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Pruss and Rasmussen on Arguments Against a Necessary Being

Many philosophers find the premises of at least some arguments for the existence of a necessary being attractive, but regard the existence of a necessary being either as itself absurd or as having absurd consequences. Pruss and Rasmussen's ninth and final chapter therefore considers a series of six arguments against a necessary being.

For the most part, the responses have a common structure. An opponent employs certain principles of logic, epistemology, or semantics connected with possibility and necessity to argue against the existence of a necessary being. Pruss and Rasmussen respond by showing how those same principles can be employed in an argument for the existence of a necessary being. It therefore becomes necessary either to reject the principles that lead to these contradictory results, or show that the premises of one argument are more plausible than the premises of the parallel argument.

Here I want to discuss three of these arguments: the argument from conceivability (sect. 9.2), the argument subtraction arguments (sect. 9.5), and the argument from causation (sect. 9.6). I've selected these arguments because there are issues here that connect to the concerns about causation I raised in my posts on chapters one and three.

Pruss and Rasmussen formulate the argument from conceivability as follows:

1. A world empty of concrete things is conceivable.


2. If a world empty of concrete things is conceivable, then such a world is possible.


3. Therefore, a world empty of concrete things is possible.


4. If a world empty of concrete things is possible, then there is no necessary concrete thing.


5. Therefore, there is no necessary concrete thing. (p. 174)

This argument is based on a principle of modal epistemology according to which conceivability provides evidence of possibility. There are some difficulties about exactly how to formulate the correct version of this principle, but Pruss and Rasmussen assume that some suitable version can be constructed (pp. 175-176).

Pruss and Rasmussen's parallel argument is formulated as follows:

6. Suppose there is no necessary concrete thing.


7. Then there cannot be a necessary concrete thing.


8. If there cannot be a necessary concrete thing, then there cannot be an explanation of the existence of all contingent (i.e. non-necessary) concrete things.


9. But there can be an explanation of the existence of all contingent concrete things...


10. Therefore, the starting assumption is false: there is a necessary concrete thing. (pp. 177-178)

Premise 9 of this argument is meant to be supported by the same principle of modal epistemology that supported premise 2 of the previous argument: we can conceive that there is an explanation of all concrete contingent things. (This is meant to be better than just asserting that we can conceive that there is a necessary being, and this is therefore possible, because one might be suspicious of the conceivability test as applied to explicitly modal claims.)

The problem in this argument is with premise 8. According to Pruss and Rasmussen, "Claim (8) follows from an ordinary meaning of 'explanation'" on which circularity is prohibited. However, non-circularity is not the only assumption here, since, one again, 'concrete' means 'causally capable'. The possibility of non-causal explanation opens up a major hole in the justification for premise 8. The non-circularity constraint only means that the existence of all contingent concrete things cannot be explained by something that is itself both contingent and concrete. Pruss and Rasmussen want to conclude that there must be a necessary (i.e., non-contingent) concrete thing, but as far as the logic goes a non-concrete thing (i.e., a thing incapable of causation), whether necessary or contingent, would do just as well.

Turning now to the subtraction argument, Pruss and Rasmussen formulate that argument as follows:

13. Finite: Possibly, there is a finite number of concrete things.


14. Subtraction: For any non-zero number of concrete things there might be in total, if there could be that number of concrete things, then there could be fewer.


15. Leap: If Finite and Subtraction are true, then there is no necessary being.


16. Therefore, there is no necessary being. (p. 185)

As Pruss and Rasmussen note, Subtraction is supported by the Principle of Modal Uniformity they had employed in chapter six.

Pruss and Rasmussen then formulate their parallel argument as follows:

17. Finite 2: Possibly, there is an explanation of there being at least n concrete things, for some finite n.


18. Subtraction 2: For any finite number n, if there could be an explanation of there being at least n concrete things, then there could be an explanation of there being at least n-1 concrete things, where n-1 is a positive number.


19. Leap 2: If Finite 2 and Subtraction 2 are true, then there could not have been no concrete things.


20. Therefore, there could not have been no concrete things. (p.187)

In defense of Leap 2, Pruss and Rasmussen write, "First, it follows from the premises (via mathematical induction) that there could be an explanation of there being at least 1 concrete thing. Second, the only possible explanation of there being at least 1 concrete thing is that there couldn't have been no concrete things" (p. 188).

Here Pruss and Rasmussen at least provide some defense of their second claim. They suggest that "one might think that it is objectively unlikely for there to have been no concrete things" and that this explains why there is at least one concrete thing (p. 188). They respond that the argument will still be plausible if we stipulate that by 'explanation' we mean 'non-probabilistic and non-circular explanation'.

This response seems to me to have a few problems. In the first place, if this is not to result in necessitarianism, the mere existence of the necessary being must not necessitate the existence of the particular concrete things that there are. So somewhere along the line there appears to be either a non-necessitating explanation or a brute fact (i.e., an unexplained contingency). Some of the arguments Pruss and Rasmussen employ for a necessary being are basically directed at getting rid of brute facts, so assume it's not a brute fact. Then there's a non-necessitating explanation in here somewhere.

There are two possibilities here: either the immediate explanation of why there is at least one concrete thing is non-necessitating, or there is a non-necessitating explanation prior to that point in a chain of explanations. For instance, if you think the necessary being is God, you might think God's reasons provide a non-necessitating explanation of God's choice and God's choice provides a necessitating reason for the existence of concrete contingent things.

The reason why this is important is that when they speak of non-probabilistic explanation, Pruss and Rasmussen can't just mean to require a chain of explanation with necessitation all the way down. What I suspect they mean is that the explanation can't be of the form "p is true because p was antecedently objectively probable." But if so then they have only ruled out one very specific possibility for non-causal explanation. I previously suggested that grounding explanations or nomological explanations might do the needed work here. Pruss and Rasmussen could of course just keep ruling out alternative forms of explanation by fiat, but then they are relying on our ability to conceive a very specific scenario, and there could be alternative arguments that ruled out by fiat Pruss and Rasmussen's preferred form of explanation.

I turn, finally to the argument from causation. Pruss and Rasmussen do not formulate this as an explicit argument and set up a parallel argument. Instead they simply frame this as the suggestion that a necessary being couldn't cause anything, and then discuss a few reasons that might be given for this claim. However, in this very short discussion they essentially just assert that "there doesn't seem to be any ... theory" of causation that rules out causation by a necessary being (p. 190).

It seems to me that they haven't tried very hard here. According to Hume (in his reductive rather than eliminativist moods), a necessary condition for causation is spatiotemporal contiguity. But Pruss and Rasmussen themselves have just said (p. 189) that none of their objections to the subtraction argument work against the version whose conclusion is that possibly there are no spatial entities. So here's an argument:

1. Possibly there are no spatiotemporal entities.


2. Necessarily, every cause is spatiotemporally contiguous to its effect.


3. Necessarily, no non-spatiotemporal entity is spatiotemporally contiguous to anything.


4. Therefore, necessarily, every cause is spatiotemporal. (From (2) and (3))


5. Necessarily, every spatiotemporal entity is essentially spatiotemporal.


6. Therefore, necessarily every cause is essentially spatiotemporal. (From (4) and (5))


7. Therefore, possibly there are no causally capable entities. (From (1), (6), and the necessity of essence)

Maybe the contiguity requirement is undermined by quantum non-locality or some other considerations. However, similar arguments could be run with any theory of causation that makes use of physical concepts like energy or entropy, and there are plenty of these in the recent philosophy of physics literature.

Here, then is my central criticism of this book (a book which, to reiterate, I like quite a lot!): Pruss and Rasmussen try to be 'ecumenical' with respect to theories of causation, and for that reason they don't say much about it. However, this concept plays a central role in all of their arguments (since it is built into their definition of 'necessary being') and they don't always seem to succeed in remaining neutral. Much of the time it seems they are implicitly assuming an Aristotelian powers ontology, and when they explicitly disavow this assumption (as on pp. 190-191), they only consider the Lewisian alternative. Now, these are two popular theories of causation and they are radically different from each other, so the fact that the arguments work with these two theories makes them quite significant and also suggests that they may work with other theories. It seems to me, however, that more attention to this issue is needed.

Posted by Kenny at June 25, 2019 5:25 PM