The term “transcendental unity of apperception” seems pretty forbidding on the face of it. But in actual fact, there's a relatively straightforward idea behind it. In the very simplest of terms, the transcendental unity of apperception is a pre-condition for the possibility of experiencing the world around us.
What Kant is trying to do here is to demonstrate that, in order to have perceptions, those perceptions have to belong to a unified self. This is a direct challenge to Hume, who argued that there is no unified self, just a bundle of perceptions.
Kant argues that, in order to have the perceptions that form the basis of possible knowledge, there has to be a unified self that exists in space and through time that can organize and make sense of the many perceptions that we have. In order for those perceptions to give a true and honest account of the world in which we live, the world of empirical objects, then it must be possible for there to be a unified, coherent self.
Or, to put it another way, the statement “I think” must be able to accompany all my perceptions of the world. Otherwise, argues Kant, there would be something out there in the world represented in me that could not be thought at all. And that's tantamount to saying that the representation in question is impossible or “at least would be nothing to me.”
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