Personally, I don't use the term correction at all in terms of dogs. Maybe it's because I've been schooled in pretty straightforward terms - punishment, reinforcement, redirection, extinction. I think the terminology "correction" is just a different word with the same meanings. The problem is it has a different meaning for every person.
Some people use it to mean they redirect on to something else (get a toy, and distract the dog from the kitty). Some people use it to explain a management situation (no learning is taking place - take the dog by the collar and move it inside, as Liesje explained). Some people use it to indicate a punishment (ie. collar "correction";). Some people actually use it in place of what a reinforcer defines ("correct the behaviour by reinforcing four on the floor";).
That's why I don't care for the word. Because it doesn't have one meaning, therefore I don't find it is at all useful in conversation. All of the above examples have very different outcomes, and actually are observed very differently by a dog. When somebody says "I corrected my dog for ______", it doesn't give me any idea of what process was used, how the dog reacted, how the behaviour changed (or didn't).
In terms of the philosophical basis of the word, that it somehow means dogs are "wrong" and we have to "correct" them, I base my life with dogs to accomodate their needs as dogs as best I can. With that said, they do unfortunately need to alter some behaviours in order to live in modern society. That's just how it is. But I do my best to prevent behaviours where possible, manage others where necessary, so that I don't have to try to humanize them too too much.
For instance, when Zipper first came to my house, the first thing he did was mark on his own kennel. At first glance, you would think *Whoah, what the heck are you doing!?!?!?*. But in reality it made perfect sense. He just moved to a foreign place, where there are two humans, but also two other canine inhabitants. The only thing familiar to him was the kennel he brought with him, so it was totally natural for him to identify it with marking behaviour. What totally enthralled me was the return response (yeah yeah, what others find repulsive I find intriguing). I then found that Gaci had gone on and very discretely marked the two dog beds on the floor in the same room. She effectively understood his meaning, and replied with her own. That's all that happened, and there have been no more markings in the house since. Gaci has never marked before that either. It was pure communication between dogs.
Did I punish any of them? Nope. Should I have? I don't see why. I look at it from a purely normal, natural standpoint and to be honest I understood it completely. Some would have "corrected" the marking behaviour, but the dogs sorted it out quickly so I had no need to intervene.
Another example is when Zipper moved in, he fixated on the mouse cage. It was low enough that he stood there and watched them for hours on end. If the mice were sleeping, he would take his paw and THWAP the cage to wake them up so he could watch them run on the wheel. I did try redirecting him in the beginning, with toys and attention and calling him off, but I clearly realized how important the mice were to him - not the bird, or the fish, just the mice - so I moved them. Problem solved. Instantly. I didn't question why he was so interested in the mice - he's a terrier, beyond that, he's a dog - a predator. Of course he's going to be interested in them. So I didn't waste my time punishing that behaviour, and to be honest I didn't even waste time *training* anything with reinforcers.
Don't get me wrong, I do a lot of training with my dogs. But I also take a quite ethological approach to living with my dogs, in that I spend a lot of time understanding why they do what they do, what results their behaviours have on the environment, and studying that deep-rooted stuff that goes beyond the observable behaviour, beyond the simple laws of learning. I love knowing that all animals learn in the same ways, through the ABC's (antecedent, behaviour, consequence), but I also love knowing what motivates them to do in the first place, what turns those wheels inside that little head, what naturally inhibits them, because going a little deeper often allows you to better work with the animal and gives you a wider toolbox.