Let's start with the actual meaning of positive reinforcement. Positive reinforcement is a form of training which provides or adds (the positive part) a reward for a behavior that the trainer wishes to be repeated (the reinforcement part). Positive in this context does not mean good or bad. The opposite of positive reinforcement is negative punishment. The negative refers to the removal of a reward to discourage a behavior from being repeated ("punishment"). A simple example: When a dog sits, it gets petted (the reward), and when it jumps (an unwanted behavior) it does not get petted (removal of reward). Again, the "punishment" isn't wrong or harmful. Using these literal definitions, training that uses positive-reinforcement-only is impossible. Positive-reinforcement-only training means that there is no punishment, or acknowledgement of inappropriate behavior. Even taking no action is the same as removing a reward (because the dog does not get the reward) or negative punishment.
A common argument supporting positive reinforcement-only-training is based on several experiments undertaken in human education. When children are only "punished" for wrong answers, they become frustrated and stop trying. When the children are rewarded for providing the correct answers, they become encouraged and try even harder. All great! But the children who are being rewarded for correct answers are in essence being punished when they receive no reward (negative punishment) for the incorrect answers. There is no way of using positive-reward-based training without utilizing negative punishment.
Remember the game "Hot/Cold" that you may have played as a child? Someone hides an object and you search for it. The hider guides you with descriptions of hot (you are getting closer) and cold (you are getting farther away). Now picture the game with only one set of those directions. "You are ice cold.......nothing said..... nothing said... you are getting colder" is an example of what is termed positive punishment — receiving something unpleasant, the word "cold," to discourage a behavior. You can assume that the "nothing said" is a indication that you are getting "warmer" — negative reinforcement through the removal of an unpleasant experience to encourage a behavior. Most players get frustrated quickly and may stop playing.
Now picture the game in which you are only told when you are getting "warmer". Much more encouraging, but you have no guidance when you are moving away from the object. You are not "warm" or close, but how far away are you? You have only one direction of guidance. You are experiencing positive-reinforcement-only training (and by elimination, negative punishment because you hear no comment when you are not on the right track).
What is the best way to find the hidden object? Receiving both sets of guidance — you are either warmer or cooler. Using both boundaries, you can narrow down the expected direction more quickly and with less frustration. You have now learned using a technique called "balanced training".
The same applies to animals. They learn more quickly and gain more confidence when taught what is expected and what is not appropriate.
Now, take the hot/cold game one step further. What if you were offered alternative actions and directions that bring you closer to your goal quicker? You get to the shelf holding the object you are seeking — a book, for example. Remember that you do not yet know exactly what that object is. One book is on either end of the shelf. You touch one book and are told you are getting cooler. Which direction do you turn? What if someone pointed to the correct book as you were told you are getting cooler? The answer is simple! This is called re-directional training.
So when your dog grabs your favorite slipper, instead of just taking it away from him (negative punishment), hand him a kong full of treats (positive reinforcement). You have just acknowledged your dog's need to chew and offered an alternative course of action. You have provided "punishment" by saying no to the slipper, "redirected" your dog to the behavior you want, "rewarded" him by letting him chew on the kong and hopefully praised him for doing so. You are teaching him through balanced redirectional training!
Learning (for humans and dogs) is a process utilizing a multitude of tools. No single tool or technique can be successfully utilized on all students in all situations. Animals (including humans) learn best through the combination of several techniques which best fit the situation.
Now look at training from a dog's (or other animal's) perspective. Watch a bitch (mother dog) with her puppies. Does she punish her puppies for acting in ways she does not want? Does she pull away or growl when a puppy bites too hard when nursing? Do puppies bite at each other? ("You bite me, I bite you, which hurts" provides a punishment so you learn not to bite). Dogs even growl at humans who are behaving inappropriately, grabbing at the dog's face for example-. Why do we feel that punishing a dog is wrong?
The answer: It is the degree, means and timing of punishment, not the entire concept of punishment, that are often wrong. The word punishment itself has "a bad feeling." A more appropriate term may be correction, or marking/labeling of undesired behavior.