I was going to ignore these posts at first, it usually just isn't worth it. But seeing that so many people seem to have this belief, I'd like to point out the fallacy.
Human population is NOWHERE near the earth's capacity. Seriously, people have been worrying about this for over a century now. And yet, we live in more abundance now than ever.
The people who have little in this world is not the result of over-population. It's a result of under-development. There are plethora of reasons why those regions are under-developed, but global overpopulation is not one of them.
Humans could, right now, double, triple, quintuple, what ever is needed, food production within just a few years, if the profit motive was there. People starving in this world is not because of others overeating, or wasting food, or just too many rich people. Did you know that European and American Governments pay farmers to NOT produce food?
Disease is another common misconception. I think this is a population-density thing. If people are all crowded together, then it must be easy for diseases to spread? I live in Hong Kong. Did you know that in some districts of Hong Kong, there are almost 35,000 people per square mile? By comparison, New York City has a mere 1,300 per square mile. Hong Kong does not suffer from any plague like events. You could increase the population of NYC by a factor of 25, and viral disease would not be much of an issue (for population reasons alone, of course, vaccine programs and the such play a role in this).
Remember, the worst plague in human history was the Black Death, from the 1300s. The total human population at that time was estimated to be between 300 and 400 million. Human population has increased by a factor of 20. By many estimates, more people live in the USA now than lived on the entire planet at that time.
War is another one. As if war is some product of over-population, it isn't. That's such a cartoonish view of things, it almost doesn't even warrant mention. I will point out that at the time of WW2, the largest war in human history, human population was 2.3 billion.
This post is getting a bit long, so I won't carry on. But I can keep going on, in relation to water, oil, etc. I won't, but I will summarise: people have been complaining about over-population for more than a century. Those people have been wrong for more than a century. At this point, it's like betting against the Harlem Globetrotters.
For the overpopulation :
Even in the case of maximum efficiency, in which all the grains grown are dedicated to feeding humans (instead of livestock, which is an inefficient way to convert plant energy into food energy), there's still a limit to how far the available quantities can stretch. "If everyone agreed to become vegetarian, leaving little or nothing for livestock, the present 1.4 billion hectares of arable land (3.5 billion acres) would support about 10 billion people," Wilson wrote.
The 3.5 billion acres would produce approximately 2 billion tons of grains annually, he explained. That's enough to feed 10 billion vegetarians, but would only feed 2.5 billion U.S. omnivores, because so much vegetation is dedicated to livestock and poultry in the United States.
So yes, we can maybe feed 50 billions africans, but only 2.5 bilions americans. We are at 7.4 billions people now, and not all africans... You can also read about the http://www.overshootday.org/ to see that the human's demand in ressources is way too high already, and you can't solve that with a miraculous technology in just a few years, it's also a population issue.
Wars and diseases are indeed caused by population density, but also population movements and needs. The population is really badly distributed, some populated areas will be drowned because of the global warming, and vital resources will become scarcer. So yes, it is known that there will be wars, nothing to do with WW2 here : http://www.gechs.org/will-global-warming-cause-more-wars/
I agree we could manage a lot bigger population with a perfect geopolitic peace, some technological breaktroughs, a well managed and distributed population, new ways of consommation for everyone... But that's not how the human population is and it won't be, maybe ever. So no, in this current state, the population can't grow too much without consequences.