an object that has the properties normally associated, or which more immediately come to mind, with the object being described.

An accidental property might be me cutting my finger and leaving a scar. I'm still TickTockMan, I just have a scar now.

I'm sure I'm overlooking some vital point here, but I haven't quite isolated it yet . . . perhaps this is a good opening gambit though?


TTM

Suppose, though, that the "sameness" does not reside in the object (and here science tells us that objects always change, even if minutely), but in us, and how we understand the being of objects, or what it means for an object to "be"? And if this is the case, don't we have different criteria for different kinds of objects in our world? The sameness of the frying pan is surely different from the sameness of a close friend we meet after a ten-year separation.

The sameness certainly does not reside in the object. If a factory makes both pots and pans from the same load of iron, it does not mean that the pots and pans are the same. Human beings give inanimate objects identity.
The identity only stands if the judging human has seen a previous identity of the object. For example, a purchaser of a frying pan will only see a frying pan, but a factory worker at the same store will see it as both iron and pan.

I accept that there is no answer to that question.
The previous things that defined a frying pan - shape, size, handle - are dependent on the observer. With no observer, these qualities of a frying pan would not exist. True, the frying pan would still have a configuration in space-time, but its circular shape would no longer matter.
With no definitions or guidelines set by an observing sentient mind, it is impossible to say when the star would become truly different.

Every frying pan has a shape and size, but these things do not grant an identity.

That objects always change is just the issue. The question is (again) how it is possible that they change, but yet remain the same object.

That is not the question (or maybe what I'm about to say is what you meant, but it wasn't clear). Because, obviously, they do not remain the same object. What does remain, is the identity we have assigned the object. And that, I think, to a large degree, can be explained through sentimentality.

But if identity does not exist as anything more than a thought, then there would be no set way to define things as "the same" or "different."

Imagine two frying pans, one metal, one made out of leaves. If every quality of the two pans was identical save the material, then the leaf frying pan would still not be a frying pan. A frying pan is a pan you can fry on, and frying is a human invention and concept.
In this case, the identity of the object is meaningless in a universal sense. The identity of the frying pan is mere thought.

So whomever looks at a star and thinks it is different is correct. And anyone who looks at the same star and deems it the same is correct.

While I do think there is a difference between the identity of living and nonliving things, I see your point.
So what is the main deciding factor in differentiating between living creatures?