Well no, the wishy-washy "properties are certain kinds of methods that we can't really define in a particularly concrete manner" definition of properties is the arbitrary one. Saying that properties are those things which are declared with @property is pretty non-arbitrary. That's the definition the compiler users, that's the definition the runtime uses, and that's the definition I use.
Using the wishy-washy definition doesn't help, in any case. Nobody would say that e.g. autorelease is a "property", but you can still call it with dot syntax.
I seriously doubt your intellectual integrity here.
You know that the dot syntax is a mechanism that matches with the conventions for property access, and no other access pattern.
You also know that its possible to call zero argument methods that aren't accessors using the dot syntax.
I don't believe that you think that this is the purpose for which the dot syntax was designed, and yet you bring up 'autorelease' to support your position.
As I said, based on your specific definition, you are correct, but using denigration, a false straw-man 'quotation', and dishonest examples doesn't make your definition fit the evidence.
As I said, and you sidestepped, properties pre-date the directive, therefore the directive cannot be the sole definition of what properties are.
Using the wishy-washy definition doesn't help, in any case. Nobody would say that e.g. autorelease is a "property", but you can still call it with dot syntax.