The question is hotly contested. Right now, about two percent of the world's farmland is organic, so there's long way to go. Still, some say it's do-able, citing stats about the high productivity of small organic farms. But the Food and Agriculture Organization of the United Nations, which has every PR and political motivation to agree with organic boosters, reluctantly declared that the world simply can't get by on organic farming alone in the near to mid-term.
“We should use organic agriculture and promote it,” [Dr. Jacques Diouf, FAO Director-General] said. “It produces wholesome, nutritious food and represents a growing source of income for developed and developing countries. But you cannot feed six billion people today and nine billion in 2050 without judicious use of chemical fertilizers.”
And the FAO isn't going it alone among world organizations:
In its annual World Development Report, the World Bank noted this year, that “low fertilizer use is one of the major constraints on increasing agricultural productivity in Sub-Sahara Africa”....Much of African soil suffers from constraints such as acidity and lowered fertility and is greatly in need of soil amendments and nutrients.