Dear Liza: In a copy of my fathers will it states that Jane Doe is hereby appointed Executor of my Last Will, to do all lawful things to carry out its terms, with all those powers and subject to qualify, or having qualified shall die, resign or become incapacitated during the administration of my estate, I hereby appoint John Doe, or the survivor of him, to be Executor to serve.
Who is the survivor of John Doe? (there are four children, Jane and John are two of them). Yikes, this is like an evil law school exam question. Here's the problem for you, the Will is drafted unclearly, or at least the question is confusing. I'm sort of stumped by who 'Jane" and "John" are for a start--I can't tell if we have two generations here, or an endless loop. If "Jane" is alive, though, she's first in line; then "John." If he's not alive, "John", as you've described it (assuming here you're not talking about your father here but that second choice executor), has four survivors--each of his children (which is where I'm getting a headache, because you said that "Jane" and "John" are two of those children).
I would expect to see a reference to "survivors" in the Will section distributing money, which can be divided equally, not authority, which is not so easily divided. If "Jane" and "John" are not able to serve as executors, and indeed you need to figure out which of four people should represent your father's estate in probate, this is a situation where your family should see an attorney in your state. If your father's Will needs to be submitted to probate, you can decide who should request authority as the executor. State law sets out a priority for this role, but families can often work it out and petition the court to name the family member they've chosen.