Allan Gibbard tries to understand when a lump of clay and a statue made from this lump are identical. There are situations in which they are not, if the clay and the statue are generated or corrupt at different times. But:
I make a clay statue of the infant Goliath in two pieces, one part above the waist and the other part below the waste.
Once I finish the two halves, I stick them together, thereby bringing into existence simultaneously a new piece of clay and a new statue. A day later I smash the statue, thereby bringing to an end both statue and piece of clay.
The statue and piece of clay persisted during exactly the same period of time. (“Contingent Identity,” Journal of Philosophical Logic 4 (1975), 187-221)
Gibbard in this part of the paper thinks of the statue (Goliath) as form-in-matter: “By a statue here, I do not mean a shape of which there could be more than one token, but a concrete particular thing… A clay statue consists of a piece of clay in a specific shape.”
And he thinks of the clay (Lumpl) as matter-under-particular-form: “They began at the same time, and on any usual account, they had the same shape, location, color, and so forth at each instant in their history; everything that happened to the one happened to the other…”
Obviously, the two are one and the same thing, even if different aspects of them are emphasized in their definitions.
But later on Gibbard suggests otherwise: “Take a possible world in which I squeeze Lumpl into a ball, and suppose all the molecules involved are clearly identified. There are still two distinct things in that world, the statue Goliath which I destroy by squeezing, and the piece of clay Lumpl which survives the squeezing.”
If Lumpl survives the squeezing, then its particular shape cannot be its essential but must inevitably be an accidental property. But the statue’s exact shape is essential to it. If it were remade into a statue of David, then the old statue would cease to exist and a new statue would come into being. What our author calls “persistence criteria” for the two things differ. Goliath’s persistence criteria are more stringent that Lumpl’s.
In short, Lumpl has the power to endure even if squeezed into a ball; Goliath does not have this power. Consequently, their essences differ, and they are discernible.
We can conclude that if Goliath and Lumpl are identical, then only contingently, in the actual world; but not necessarily, as in the possible world in which the statue is squeezed into a ball, Goliath corrupts, and Lumpl persists.
Therefore, the Leibniz’s law of indiscernibility of identicals is false; but a weaker relation, “necessarily identical → indiscernible” probably holds.