There is no part of the statement "there is no objective purpose in the world" that afirms objective purpose or value.
This will become an impossible subject to talk about if everything I state will be taken as an example confirming that there is objective value, or purpose. You are begging the question here. Try not to assume the conclusion of your argument.
Let me say that I'm not going all Socretes on you here ala "The only thing I know is that I know nothing.". My statement is not an epistemological one, it's more of a comment on the human condition. We all have different purposes in the world and there is no way to sum these to some kind of objective purpose.
To highlight my point further: Science is generally seen as the fountain of objective truth, it deals in theories based on facts and logic. A scientist would say if you eat above a certain amount of ice-cream per day you would increase your risk of diabetes, but there is no way a scientist could ever say that you shouldn't eat that amount of ice-cream. The should's and should not's are in the realms of the clergy and politicians. As you can see I'm not saying we can't find objective facts in the world, I'm just saying when it comes to purpose, it's an individual thing.
Determining a purpose for society, or for some other individual, is different then determining a fact of the world.