Two kinds of theoretical framework for syntax are encountered in current linguistics. One emerged from the mathematization of proof theory, and is referred to here as generative-enumerative syntax (GES). A less explored alternative stems from the semantic side of logic, and is here called model-theoretic syntax (MTS). I sketch the outlines of each, and give a capsule summary of some mathematical results pertaining to the latter. I then briefly survey some diverse types of evidence suggesting that in some ways MTS seems better suited to theorizing about the relevant linguistic phenomena