Exercise! Spot the many missteps in the following argument schema:

**P1**: States S1 and S2 seem the same in a situation I can imagine.

**P2**: In this situation I can imagine, S2 seems possible without external connections.

Therefore,

**C**: S1 does not in fact require external connections.

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P1: States S1 and S2 seem the same in a situation I can imagine.

P2: In this situation I can imagine, S2 seems possible without external connections.

Therefore,

C: S1 does not in fact require external connections.

_______________

Without knowing anything about the context of this argument, or indeed what it is even about, let me nevertheless hazard a charitable reconstruction in (very) informal modal logic:

P1: There exists a world W1 such that S1=S2.

P2: At W1, it is possible that S2 & ~E.

C: It is not necessary that S1 requires external connections.

There are steps missing in the derivation, but the argument seems valid to me.

Proof: If the premises are true, then there is some possible world where S1 and S2 are identical. In that possible world, further, it is possible that S2 has no external connections.

Assume S5 modal logic. If S1=S2 is true at W1, then the identity, being necessary, holds at all worlds. If P2 is true, then there exists an accessible world from world W1 (call it W2) where S2 is the case without external connections. But S2 and S1 are identical at all worlds, so, therefore, S1 is also the case without external connections at W2.

Conclusion: ‘it is not necessary that S1 has external connections’ is true from that fact that at W2, S1 does not have external connections.

I think I am being fair to the premises as written. The original conclusion was worded “does not in fact *require* external connections”: if some X is not required for Y then X is not necessary for Y; or it is possible that ~X and Y. But if P2 shows that S2 does not require ‘external connections’ at some world, and P1 shows that S1=S2, then the conclusion follows, fairly trivially. (I’m assuming S5.)

What’s doing the heavy lifting is of course P1. But if P1 is the case, the argument is valid; whether P1 is true is a question of soundness, not validity. So I don’t see the problem with the argument schema itself. (“Seem the same” isn’t “is the same,” but that’s an epistemic hedge, e.g., a soundness issue.)