1. Leibnizian substance: Something is a substance if and only if it evolves by the fundamental laws
2. Russellian laws: The cosmos is the one and only thing that evolves by the fundamental laws
3. Spinozan monism: The cosmos is the one and only substance (from 1 and 2)
As Schaffer is well aware, there is lots of irony in all of this. (At NewAPPS we have discussed Russell's reservations about Spinoza several times here, here, and also Jeff. [Recall also Russell's debts to Boole on Clarke vs Spinoza; and Stebbing on Spinoza.]) Now, my objection to this argument is inspired by my reading of Spinoza's so-called "Letter on the Infinite," but what follows is not meant to be a historical argument (or a gotcha, 'you got the history wrong' moment). Recall that I read Spinoza as claming that characterizing and grasping substance as such does not involve our ordinary scientific 'utensils' (e.g., measures, mathematics, laws of nature), but rather concepts like essence and eternity. Mathematical physics can only give a partial view of substance as such. Now one reason for this is that mathematical physics of Spinoza's day, treats some part of nature as a closed system (governed by its own 'conservation' rules/laws). Moreover, Spinoza would deny that fundamentally the universe evolves. For, applying temporal concepts to the universe is, however useful it may be, always a less than fully adequate conceptualization of the universe.
Yes, there are at least two ways to treat the 'no outside' clause: (I) the cosmos has a 'boundary' and there just is nothing on the other side of the boundary (there was a once famous debate between, I believe, the Epicureans and Aristotelians over this), or (II) the cosmos simply has no boundary. I am no expert in topology so I am not going to try to explain this further, but I hope it is clear that there is a non-trivial metaphysical difference between (I) & (II). For example, I think Spinoza's absolutely infinite substance is more akin to (II) than to (I), for any boundary on the infinite cosmos would just be arbitrary (hence, not adequate, etc.).
Even so, when we apply conservation laws, we tend to draw a boundary around the system (or we just tacitly assume such a boundary). (Recall I posted about this issue in context of Maudlin and Einstein.) So, I think Schaffer's cosmos is more akin to (I) than to (II) away from historical Spinoza and maybe Spinozism generally. That is to say, Schaffer's preferred way of treating fundamental laws would have to push him to take a non-trivial metaphysical stance between (I) & (II) without argument. But, in fact, Schaffer's actual position is a kind of tacit equivocation between (I) and (II). And, Schaffer has no obvious right to (II). I also happen to believe it is, in fact, an open empirical question to what degree we are allowed treat the cosmos as governed by the fundamental laws as a closed system. (But undoubtedly some philosophers of physics can help me out here.)
Now, Schaffer has a potentially bad and a good response to this argument. The bad response is to say that one could extend our fundamental laws indefinitely 'outward.' The better response, I think, is to adopt a modest skepticism about existing conservation laws and so remain neutral between (I) and (II). He could claim that when he is treating of fundamental laws he is not treating of any known laws, but just possible future (end-of-physics) fundamental laws. (I think I heard him say something like this in discussion.) These end-state fundamental laws will also tell us if we have to choose between (I) and (II). But, of course, such modest, but non-trivial, skepticism is not very popular among the hyper-realist metaphysicans of our day. Then again, that probably wouldn't bother Schaffer.
Of course, while Schaffer's monism is both indebted to and a non-trivial creative extension of Spinoza, Spinoza would have, in my opinion, frowned on the very project of tying fundamental metaphysics to a kind of scientific naturalism. But that is a topic for another day.