So I'm writing an essay on the Sorites paradox and how it relates to the abortion debate. One resolution to the paradox I was reading about came from supervaluationism, but I'm not entirely sure if or how this resolution could be applied to the abortion debate. Any ideas?
When confronted with a paradox such as the sorites, there's always the theoretical option of taking the paradoxical argument to be valid and accepting its premises.
Your way of applying sorites reasoning seems to fall into exactly this camp of theoretical possibilities. But then you cannot consistently adopt supervaluationism, since this position takes one of the sorites argument's premises to be false.
Apart from that your idea is interesting. Just a few critical remarks:
I would rather consider the vague predicate 'human being' or 'human', since personhood is a philosophically very loaded concept that may bring its own complications that have nothing to do with the abortion debate.
Furthermore, I would construct the 'sorites sequence' not as a succession of times but rather as a succession of collections of human cells. This allows you to have the vague predicate applicable to members of the sorites sequence, which makes things much easier.
There are some challenges and problems with your proposal you maybe should address:
Firstly, many have the strong intuition that the sorites argument you use your is not a correct argument. You should give an explanation for that widespread intuition, which is false according to your position.
Secondly, you have a sort of dual sorites your position cannot consistently accept. Your proposed argument uses the non-negated predicate 'human' (I'm using my own example predicate). But you can equally build a sorites with the negated predicate 'non-human', where the sorites sequence is reversed. This sorites starts from the claim that one human cell is not a human being and concludes that one quadrillion human cells (with the right structure) does not make a human being, which seems false. Your adoption of the first sorites as a correct argument forces you to deny the first premise of the dual sorites, but you should give an independent argument for the falsity of that premise.
Peter Unger is virtually the only philosopher accepting some sorites arguments. So, maybe some of his writings on this topic could be of interest to you.