At this age, babies start noticing their surroundings more during the day. I'm sure you've noticed he's a little wiggly during nursing sessions, right?!? Since they take in less during the day, they need to make up for it at night. I'm sure he wakes, eats, and goes right back to sleep, right? He really is hungry. Most exclusively breastfed babies do NOT sleep through the night for many months or longer. Don't let anyone tell you that cereal or baby food will hold him longer. It's doubtful he's ready, and even though pedis will tell you it's ok to start them at 4 months, the American Academy of Pediatrics says to wait on all solids (including rice cereal) until 6 months.
Eating is just what he needs to do, so don't do it as a last resort. Do it first and you'll both get more sleep!
Sometimes your baby will seem super hungry and you think, "I've got to give this baby food. He's always hungry!" That's just his way of upping your supply to meet his growing demands/needs. He'll nurse more. Growth spurts *typically* happen at 3, 6, and 9 weeks old, and then at 3, 6, and 9 months. He may be going through his 3 month growth spurt a little late. They need to be fed on demand to make your supply meet his demand.
But what you've got is a very normal little 4 month old who has discovered the world around him. In order to get the nutrition he needs, he makes up for it at night. Here is an article about it: http://www.kellymom.com/parenting/sleep/4mo-sleep.html
So whether you have a growth spurt like many have suggested or a "wakeful 4 month old" (I have experienced this with my other two and am going through it RIGHT NOW with MY 4 month old!), the best bet is to feed him when he wakes and go back to sleep. YOu are not forming bad habits. That comes from a generation or a few ago where they thought this. We know better - babies need to be fed when they're hungry, and breastfed babies especially do! They use all the good stuff in breastmilk and there is no "filler" so they need to eat more often than formula fed babies.
And look at the bright side: him eating a few times at night will possibly keep you from ovulating and thus having a menstrual cycle longer! My first didn't night wean for a long long time, and I didn't have my first cycle until he was 17 months old!