I think 'normal' depends on how he was raised. If he is used to not having to worry about a dirty diaper, then he isn't going to change his mind set just because he has aged a bit. It's what he is used to.
My DD was NEVER allowed to be in a dirty diaper... I would change her at the first sign that she was wet. So she never got used to the sensation. Once she was able to support herself sitting up, I would sit her on a training potty when she wet/soiled her diaper, and talk about the poop and potty in a fun voice for a minute or two. When she learned to walk around 9 months, I took her out of disposable diapers, and put her into training pants with incontinence liners in them. Same concept with the training potty. She wasn't even a year old before she started coming to me as she was in the process of soiling herself. By the time she was 18 months, she was letting me know before she needed to go... even though she didn't have the control to 'hold it' until she was a bit older. (I later learned that the 'technique' I used is similar to something called 'elimination communication'.)
I know my younger stepbrother was not potty trained at all when our families became blended. He was 3, and was not bothered in the least running around in a diaper that sagged down to his knees. My dad and step-mom worked, and I moved back home to help them with the kids. (They were all boys, at newborn, 3, 5, 8, 12, and 16...) Because I was home with him all day, it fell to me to potty train him. It took about 2 days of bathroom naked time, then another week of only underwear, before he finally realized his control of his body. Then it took about 2 week to teach him to use the potty exclusively. After that, he still had an occasional accident, but only rarely... which is kind of to be expected anyway.
For your son, I would recommend teaching him about his body functions. Take him in the bathroom, and let him run around buck naked. Take some toys and books, and just hang out. (Maybe push a little extra fluid, so he will have to 'go' faster... When he does go, pop him onto the seat, and get happy and excited. "Look! You went POTTY!!!! GOOD JOB!!!" If you believe in rewards, give him whatever you deem appropriate. (I know a lot of mothers tend to advise against food rewards though...)
Or, you might try putting him in the 'cool alert' pull ups, that supposedly get cold feeling when they get wet.
Just SOMETHING that makes him realize that going potty is an action that his body tells him about. Once he realizes that his body gives him the urge to go ahead of time, and that he can control when it comes out, potty training just becomes a matter of forming a new habit.