Staying with my recent approach of tossing up new arguments and seeing what sticks, I thought I'd give this a try. I've defended several modal cosmological arguments before, but this time I want to take some Leibnizian and kalam considerations into account.

1. Possibly, everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise, W-PSR)

2. Necessarily, whatever begins to exist is contingent. (Premise)

3. Possibly, the universe began to exist. (Premise)

4. Possibly, the universe is contingent. (From 2 and 3)

5. Hence, the universe is contingent. (From 4 and S5)

6. Possibly, whatever is contingent has an external cause. (Premise, implied by W-PSR)

7. Possibly, the universe has an external cause. (From 5 and 6)

8. Necessarily, if the universe has an external cause, that cause is a timeless, changeless, immaterial, and very powerful first cause. (Premise)

9. Possibly, a timeless, changeless, immaterial, and very powerful first cause exists. (From 7 and 8)

10. Necessarily, a first cause is either necessary or contingent. (Definition)

11. Necessarily, a first cause cannot be explained by anything else. (Premise)

12. Necessarily, a first cause is explained by a necessity of its own nature. (From 1 and 11)

13. Therefore, a timeless, changeless, immaterial, and very powerful first cause exists. (Implied by 12)

## Monday, September 26, 2011

## Monday, September 19, 2011

### Modalizing Descartes

1. Whatever is conceivable C is possibly caused by an existing C's impression. (Premise)

2. A perfect being is conceivable. (Premise)

3. Hence, the conception of a perfect being is possibly caused by a perfect being's impression. (From 1 and 2)

4. Hence, a perfect being possibly exists. (Implied by 3)

5. Therefore, a perfect being exists. (From 4 and S5)

Besides the usual unpackaging of (4), this argument is defensible. Descartes held that in order to conceive of something, there had to be an impression of that conception caused by the entity being conceived. That's a bit of a mouthful, but the idea can be illustrated by connotation, as opposed to strict denotation. The reason I can conceive of a horse is because I have seen an existing horse. Even imaginary entities, such as a unicorn, are just an amalgamation of existing things, e.g. a horse (which exists) and a horn (which exists on other animals).

Now, instead of contending that Descartes' strong principle is correct, we can actually weaken it and still arrive at the same conclusion. If it is even possible for a conception to be caused in the manner described above, it follows that a perfect being (omnipotent, omniscient, and morally perfect in every possible world) possibly exists. All that's left is a defense of the rather uncontroversial S5 axiom, and we have a successful ontological argument for God's existence.

Of course, I don't expect anyone to be persuaded by this argument if they're not persuaded by similar ones, e.g. the modal third way, that have arguably even more modest premises.

2. A perfect being is conceivable. (Premise)

3. Hence, the conception of a perfect being is possibly caused by a perfect being's impression. (From 1 and 2)

4. Hence, a perfect being possibly exists. (Implied by 3)

5. Therefore, a perfect being exists. (From 4 and S5)

Besides the usual unpackaging of (4), this argument is defensible. Descartes held that in order to conceive of something, there had to be an impression of that conception caused by the entity being conceived. That's a bit of a mouthful, but the idea can be illustrated by connotation, as opposed to strict denotation. The reason I can conceive of a horse is because I have seen an existing horse. Even imaginary entities, such as a unicorn, are just an amalgamation of existing things, e.g. a horse (which exists) and a horn (which exists on other animals).

Now, instead of contending that Descartes' strong principle is correct, we can actually weaken it and still arrive at the same conclusion. If it is even possible for a conception to be caused in the manner described above, it follows that a perfect being (omnipotent, omniscient, and morally perfect in every possible world) possibly exists. All that's left is a defense of the rather uncontroversial S5 axiom, and we have a successful ontological argument for God's existence.

Of course, I don't expect anyone to be persuaded by this argument if they're not persuaded by similar ones, e.g. the modal third way, that have arguably even more modest premises.

## Friday, September 16, 2011

### An Epistemological Argument Against a Beginningless Universe

Suppose that a beginningless universe is metaphysical possible. With this assumption in mind, it may still be shown that it is irrational to believe in such a universe.

1. If the universe is beginningless, then its past is infinite. (Premise)

2. An infinite past yields infinitely-many actualities. (Premise)

3. If there are infinitely-many actualities, then it is epistemically impossible to weigh any probability. (Premise)

4. Probability can be epistemically weighed. (Premise)

5. Therefore, it is irrational to believe in an infinite universe. (From 1 - 4)

The logic of the argument as stated is pretty loose, but one can follow the reasoning of the premises to the conclusion fairly naturally, I think. (1) is obviously true, and (2) is almost entirely uncontroversial. (4) must be true in order for probability and induction to survive, and these principles are indispensable toward rationality. This leaves us with (3).

Imagine the lines of evidence both for and against a beginningless universe. Further, imagine that the evidence on both sides is inexhaustible. We can represent the evidence for a beginningless universe with the set of all odd numbers {1, 2, 3, . . . n}, and the evidence against a beginningless universe with the set of all even numbers {2, 4, 6, . . . 2n}. This scenario should be expected, given the existence of infinitely-many actualities.

But if this is the case, how can the probability of either hypothesis be reasonably assessed? For every line of evidence for a beginningless universe, there is an equally strong line of evidence against it. Yet, we all know that the probability of a hypothesis can be reasonably assessed. If this is correct, then it follows that it is inconsistent with probability for there to be infinitely-many actualities to take into account. Because of the epistemic warrant for probability, then, it seems that the rejection of infinitely-many actualities, and therefore a beginningless universe, is preferable.

1. If the universe is beginningless, then its past is infinite. (Premise)

2. An infinite past yields infinitely-many actualities. (Premise)

3. If there are infinitely-many actualities, then it is epistemically impossible to weigh any probability. (Premise)

4. Probability can be epistemically weighed. (Premise)

5. Therefore, it is irrational to believe in an infinite universe. (From 1 - 4)

The logic of the argument as stated is pretty loose, but one can follow the reasoning of the premises to the conclusion fairly naturally, I think. (1) is obviously true, and (2) is almost entirely uncontroversial. (4) must be true in order for probability and induction to survive, and these principles are indispensable toward rationality. This leaves us with (3).

Imagine the lines of evidence both for and against a beginningless universe. Further, imagine that the evidence on both sides is inexhaustible. We can represent the evidence for a beginningless universe with the set of all odd numbers {1, 2, 3, . . . n}, and the evidence against a beginningless universe with the set of all even numbers {2, 4, 6, . . . 2n}. This scenario should be expected, given the existence of infinitely-many actualities.

But if this is the case, how can the probability of either hypothesis be reasonably assessed? For every line of evidence for a beginningless universe, there is an equally strong line of evidence against it. Yet, we all know that the probability of a hypothesis can be reasonably assessed. If this is correct, then it follows that it is inconsistent with probability for there to be infinitely-many actualities to take into account. Because of the epistemic warrant for probability, then, it seems that the rejection of infinitely-many actualities, and therefore a beginningless universe, is preferable.

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