1. Something exists.
2. Every existing being is either contingent or necessary.
3. There is a possible state of affairs in which no contingent being exists.
4. It is necessarily the case that possible states of affairs are explicable.
5. Hence, a necessary being is possible.
6. Whatever is possibly necessary exists in all possible worlds.
7. Therefore, a necessary being exists.
(1) and (2) are easily granted. I cannot doubt my own existence without first existing to doubt it. As for (2), something can either exist in at least one (but not all) possible worlds (contingent existence), or else exist in all possible worlds (necessary existence). Existence in no possible worlds would yield that a thing is impossible, and therefore necessarily non-existent.
(3) is highly plausible. If we represent the sum total of all contingent beings as C, and if all the members of C can at some time fail to exist, it's reasonable to infer that C itself may at some time fail to exist. By analogy, if every part of a house can possibly fail to exist, then the house as a whole can also fail to exist.
(4) doesn't entail that every state of affairs must have an explanation in the actual world. Rather, a state of affairs is defined as "explicable" so long as it is explained in at least one possible world W. Yet, the only thing that is left to explain ~C in W would be a necessary being. So, if it is possible that ~C obtains and that ~C has an explanation in some possible world, then a necessary being exists in some possible world, in confirmation of (5).
(6) and (7) are necessary inferences under the S5 axiom of modal logic. If something necessary does not exist in some possible world, then it is not necessary at all, but contingent, which is contradictory.
Maydole argues very similarly, here. The key difference (besides the use of S5 in the argument above) is that Maydole narrows the scope of his argument to the possibility of C not obtaining in the past, whereas the argument above is more general.
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Hi Doug,
ReplyDeleteYou said,
“(3) is highly plausible. If we represent the sum total of all contingent beings as C, and if all the members of C can at some time fail to exist, it's reasonable to infer that C itself may at some time fail to exist. By analogy, if every part of a house can possibly fail to exist, then the house as a whole can also fail to exist.”
I’m confused. If C is the set of contingent beings (which is different than calling them a set of contingently actual beings), then we can simply state from this alone that C, as a set of all contingent beings, fails to exist in some possible world. Heck, it follows by definition since C is a set of all contingent beings. But, this doesn’t mean that there is a world without a contingent being. It just means that there is a world without C. That is, there is a world without the set of all contingent beings. When we say that “C itself may at some time fail to exist”, we are only saying that in some world, it is not the case that all contingent beings exist; we are not saying that no contingent being exists within that world.
Lastly, you should consider changing your premise 4 to: It is necessarily the case any states of affairs have a possible explanation.
You need to qualify the explanation as possible; otherwise it's actual.
Consider something I'm working on-
1. Necessarily, everything that exists is either contingent or necessary.
2. Nothing contingent exists in possible world w.
3. Hence, either something is a necessary existent or nothing exists in possible world w.
4. It is impossible that ‘nothing exists’ is true.
5. Hence, something is necessary existent in world w.
6. Whatever is possibly necessary existent is a necessary existent.
7. Hence, it is necessary that the being listed in 5 exists;
8. Hence, there is a necessary existent.
1 is a necessary truth. 2 needs to be argued for and 3 is deduced from 2. Premise 4 is plausible, although there is some scholarly debate on it. 5 is a deduction; 6 is a modal truth while 7 and 8 are deductions.
Your only problems are 2 and 4. Mind you, the atheist can agree with you and state that numbers necessarily exist or abstract objects. I think it’s best to either prove there something necessary exists or function contributively to some larger argument for God's existence.
Thanks again for your thoughts, Mickey. You always have some good things to say.
ReplyDelete"When we say that 'C itself may at some time fail to exist', we are only saying that in some world, it is not the case that all contingent beings exist; we are not saying that no contingent being exists within that world."
That's technically true. What I was getting at is that there is a possible states of affairs in which nothing contingent exists. When I say ~C, I don't just mean the sum total of contingent beings, but literally every contingent being of that sum total. That's why I offered the house analogy, in which at least two things are true: A) every part of the house possibly fails to exist; and B) the house as a whole possibly fails to exist. A contingent being has its parallel in A, whereas C has its parallel in B. I just don't think one can be true without the other.
Your revised premise, "2. Nothing contingent exists in possible world w," states exactly what I'm thinking. Nevertheless, you may have put it more articulately. :)
"Your only problems are 2 and 4. Mind you, the atheist can agree with you and state that numbers necessarily exist or abstract objects."
This is why I qualified my argument with the bit about explication. Abstract objects, such as numbers, don't stand in causal relations, so they aren't really capable of explaining anything in the most pertinent sense of "explain." By explicable, I don't mean actually explained, but simply "explained in some possible world." However, your suggestion that I change (4) to "possibly explained" is likely good advice. This way, we can avoid miscommunication.
Try this...although i think 6 is false.
ReplyDelete1. Necessarily, every thing that exists is either contingent or necessary.
2. Nothing contingent exists in possible world w.
3. Hence, either something is a necessary existent in possible world w or nothing exists in possible world w.
4. Necessarily, every state of affairs has a possible explanation.
5. Hence, either 'something is a necessary existent in possible world w' has a possible explanation or 'nothing exists in possible world w' has a possible explanation.
6. Necessarily, only things enter into explanatory relations.
7. Presume that 'nothing exists in possible world w' has a possible explanation in possible world w2.
8. Hence, 'nothing exists in possible world w' has a possible explanation in possible world w2 and only things in possible world w2 enter into explanatory relations.
9. But nothing exists in possible world w2.
10. Hence, 7 is false. But given the truth of 6, it follows that 9 is false, too.
11. Thus, "'something is a necessary existent in possible world w' has a possible explanation" is deduced from a disjunctive syllogism with 10 and 5.
12. It is possible that a necessary being exists. (From 11)
13. Whatever is possibly necessary existent is a necessary existent.
14. Hence, it is necessary that the being listed in 5 exists;
15. Hence, there is a necessary existent.
are all the steps clear in this argument of mine?
ReplyDeleteYes, it's a clear argument. I'd like to clarify my earlier comment about abstract objects not being able to explain anything. A better way of putting it may be that abstract objects don't cause anything. "Cause" is a specific type of explanation - namely, it is something active. Abstract objects, if they exist at all, don't actively cause anything, even if they may be used in an explanation.
ReplyDeleteHere's an example. "2+2=4" may explain why whenever we add two apples to two apples, we get four apples. However, "2+2=4" doesn't do the actual addition (the act of causing) of the apples. That's something we have to do by putting the apples together.
We might, therefore, revise our premise to this: "It is necessarily the case that possible states of affairs are possibly caused."
"States of affairs" should also be interpreted as the instantiation or non-instantiation of some concrete object or objects.
Hi Doug,
ReplyDeleteYeah, we really do need to limit the premises to causal explanations. Consider that the axioms of Peano arithmetic are explanatorily prior to 2+2=4. This point was given by William Lane Craig in 'Is Goodness without God Enough?', p.170. On the same point, metaphysicans J. Hoffman and G. Rosenkrantz state that in Euclidean geometry, "we can explain theorems about triangles and their angles by logically deriving these theorems from axioms." (See: The Divine Attributes, p.89) Hence, I suspect that we're on the right track to limit such explanations to causal explanations.