You are making two errors here.
1) An atom is an entity, and so is a molecule. A molecule is an entity, and so is a marble block. A marble block is an entity, and so is the planet Earth that contains the block. The Earth is an entity, and so is the galaxy that contains the Earth.
The boundaries of entities are mentally determined. There is nothing metaphysical that determines where those boundaries are.
2) Assuming that one finds it convenient to distinguish between the sculptor and the marble block and treat them as separate entities, simply giving that example does not show that there must be "two entities". It's just an example that happens to contain two entities. There is such a thing as self-causation, such as proton decay, or the growth and maturation of the sculptor, for which the cause is internal.
eudaimonia,
Mark
First of all, in regards to this:
Assuming that one finds it convenient to distinguish between the sculptor and the marble block and treat them as separate entities, simply giving that example does not show that there must be "two entities".
You are not representing my position. Recall I said this:
So you just admitted that causality can, at least in some cases, involve two entities. Now please acknowledge that the law of identity cannot involve two entities. Not ever. Please conclude that the law of identity is not related to causality.
With few inference skills you can see my position, at least in this bizarre debate, is that causality CAN involve two entities. Your straw man has me saying causality MUST involve two entities.
So how on earth can you have one law that accommodates ONLY ONE entity and another law that CAN ACCOMMODATE TWO entities and then conclude they are the same law? Baffling, to say the least.
Secondly, your definition of causality is inadequate. In the OP, presuming you did read it, I laid out my definition:
A system is a region of space.
A state is the arrangement of matter, energy, and otherwise existing things within a system.
Causality acts on a system to take it from one state to another over a duration of time.
So this acknowledges that the partition of an entity is arbitrary, just as you desire. Also we see the two entities are the two states, and perhaps with some fudging of the language we might say that the initial and resulting states are the same entity if they are comprised of the same particles (assuming this is well defined in terms of quantum uncertainty). My definition also comports with your statement, "Causality is the law of identity applied to action/change" to the extent that I agree causality is a process.
The law of identity is useful to distinguish things from other things... I suppose. If you want to group all of existence together and refer to it as one entity, then the law of identity is pointless. You can only possibly be correct if we both first agree that the law of identity is pointless.
Or else at some point we start drawing lines, and we say that we can distinguish one entity from another, and then you are unequivocally wrong in what you have presented. I only started discussing material and efficient causes when you invoked Aristotle. But Aristotle in no way advocated single-entity causality, so you then start switching it up talking about molecules and dogs barking. Even in the example of a dog barking, Aristotle's model is well defined: the dog's throat is acting on air. Two entities in that instance.
You are going through the cartwheels and gymnastics that apologists are known for. Have some self respect, but more importantly, have respect for reality - just admit you're wrong. You're head over heels wrong. Seriously, this has gone on long enough.
You're literally saying that a sculptor and a marble slab are the same entity in order to weasel out of this.
