Barrier's a problem for Searle's theory too
Searle insists intentionality is caused by and realised in brains. But intentional systems are made of parts that lack intentionality. This applies as much to brain neurons as to computer parts.
Because Searle insists that intentionality is caused by and realised in brains (see the Biological Naturalism arugument), the syntax semantics barrier is as much a problem for Searle's theory as it is for AI.
Intentional systems are made up of parts that lack intentionality. For example, many biological systems are composed of neurons that lack intentionality. These neurons work on a purely syntactic level, just as computational elements do in a computer.
So it seems the syntactic-semantics barrier is as much a problem for brains as it is for machines.
Richard Double, 1983.