Towards other dogs
It is very unusual for a bulldog to be truly aggressive towards people and if yours is there will almost always be an underlying cause which needs to be carefully assessed before any long term decisions are made. However, dog aggression is more common and is in some bulldogs (in fact in most bull breeds) an instinctive behaviour as bull breeds often go back through a violent fighting history. As with all pure bred dogs history has an original purpose and in bulldogs this history is quite violent. Bull baiting and dog fighting were the origins of this breed and in some is instinctive. In others there will be a bad experience with another dog that triggered the behaviour. Because of the unique shape other breeds find it quite hard to read the face and the body language of a bulldog and therefore find it very difficult to work out if your dog is friend or foe. Every breed has an instinctive reaction that experts refer to as the "Flight or Fight" reaction. Put simply this means that when a dog feels threatened they will react to it in one of two ways – “flight” which means to run away, or “fight” which means to stand and face it. If a dog has been in a situation in the past that has required this reaction they will remember it if they are in that situation again. If they have been attacked by another dog they will remember (often they will even remember which breed or colour dog it was and the reaction could be restricted just to dogs that match that description) and depending on the wiring of that dog will attack before they are attacked. Once that memory has been etched it will never be erased and if you know your dog is dog aggressive you must act responsibly. Never allow these dogs to run off lead as an attack in a public place could land you in all kinds of serious trouble.
Dog on dog aggression within a family unit is also very common amongst multiple bulldog households, especially between same sex dogs. Talk to anyone that has several bulldogs and you'll find that they are often in a situation where one has to be kept separate from one or more of the other dogs. This kind of aggression is usually jealousy fuelled, where as almost every breed of dog thrives as a pack member, the bulldog is a breed that almost laughs in the face of normal dog behaviour and I think that even those that appear to be quite happy in a multi dog household would secretly rather be a single dog. The jealousy can also manifest when visitors arrive, and two dogs that get on great will suddenly turn on each other when someone comes to the door, this kind of behaviour can be compared to spoilt children, desperate for the attention. It is quite common to find one or more bulldog crated when you enter a multi bulldog household. These dogs don't live like this all the time, it just makes the duration of your visit much easier for the owner to deal with.
One of the saddest aspects of serious fallings out is that they are nearly always permanent. They find it very hard to forgive each other once they have had a serious fight and even when you think things have settled down, there'll suddenly be a situation where they look at each other and bang - another fight ensues. Be careful splitting up fights of this nature as they will be totally focused on each other and you are more likely to be accidentally bitten. Bites of this nature need to be forgiven as they are not intended for you.