  To avoid this kind of awkwardness, we think that the Skolemite should frame his argument, less as a criticism of our ordinary set-theoretic notions, and more as a constructive analysis of the algebraic conception of set theory. That is, he should focus primarily on defending the algebraic conception of set theory as an independently plausible conception of set theory (step 1), and he should then present set-theoretic relativity as simply a new and surprising consequence of this positive conception (steps 2–3). This argumentative strategy leaves room for the Löwenheim-Skolem theorems to do some real philosophical work—e.g., as described two paragraphs ago. It also gives step 1 a tighter—and a more constructive—focus. On this reading, step 1 serves mainly to highlight the positive virtues of the algebraic conception; criticizing ordinary set-theoretic notions is (at best) a secondary  concern.[40] (See section 3.3 for more on this kind of point.)