What is the philosophical notion of personhood? Sorry if this is a bad question. I'm new to philosophy.

Not a bad question. But too big fully to answer here, especially because there is so much debate about this among philosophers. So let me just give a brief structural outline.

There are two main questions philosophers have addressed: What distinguished persons from non-persons? And what makes this person at one time the same person as that person at another time?

On the first question, capacities or faculties have figured prominently. Some are theoretical or cognitive capacities such as, in particular, self-consciousness (awareness of oneself as distinct from other physical objects and thinking beings). Others are practical or moral capacities such as, in particular, the capacity to act morally even when doing so goes against one's self-interest and inclinations. Once a philosopher has argued for an account of the capacities that are necessary and jointly sufficient for personhood, one can then work out whether some higher animals may qualify and whether infants, the senile, some humans with cognitive disabilities, etc., may fail to qualify.

On the second question, there is again a great deal of interesting writing and disagreement going back several centuries. Some philosophers focus on the memories of the later person, some on what the earlier person has reason to care about, and other on further features that may relate (or fail to relate) the earlier and later person appropriately for identity. In these debates, thought experiments about the fission (splitting) and fusion (joining) of persons have played a major role.

So much for a thumbnail sketch. For further reading about the first question, I would begin with Immanuel Kant's writings. But these are hard. Better then to begin with the second question on which you can read Part 3 of Derek Parfit's wonderfully clear and engaging book Reasons and Persons.

One point that's implicit in Professor Pogge's answer above, but that it might be useful to make explicit, is that philosophers often use the notion of "person" in such a way that it contrasts with the genetic notion of "human". Whether or not you are human is a matter of your DNA. But whether or not you are a person cannot be settled by genetic testing. Rather, as Professor Pogge notes, it is usually taken to be a matter of having certain capacities. Thus, there may well be humans who are non-persons (for example, some philosophers have suggested that humans in persistent vegetative states fall into this category -- another controversial example concerns fetuses) and there may be persons who are non-humans (some advanced mammals, for example -- or if you want to get into the realm of science fiction, Data or Spock from Star Trek).

Specifying which capacities are necessary and/or sufficient for personhood turns out to be quite difficult. Some of the essays in Matters of Life and Death (edited by Tom Regan) give a good introduction to the issue of personhood. See in particular the essays on abortion and animal rights.

On the question of personal identity over time, John Perry's A Dialogue on Personal Identity and Immortality provides a useful introduction to the relevant issues.

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