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In the world in which we live, a chair remains a chair - it does not turn into a table; and if there were two chairs in this room, I could distinguish one from the other and I would have no trouble in identifying which was which in the future so long as I kept my eye on them.

However, Schrodinger wrote:

We are now obliged to assert that the ultimate constituents of matter have no sameness at all. When you observe a particle of a certain type, say an electron, now and here, this is to be regarded in principle as an isolated event. Even of you observe a similar particle a very short time later and at a spot very close to the first there is no true unambiguous meaning to the assertion that it is the same particle you have observed in the two cases.

According to Aristotles principle of identity each thing is identical with itself. Yet here we see a naive reading of this fails. The concept requires temporalising: Each thing, at that time, is identical to itself.

However, given that physical identity does obtain classically how then does identity arise?

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    Whence things have their origin, Thence also their destruction happens, As is the order of things; For they execute the sentence upon one another - The condemnation for the crime - In conformity with the ordinance of Time. Anaximander – Gordon Jan 19 '18 at 1:37
  • The questions about the one and the many are so important I think. "Thence also their destruction happens." I.e. They will tend to unity, death. "All reification [unity] is indeed a forgetting." T.W. Adorno. Unity=death, the womb, reductions, forgettings. This sounds ridiculous but it seems like the universe is afraid and has a tendency to unity, but the unity won't hold. Anyway, the "one and the many" comes up time and time again. Reification, Diremption...Hegel, Marx, Frankfurt School, etc. – Gordon Jan 19 '18 at 2:00
  • @Gordan: Great quote. Here's one from Heraclitus - all things are an exchange for fire, and fire for all things; as goods for gold, and gold for goods. I think Heisenberg was a fan of the Heraclitean fire, seeing that as the ancestral notion for energy. – Mozibur Ullah Jan 19 '18 at 2:01
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    @Gordan: for sure; it's not just in Greek philosophy, it's there in the Tao in very explicit form. – Mozibur Ullah Jan 19 '18 at 2:04
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    @Gordan: it surprises me that no-one has made a comparative study of dialectics of the one/many in Greek and Chinese philosophy. – Mozibur Ullah Jan 19 '18 at 2:05
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Identity is not merely emergent, because it is not coherent enough to constitute a tower of realizations. Although it is multiply realized, it is not just realized at different levels of complexity. It is realized multiply at every level of complexity, and higher level realizations do not supervene upon others.

I am a legal entity, a mind, a body, a collection of particles, etc. But I am multiple legal entities -- one for every legal contract into which I have entered. I can jointly and severally be parts of various groups and there is not some substrate on which those memberships are determined other than their own simple statement. I am multiple minds and bodies, past and future. And I am ambiguously a trail of particles across time, but which ones are really me is always ambiguous -- do I have a shirt, or is the shirt part of me when I wear it?

You might want to look at this 'monadically' in the sense of Leibniz or early Whitehead. The monad exists as the collection of all its effects on everything else. This allows each particle to be a monad, and for larger collections of things that have traceable effects in composite to also be monads. Identity applies at many levels and in many layers.

Whitehead argues that the imposition of static identity based upon physical composition is part of our mechanization of our sense of identity. You are focused upon the material identity. He argues for the primacy of the notion of an organism. When that organism has intelligence, his notion of organism comes very close to the modern psychoanalytic notion of intersubjectivity.

In a more organic view, things really cohere through procedural identity. An entity does not persist, but reiterates its roles in various circumstances. It is more important that my car is the thing that is available for me to drive, and for which I take a given set of responsibilities, and otherwise rely upon in various ways, than it is that it is made up of a given set of atoms, even in sequence over time. (Ask Phish.)

Identity obtains when one enters into relations with other things that have identities. Each thing is identical to itself in the sense that it has its own set of relationships and no other, and in basically no other way. We are made up of different particles, we occupy different spaces, we change both phsyically and psychologically across time, etc., etc. etc.

Identity establishes my assignment to various categories in different natural kinds, which, as Quine points out, are themselves incompletely separable. So identity, like existence is not really a property, much less one that can be clarified to the point of representing an emergent phenomenon.

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Yes, identity can be emergent.

Sea waves are nothing but the circular motion of individual molecules. Each molecule circles around a static centre, yet it looks to us as if something distinctive is being carried along with the wave. We can identify a wave and track its "movement" until it breaks apart or washes on the shore. Such wave-like phenomena are abundant in nature, anywhere from galaxies down to elementary particles.

A simpler example could be dragging windows on a computer screen. On a higher level we think of a window as keeping its identity as we drag it. On a lower level it's just pixels changing colour. When we look at the "close" button for instance, we are oblivious to the identities of its carrier pixels.

In a sense, even we are emergent phenomena. David Hume had an interesting theory about personal identity. He noticed it's impossible to perceive a real "self" - it's only an illusion created by the continuity of a bundle of perceptions, linked through memories of past experiences.

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Identity is a way of organising our experiences, including of ourselves. That is all. It is not ontic, only organisational.

The ship of Theseus attacks our material idea of ourselves, given our cell turnover. Buddhist thought attacks the procedural and informational selves.

It is commonly thought all of biology can be explained by physics. But it may be that physics is only explainable in terms of mindsm

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Concepts based on certain relations are abstracted from one’s collective experience and refer to (mental) objects for which those relations hold true. The concept that can refer to any experience the experiencer has ever had, each through the lens of the subjective I, is where his or her sense of identity is grounded. It certainly seems to the experiencer that this sense of self is greater than the sum of his or her memories and current mental states. But, it is just a sense, and no one has a single impression of the Self as a whole; once one thinks of oneself, one is referred to some perception or another, that’s it. In a similar way, we can have a sense of infinite extension, though we can never have a clear representation of it.

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In the world in which we live, a chair remains a chair

No, the ship of Theseus paradox reveals that all temporal concepts of identity are flawed and thus a false (but useful) simplification of reality.

Identity thus does not emerge from anything, it is attributed to a pair of observations as a mere social convention.

In specific artificial/theoretical settings (Maths, Solid-body physics, Computer-science, thought experiments) it can be formally defined, but then it's still not emergent.

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