Can Any Two Things Be Identical???

I'm reading this book by John Perry. He points out that if Heraclitus bought an ox and then somebody came and took the ox, noting that it's not the same one he bought, Heraclitus might have piped down about the river.

Somehow the ox he bought and the one he had a few days later are identical. For practical purposes at least.

kennethamy wrote:

The second meaning of "identical" is qualitatively identical. X and Y are qualitatively identical if and only if X and Y have exactly the same properties. That is, every property of X is a property of Y, and every property of Y is a property of X. In this sense of "identical", qualitatively identical, it is possible for two things to be identical.

If X and Y have exactly the same properties, how can they be two things rather than one? In other words, how can they be qualitatively identical without being numerically identical?

Arjuna wrote:

jeeprs wrote:

The fact that living organisms maintain an identity while constantly changing is a real conundrum isn't it? Are you the same person you were as a child? No. Are you a different person? Not really.

Yea, it's a doozy. Personal identity. Isn't all identity, though? If you didn't know good and well that the river is an unchanging entity, you wouldn't be able to make sense of Heraclitus' insight... "the same river."

But that is not true. The river is constantly changing in many different ways, but it remains the same river. And that is the puzzle. How it remains the same river even though it is constantly changing.

After all, why could there not (to use Leibniz's example) be two (numerically two) different leaves which happened to have the very same properties?

It is no longer bread and wine (although it has all the accidental properties of bread and wine) but after the Mass has been performed, the substances are transubstantiated into the body and blood of God).

kennethamy wrote:

Arjuna wrote:

jeeprs wrote:

The fact that living organisms maintain an identity while constantly changing is a real conundrum isn't it? Are you the same person you were as a child? No. Are you a different person? Not really.

Yea, it's a doozy. Personal identity. Isn't all identity, though? If you didn't know good and well that the river is an unchanging entity, you wouldn't be able to make sense of Heraclitus' insight... "the same river."

But that is not true. The river is constantly changing in many different ways, but it remains the same river. And that is the puzzle. How it remains the same river even though it is constantly changing.

The river does not remain the same river any more than we remain the same people... The river remains A river.. We can compare the river of today with the river of yesterday because of its conserved quality as a river..... A river is a river... A is A...

kennethamy wrote:

After all, why could there not (to use Leibniz's example) be two (numerically two) different leaves which happened to have the very same properties?

Because if there were two, they would have to be in different positions at any particular moment. For example, they may be lying side by side at time T. Then leaf 1 would have the property of being on the left (from my point of view) at that moment, and not on the right. Leaf 2 would have the property of being on the right and not on the left. Therefore, they would have different properties.

kennethamy wrote:

It is no longer bread and wine (although it has all the accidental properties of bread and wine) but after the Mass has been performed, the substances are transubstantiated into the body and blood of God).

What is the "it" that is no longer bread and wine? What is the thing that retains the accidental properties of bread and wine through the change?

What makes the whole process one single event, rather than two discrete events, namely (1) the disappearance of the (real) bread and wine, and (2) the acquisition of (additional?) accidental bread-and-wine properties by the body and blood of God?

It all seems a bit conceptually muddled to me. I have always found the ancient idea of "substance" rather obscure.

But would you seriously argue that because there were two different names, that there must be two different things named?

Fido wrote:

kennethamy wrote:

Arjuna wrote:

jeeprs wrote:

The fact that living organisms maintain an identity while constantly changing is a real conundrum isn't it? Are you the same person you were as a child? No. Are you a different person? Not really.

Yea, it's a doozy. Personal identity. Isn't all identity, though? If you didn't know good and well that the river is an unchanging entity, you wouldn't be able to make sense of Heraclitus' insight... "the same river."

But that is not true. The river is constantly changing in many different ways, but it remains the same river. And that is the puzzle. How it remains the same river even though it is constantly changing.

The river does not remain the same river any more than we remain the same people... The river remains A river.. We can compare the river of today with the river of yesterday because of its conserved quality as a river..... A river is a river... A is A...

Well, of course, the river remains a river. Who would deny that? But that is not the issue. The issue is whether even when the river changes, it is the very same river after the change as before the change. Everything is what it is, of course. But that is a trivial tautology no one would deny. But that does not mean that whatever it is always is the very same thing even after there are changes. And the question is this: supposing (as we do suppose) that it is the same thing after changing as it was before changing, since there were changes, what is it that remains the same? Sure, I am the very same person I was when I was an infant. But, manifestly, great changes have occurred to me since I was an infant. So, what about me is the same now as it was when I was an infant? Simply repeating that I am the same does not answer that question. Is is assumed by that questions.

Isn't it recognized that individual examples always vary from the concept/ideal???

Leibniz had two principles:

1. The indiscernability of identicals.
2. The identity of indiscernibles.

The first says that if (putatively) two things have the very same properties, then they are not two things, but really one (and the same thing). The second is the converse of the first. It says that no two things can have the very same properties.

But how does a photon in the state 0 + 1 differ from from another photon in the state 0 + 1 ? Not only can you not complain that there exists a difference between two individual photons, but you cannot even complain that that they differ in regards to they're state. So what what exactly do you mean by the first "principal" being true?

What in the world could drive a person to conclude upon such ridiculousness such as these "principles"? Yet more puzzling, what could possibly cause you to presume any truth from such nonsense?

It has recently been mention here of a philosopher that said "Whereof one cannot speak, thereof one should remain silent". It sounds as though Leibniz should have taken note, maybe he was not yet present.

But that is not true. The river is constantly changing in many different ways, but it remains the same river. And that is the puzzle. How it remains the same river even though it is constantly changing.

Sure, I am the very same person I was when I was an infant. But, manifestly, great changes have occurred to me since I was an infant. So, what about me is the same now as it was when I was an infant? Simply repeating that I am the same does not answer that question. Is is assumed by that questions.

Leibniz had two principles:

1. The indiscernability of identicals.
2. The identity of indiscernibles.

The first says that if (putatively) two things have the very same properties, then they are not two things, but really one (and the same thing). The second is the converse of the first. It says that no two things can have the very same properties.

kennethamy wrote:

But that is not true. The river is constantly changing in many different ways, but it remains the same river. And that is the puzzle. How it remains the same river even though it is constantly changing.

But that is not true. How does a changing river remain the same river? Keeping in mind that spatial location is not an attribute of the river, in which way exactly does a changing river remain the same river?

kennethamy wrote:

Sure, I am the very same person I was when I was an infant. But, manifestly, great changes have occurred to me since I was an infant. So, what about me is the same now as it was when I was an infant? Simply repeating that I am the same does not answer that question. Is is assumed by that questions.

What about you is the same now as it was when you where an infant? many things, is it not obvious? Remember you are only qualitatively different now than from the time you were an infant. You are not a river but a human being, as such there are many things that remain. For example, although every single cell in your body has been replaced countless of times, the arrangement of information that make up your genetic structure is exactly the same now as it was when you where a fetus and will remain so until the day you die, as such is also the case with your finger prints.

Hi Arjuna,
Thank you for joining in, by the way!

Would it also be correct to say: Every "individual example" can be perfect. Perfection is the equivalence to the ideal?

Have a brilliant day.
mark...