The appeal to bodily continuity might be replaced by the requirement that there is continuity in the possession by an individual of the very same brain.
But is this a plausible criterion of personal identity? The following scenario is conceivable and points to a problem. Imagine that robotics and brain science have advanced to such a stage that it is possible to construct a silicon brain which supports the very same kind of mental life as that supported by a flesh-and-blood human brain. Imagine also that parts of a human brain (say, a cancerous part) can be replaced very gradually by silicon chips which realise the very same mental functions as the damaged brain tissue.
Furthermore, one might say that something biological such as a heart, brain or liver is essentially biological. A brain could not be anything but a biological entity. This essentialist thesis is consistent with the view that the function of any given biological object (a human heart, for example) could, in principle, be carried out by a non-biological object (a mechanical pump, say). So, one can concede that my later silicon brain is indeed a brain. But, on this essentialist view, the effect of all the tissue removals and bionic insertions in my skull is to destroy one brain and replace it with another.
Our brain example shows that the sort of matter or stuff with which we replace an object's removed parts can affect the overall identity of that object, even if continuity of form or function is preserved. My (earlier) human brain is not identical to my (later) silicon brain. Yet I survived the operation. Hence, the brain criterion is false.
Of course, this approach is open to the objection that composition is not an essential feature of being a brain. Functional continuity may be sufficient to maintain identity. However, we shall leave further discussion of this issue for there is a deeper worry about the tenability of the brain criterion.
We moved to the brain criterion in response to challenges to the bodily criterion. In examining why the move seemed plausible we don’t say it’s because the human brain is a three-pound pinkish-grey spongy organ that occupies human skulls. Instead the move seemed the natural one because of what the brain does. It realises our mental life. It is because of this mind-supporting function that we single out the brain as the seat of personal identity.
As long as there is continuity in mental life one can press the claim that the stuff from which a brain is composed does not matter to personal identity. Nor does the issue of whether I have the very same brain through time. Instead it is precisely that mental life in which we locate the criterion of personal identity, and we care about or focus on the brain just because it is the seat of that mental activity. Perhaps, then, it’s psychological continuity that matters.