Humans have the ability to understand multiple meanings, modify the meanings and understand the mis-meanings.
Example joke: "Ever notice how we park on driveways, drive on parkways, pay tolls to go on freeways and it takes longer to get where you want on an expressway." All illustrate how our usage and the meanings of our words have been modified over time.
A driveway is a section of personal roadway that leads to a personal garage (you would never have left one of the old 70% wooden cars outside with zero rust proofing on the metal, ever). A parkway was supposed to be a scenic roadway to link urban and suburban parks with pleasure roads where people could park freely and enjoy the area, now it's commonly a synonym for any general highway. Freeways were actually speed-limit-free highways, the 'free' never had anything to do with cost until the very late 20th century. An expressway was designed as a high-speed arterial road, which may have a limited number of driveways.
None of that addresses the issues of whether the dog understands. Yes, humans have a higher level of understanding in the sense that we understand abstractions, but our greater abilities in that area don't disqualify the dog's simpler ability from being called understanding.
If the dog can tell the difference between being told to fetch the paper vs fetch my shoes, then he understands.
Beyond that, the statement...
> their brains are merely receiving a signal and performing an associated action
Equally applies to humans; our brains just have a more complex form of association. There is no inherent meaning to any of the noises we make that we call words other than they're associated to something. Your associations to those noises is far more complex than the dogs, but you can't call yours understanding and not his; his understanding is simpler, but if he performs the correct trick, then he understands the word in the same sense you do, he associated some kind of meaning to that word, just like you do.
That's fair to say. Any comprehension is understanding even if it is just rote learning of single words to commands.
You're right, just because the dog doesn't understand 50+ words for 'drink' (water, coke, pepsi, coffee, tea, etc etc.) doesn't mean it isn't understanding in the same comprehension as if you got a 3 year old to bring you a 'drink'.
I don't know what I was thinking, I must have been in a state of sleep deprived idiocy. The simple fact you can teach a dog in human linguistics to sit when you say 'sit' signifies its understanding. You wouldn't get this response in an animal that all its communication skills are genetically encoded.
I remember reading about how Native Americans used to hunt Wolves with pitfall traps and how wolves would teach their young how to avoid the traps, like they would hunt a deer, they can also do the same with poisoned meats. These clearly show wolves are capable of understanding abstract concepts. Unless sink holes are a natural predator of wolves I doubt there's a genetic cue for "you see that flat piece of ground, you'll fall through that into a big pit" or "you see that steak, that's poisoned, but the one sat on the side of that metal contraption in their yard isn't!"
I was thinking of understanding along the lines that we can understand multiple meanings and abstract ideas. However, 1:1 learning is still understanding, and clearly Canis Lupis is capable of learning abstract ideas so a dog certainly has the ability to (even if we have to rebreed it into the species).
What's funny, is you're the guy with the dog; I have no pets. You should have been the one convincing me that your dog understands. Anyway, and up-vote for you.
One major difference might be our ability to map various signals into the same internal "sign" or meaning (synonyms, explanations, relations, generalization, instantiation, specialization, negation etc.) while dogs might have a 1:1 mapping between signal and meaning.
If you had a golf ball, tennis ball and cricket ball; all small enough for a dog to fetch. Would it know which "ball" to fetch if you had a club/racket/bat in your hand?
If yes, then two forms of learning are identical. If not, well ..
And that differs from understanding exactly how?