Butchers, bakers and donutmakers probably won’t forsee all that much trouble in cutting something in half. If you’re a philosopher on the other hand . . . Problems arise when trying (to imagine) the process of cutting something exactly in half. Given that most objects could be said to have a centre point of some kind, then, if that object is cut in half, could just one of the two parts ends up with the point? If one half gets the point and the other doesn’t, then the two halves aren’t equal – so the object hasn’t been truly cut in half.
Dr Aaron J Cotnoir. who is a senior lecturer in the Department of Philosophy at the University of St Andrews, Scotland and part of the Arché Philosophical Research Centre, examines such things in his essay ‘How to make donuts and cut things in half ‘ which can be read in its entirety here.
Pointing out – en passant – that :
“As usual, there are no perfect solutions in philosophy, but there are many good ones. And not all good solutions are equally good.”
BONUS: Dr Cotnoir has also investigated whether a God could create a stone so heavy that he/she/it would be unable to lift it and the question of How Many Angels Can be in the Same Place at the Same Time
The illustration shows (one way) to cut a ring-donut (approximately) in half – creating only one boundary with no holes rather than two.