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> When I visualize software solutions in my head, not a single bit of code is up there.

If you envision a mechanical solution without anything like a mill or lathe up there, do you consider yourself to be machining?

> Syntax is just a textual representation of concepts.

Mechanical parts are just the metal (or whatever material) representation of concepts. Does programming not refer to processes around taking those concepts and turning them into something 'tangible' of a certain variety?

It seems to me that programming is, in fact, just syntax (within some loose interpretation). As you call attention to, syntax doesn't mean much in a vacuum, but the bigger picture that includes thinking about concepts usually gets the "engineering" moniker.