Haptic (touch) perception normally entails an active exploration of object surfaces over time. This is called active touch. When exploring the shape of an object, we experience both geometrical and force cues. For example, when sliding a finger across a surface with a rigid bump on it, the finger moves over the bump while being opposed by a force whose direction and magnitude are related to the slope of the bump. The steeper the bump, the stronger the resistance. Geometrical and force cues are correlated, but it has been commonly assumed that shape perception relies on object geometry alone. Here we show that regardless of surface geometry, subjects identified and located shape features on the basis of force cues or their correlates. Using paradoxical stimuli, for example combining the force cues of a bump with the geometry of a hole, we found that subjects perceived a bump. Conversely, when combining the force cues of a hole with the geometry of a bump, subjects typically perceived a hole.