Tibbles exists after time t. No two material objects can exactly occupy the same region at the same time. This set of sentences is inconsistent, so at least one will have to be rejected. This doctrine we may call mereological essentialism. Burke argues as follows, using the Kripkean doctrine of sortal essentialism.
All cats are essentially cats.
Therefore, Tib is essentially a non-cat. If Tib survived the annihilation of the tail, Tib would be a cat. Therefore, Tib ceased to exist when the tail was annihilated. Tib is not changed in any intrinsic way by the annihilation of the tail, so how could the annihilation of the tail cause Tib to cease to exist. Peter van Inwagen is one such philosopher.