The theory of syntax, like any other theory, comes with an ontology: phrases, categories, etc. All systematic semantic theories of natural language, in which our thoughts are expressed, come with an ontology, too: objects, propositions, events, etc. What is the relation between these? On one view, semantics and its ontology are independent of syntactic constraints. On a radical version of this view, they would be what they are even if syntax did not exist, or was of a very different nature. Another view, matching the previous one in radicalism, is that the two ontologies are the same, at least in some relevant respects. An intriguing implication of this view is that the design of the syntax-semantics interface is virtually 'perfect', and the syntax-to-semantics mapping a trivial one. In this talk, I discuss evidence from theoretical linguistics and cognitive neuroscience that supports the ways in which the latter view is too strong, in an attempt to demarcate the extent to which it might hold.