The Principle of Contingent Causation: The Impossibility of Infinite Regress.

[polymath257]

I think the  problem is in the word 'first'. The usual argument only gives the existence of an *uncaused* cause. As you point out, there is nothing that says that uncaused cause is unique.

Depends on whether the law of identity kicks because everything true of the one is also true in the same way and degree as it is of the other. Is there a difference?

Why would you think that everything true of one is also true of the other? For example, the uncaused causes could be in different positions or at different times. They may have different effects, which onw uncaused cause being the cause of one thing and others of different things. Perhaps some things are the effect of several different uncaused causes.