Discussion on interpreting Aquinas' Third Way You are proposing that the sequence of contingent beings has a beginning, in order to avoid the infinite time prior to now, and the principle of plenitude, which would indicate that in that infinite time there would be a time of nothing. But contingent beings must have a cause. If there is a first contingent being, one which is prior to all other contingent beings, it cannot have a contingent being as its cause, then its cause is necessary, and this is necessary being as distinct from contingent being. — Metaphysician Undercover
Not exactly, what I am proposing is this: First, let's assume that all beings are contingent only; that is, that there are no necessary beings. On that assumption, whether the principle of plenitude is applicable or not, but especially when it is applicable, the problem I articulated is salient. The problem is not that there are contingents posterior to "now." The problem is that there will be or may be
nothing posterior to "now," that is, if we are still operating on the hypothetical assumption that everything is contingent only.
That is why I am forwarding the argument that I forwarded. But you mentioned an objection to that argument:
This is sort of like Aristotle's law of identity. Whatever exists [now] must be what it is, and not something else. This is expressed as the following necessity: "A thing is the same as itself". Notice though, that this relates to a thing's essence, what the thing is, which cannot be other than the thing's essence, what the thing is. But this principle has not been extended to a thing's existence, as you propose, and I believe it cannot be, for the following reason. — Metaphysician Undercover
I am not sure if the law of identity can be extended to a thing's existence either. Fortunately, I am not appealing to the law of identity; rather, I am appealing to the law of noncontradiction. In particular, I am appealing to what Aristotle says in De Interpretatione. The first sentence of Part 9 especially: "In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false." In other words, it must be true or false that something exists now, it cannot be both true and false.
And I would like to address the further objection you described concerning "now" --
In fact, the "now" changes as we speak. Therefore we cannot make the proposed statement, "it is necessary that what exists now exists now", because time has past between the first "now" and the second "now" such that they refer to different times which accordingly have different existents. — Metaphysician Undercover
I am not using now in a purely indexical sense. By "now" I mean this exact present moment. Which, in a few seconds will have become "then." Still, something must have existed in "that" moment.