This is why artificial neural nets do so well: they work similar to humans. They can capture the nuance of dogness, because a neural net is the right structure to encode it. Because "dogness" is just that, a configuration of a neural net.
A computer *could* recognize a dog by the biological definition, but not from a photo. You could describe a dog by properties, but that's just describing what the neural net does. So why not go to the source.