God, Faith and Infinity » Lecture 2
An argument is not a dispute or disagreement (though disputing people may make use of arguments).
Rather, arguments are something we give in order to persuade:
Giving an argument … is something more like making a case. An argument presents reasons [the premises] that purport to favour – or support – a specific claim [the conclusion]. … If the argument is well-constructed, the premises provide reasons in favour of the conclusion. (Eagle, Magnus, and Button 2022: §1)
An argument for the existence of God is one with the conclusion God exists.
Which God? Our Scholastic-inspired arguments aim at the ‘perfect being’ conception of God discussed in the previous lecture.
All the paths leading to this goal begin either from determinate experience and the specific constitution of the world of sense as thereby known, and ascend from it, in accordance with laws of causality, to the supreme cause outside the world; or they start from experience which is purely indeterminate, that is, from experience of existence in general; or finally they abstract from all experience, and argue completely a priori, from mere concepts, to the existence of a supreme cause. The first proof is the physico-theological, the second the cosmological, the third the ontological. There are, and there can be, no others. (Kant 1787: A 590/B 618)
Lord … we believe You to be something than which nothing greater can be thought. Or is there, then, no such nature [as You], for the Fool has said in his heart that God does not exist? But surely when this very same Fool hears my words “something than which nothing greater can be thought,” he understands what he hears. … So even the Fool is convinced that something than which nothing greater can be thought is at least in his understanding; for when he hears of this [being], he understands [what he hears], and whatever is understood is in the understanding. But surely that than which a greater cannot be thought cannot be only in the understanding. For if it were only in the understanding, it could be thought to exist also in reality – something which is greater. Therefore, if that than which a greater cannot be thought were only in the understanding, then that than which a greater cannot be thought would be that than which a greater can be thought! But surely this [conclusion] is impossible. Hence, without doubt, something than which a greater cannot be thought exists both in the understanding and in reality. (Anselm 1078: 93–94)
If AN1 is correct, then so is the greatest conceivable \(F\) exists in the understanding, for pretty much any \(F\):
it is said that somewhere in the ocean is an island, which, because of the difficulty, or rather the impossibility, of discovering what does not exist, is called the lost island. And they say that this island has an inestimable wealth of all manner of riches and delicacies in greater abundance than is told of the Islands of the Blest; and that … it is more excellent than all other countries….
Now if someone … went on to say, as if by a logical inference: ‘You can no longer doubt that this island which is more excellent than all lands exists somewhere…’ … I know not which I ought to regard as the greater fool: myself, supposing that I should allow this proof; or him, if he should suppose that he had established with any certainty the existence of this island. (Gaunilo 1903: §6)
The second way is based on the notion of an efficient cause:
We find that among sensible things there is an ordering of efficient causes, and yet we do not find – nor is it possible to find – anything that is an efficient cause of its own self. For if something were an efficient cause of itself, then it would be prior to itself – which is impossible.
But it is impossible to go on to infinity among efficient causes. For in every case of ordered efficient causes, the first is a cause of the intermediate and the intermediate is a cause of the last – and this regardless of whether the intermediate is constituted by many causes or by just one. But when a cause is removed, its effect is removed. Therefore, if there were no first among the efficient causes, then neither would there be a last or an intermediate. But if the efficient causes went on to infinity, there would not be a first efficient cause, and so there would not be a last effect or any intermediate efficient causes, either – which is obviously false. Therefore, one must posit some first efficient cause – which everyone calls a God. (Aquinas 1274: 15)
Aquinas seems to have the picture that every event can be fitted into a single causal chain.
So maybe there are many actual causal chains – and possibly many first causes? To get his desired conclusion we need a substantial additional premise:
But rather than thinking of the causes Aquinas is talking about as ordinary localised events, let us take them to be maximal simultaneous states.
Since time is linearly ordered, it is true that these world states come ordered in series, and plausible that each is causally dependent on those earlier than it.