  This second point shows that Skolem's Paradox goes away if our logic is strong enough. The third point shows that weakening our logic has a similar effect. In Tennant and McCarty 1987, Tennant and McCarty show that standard proofs of the Löwenheim-Skolem theorem fail in constructivist set theory, and they argue that the theorem itself is probably constructively  invalid.[29]  This means that there's no way to generate Skolem's Paradox from within the framework of constructivist mathematics. For constructivists, therefore, as for those who are willing to countenance second-order axiomatizations of set theory, Skolem's paradox simply doesn't arise.