donderdag 13 juli 2017
Yet another implication
Here is yet another implication of the conclusion of my semantic argument. Take the positive property of being numerically finite. An object is numerically finite if and only if it has finitely many parts. Now, if this property is universally held in the actual world, the conclusion of my semantic argument (i.e., universally held positive properties are necessarily universally held) entails that all objects in all possible worlds are numerically finite. That is to say, if there is no numerically infinite object in the actual world, it follows that a numerically infinite object is in fact metaphysically impossible. Note that the absence of a numerically infinite object in some possible world does not entail that there is no actual infinite in that world. For there might be an infinite set of objects in a possible world whose members do not compose an object in that world. One thus needs a further premise - such as mereological universalism being necessarily true - in order to conclude that there being no actual infinite in the actual world entails the impossibility of such an infinite.