An existing basement wall is not insulated on either side. Humidity inside is causing significant sweating on the cold wall in the winter months. Outside, the top 4 feet of wall are exposed above the ground. I am less interested in insulating for energy savings and more interested in avoiding the condensation problem as the basement space is actually a garage. Will I solve the condensation problem by insulating only the outside wall to a depth of about 2 feet below grade. If not, then what is the best way to insulate the inside with a proper vapour barrier to isolate the humid air from the cold wall?
Insulation slows the loss of heat, it will not raise the temp of the wall above the dew point unless there is a source of heat inside. (Heater, leakage from another source, or a day/night average temp above the dewpoint.
You may be best looking for a way to lower the humidity in the space. Removing standing or leaking water, finding vapor leakage from the conditioned space or other sources of moisture (clothes dryer vented into the space). You may want to contact a basement specialist contractor. Concrete is porous, and if the wall were not sealed with a watertight membrane before backfilling moisture can be leaking through the walls. If you do not wish to heat the space, adding ventilation to get the wet air out will help.
Once that is done you can think about insulating. The easiest, though expensive, solution is to spray cold cell polyurethane spray foam on the wall. This will act as a vapor barrier and insulation, and it has no air space behind it for condensation. Second best is solid foam board insulation outside, from top to bottom of the wall (even underground).