Full Idea
The Löwenheim-Skolem theorem is usually taken as a sort of defect (often thought to be inevitable) of the first-order logic.
Gist of Idea
The Löwenheim-Skolem theorem seems to be a defect of first-order logic
Source
Stewart Shapiro (Higher-Order Logic [2001], 2.4)
Book Reference
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.49
A Reaction
[He is quoting Wang 1974 p.154]