Question Regarding "Existence"


Question: Is the following argument valid or invalid?

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Argument: 

Let us consider the statement:
S1: "Nothing exists."

There seems to be something inherently contradictory in this statement.

In order for a situation to exist, the situation has to persist. The word "persistence" implies a "passage of time." If a situation persists, then time necessarily passes (i.e., time necessarily exists).

Can a state of affairs in which "nothing exists" persist? The answer seems to be "no." If this state of affairs were to persist, time would exist (i.e., time would pass). If time were to exist, then, obviously, something would exist. (Time would exist.) And we would not be able to claim that "nothing exists."

In order for a situation to exist, the situation has to persist. A state of affairs in which "nothing exists" cannot persist. Therefore, a state of affairs in which "nothing exists" cannot exist.

Something must always exist.

(But what could this "something" be? An eternal "mind" of some sort?)

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