“Traditionally, this puzzle has been solved in various ways. Aristotle, for example, distinguished between “accidental” and “essential” changes.”
“Accidental changes are ones that don’t result in a change in an objects’ identity after the change, such as when a house is painted, or one’s hair turns gray, etc.”
“Essential changes, by contrast, are those which don’t preserve the identity of the object when it changes, such as when a house burns to the ground and becomes ashes, or when someone dies.”
“David Lewis gives striking expression to this sentiment when he says:
More important, we should not suppose that we have here any problem about identity. We never have. Identity is utterly simple and unproblematic. Everything is identical to itself; nothing is ever identical to anything except itself. There is never any problem about what makes something identical to itself; nothing can ever fail to be. (Lewis 1986, 192–193)”
“Despite that, problems about identity appear to play a central role in a large number of philosophical issues whose discussion dates back to the ancient world.”
“One of the most venerable concerns identity and change. Things change, but remain the same.”
“Identity looms large in Leibniz’s philosophy. He is responsible for articulating two principles that, he claims, are constitutive of identity. The first, more controversial, of these, called the identity of indiscernibles, says that qualitative indiscernibility implies identity. The second, often referred to as Leibniz’s Law or the Indiscernibility of Identicals, says that identity implies qualitative indiscernibility.”
“According to Leibniz’s Law, if a is identical with b, every quality of a will be a quality of b.”
“By synchronic identity we mean an identity holding at a single time. By diachronic identity we mean an identity holding between something existing at one time and something existing at another.”
“One question is whether synchronic and diachronic identity are different kinds of identity. Some philosophers are willing to countenance different kinds of identity. Others are reluctant to do so.”
“One philosopher who is willing to postulate a multiplicity of different kinds of identity is Peter Geach. Geach, among others, has addressed puzzles about both synchronic and diachronic identity by denying that there is a single absolute relation of identity rather than a host of relative identity relations.”
“On this view we cannot simply say that a is identical with b. Instead there must be a concept of a kind of thing, a so called sortal concept, that serves to answer the question: a is the same what as b? This is so, according to the champions of relative identity, because the following can happen: a and b both fall under the sortal concepts F and G, a is the same F as b, but a is not the same G as b (Geach 1967, and see the entry on relative identity).”
“According to one tradition that goes back, at least, to Wittgenstein’s Tractatus, we can theoretically dispense with identity talk without loss of information. Some, but by no means all, who take this view, do so because they hold that the predicate ‘is identical with’ corresponds to no genuine property.”
“According to a four dimensionalist like David Lewis a table is extended through the time of its life, and constituted from temporal parts which are themselves short lived tables. As such a four dimensionalist like Lewis would not hesitate to give the following answer to the above question. The problem is, in part, a problem about whether a cup-like object that exists only at t′ is suitably related to a cup-like object, itself a proper part of a larger cup-like object, that exists only at t so that both cup-like objects are temporal stages or parts of a four-dimensionally extended cup.”