Biological organisms, as Snowdon and van Inwagen establish, persist through brute physical-causal continuity that neither admits of degrees nor permits branching in the relevant sense.

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Admits of degrees(Explaining that responsibility isn't simply present or absent): Can exist in different amounts or levels rather than being all-or-nothing; something that comes in stronger and weaker versions.
Permits branching(describing whether an organism can split and still maintain its identity): Allows for one thing to split into two or more separate things that could each claim to be the continuation of the original.
Persist(referring to whether mathematical structures continue to exist as physical objects change): Continue to exist over time without changing or being destroyed.
Physical-causal continuity(as the mechanism that makes organisms stay the same): An unbroken chain of cause-and-effect physical events that keeps something connected to its past self—like how your body today is directly caused by your body yesterday.

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