The problem can more accurately be expressed by breaking it into several steps.
Conclusion: We can never know that there exist any other minds but our own. This is the philosophical position known as solipsism
In response to this problem there have been two main areas of attack. The reductionist viewpoint, with the likes of McDowell, has tried to tackle the first two propositions 1 and 1a, by putting forth certain modes of expression such as being in pain as privileged and allowing us direct access to the other's mind. Thus, although they would admit from the problem of pretense, that at no one time can we claim to have access to another's mental state, they are not permanently unavailable to us. <<<second method not given>>>
Counter to the reductionist argument would be a more biological theory (and somewhat materialistic viewpoint). Take the eye and its perception of color, for instance. The retina cells that react to red are similar in each person, so we can expect them to react in a similar fashion. However, we also know that the different cells in the eye can be found in different amounts and distributions; thus giving rise to color blindness and other such visual variances. Similarly, differences in the distribution of brain cells and dendritic connections (among many other potential variances) could give rise to different mental states for the same stimulus.