Skip to content

Cosmological Argument Part III: A Modal Argument.

April 23, 2010


Sorry I’m so far behind on posting this. But here is the section of my paper where I give the modal cosmological argument:

Plenty of different thinkers have cast doubt on the premises of the cosmological argument from contingency, but I believe that one can make a cosmological argument that one can make which can avoid the problems of the argument from contingency. This argument weakens some of the premises of the argument from contingency by making use of premises that are making claims about some merely possible world. This argument may suffer from other different objections but this seems to be the fate of any philosophical argument. In this section I will first make this modal cosmological argument and then defend it from potential objections.

  1. Assumptions and Argument

There are three assumptions that I need to make in order for the argument to go through. The first can be formulated in two ways:

(6) Possibly, the sovereignty thesis holds.


(6*) Possibly, there is a sovereign being.

Now (6) and (6*) need some explaining. What is the sovereignty thesis (ST from now on)? And what does it mean for a being to be sovereign? The sovereignty thesis can be stated as thus:

(ST) There is an X such that for every Y such that YX, Y depends on X for its existence.

So what the (ST) states is that there is a being, which every being distinct from it depends on that being for its existence. We can then define what it means for a being to be sovereign. A being X is sovereign if and only if everything distinct from X depends on X for its existence.

Note that (ST) is a tenant of classical theism. Theists believe that God exists independently of everything else and that everything else in existence is dependent on Him for its existence. This does not mean that to prove that the sovereignty thesis holds is to prove the truth of theism. But I just wanted to point out the connection between the two positions.

The next assumption deals with the nature of dependence:

(7) For any X and Y: If X depends on Y for its existence, then if X exists so does Y.

(7) can also be stated counterfactually:

(7*) For any X and Y: If X depends on Y for its existence, then if Y does not exist, X does not exist.

What (7) says is that if one object depends on another object then the existence of the entity, which the dependent thing depends on, is a necessary condition for the dependents existence. So let’s say that I depend on the existence of matter for my existence. Then it is the case that if there is no matter in existence then I don’t exist.

There is one last thing to note about (7). Some people have offered (7) as definition for dependence, but I am not committing myself to this strong of a claim. Instead I am just committing my self to the claim that it is a necessary condition of two existing things that depend on each other that the dependent cannot exist without the thing it depends on.

This brings me to the last assumption:

(8) Some things necessarily exist.

This is just to say that at least one entity exists in all possible worlds. Presumably there are more, but all I need is for there to be at least one thing that exists in all possible worlds.

We are now in a place to make our argument. The first conclusion seems to be trivially true:

(E)  Either the Sovereign being is (i) a Necessary thing or is (ii) not a necessary being.

The truth of (E) follows from the law of the excluded middle, making it a logical truth. If we take (i) then the sovereign being necessarily exists and whatever necessarily exist actually exists, so the sovereign being actually exists and we have the conclusion we are looking for. Assume (ii) for reductio ad absurdum, then:

(F)  The sovereign being does not necessarily exist.

(6) and (8) entail:

(G)  There is a possible world where some necessary things depend on the sovereign being for their existence.

From (7) and (G) we get:

(H)  If the necessary beings exist then the Sovereign being exists.


(I)  Necessary beings exist in all possible worlds.

Therefore from (H) and (G):

(J) The sovereign being exists in all possible worlds.

But this contradicts our assumption (F) so, this means that we must reject (F) and which gives us that the sovereign being necessarily exists.

The premises of this argument seem to be quite plausible. If theism is possibly true then so is (6). Further being committed to the truth of (6) commits one to a claim that is much weaker than just admitting the possibility of theism. Since (6) is a weaker claim it seems to just add more to its plausibility. (7) follows from most accounts of dependence. I have yet to find a view in the literature on dependence that does not at least have this as a consequence of the philosophers view. It seems to be a central intuition about what it is for one thing to depend on another. It seems hard to think of what grasp we would even have on the phenomena of dependence if the dependent thing could exist without what it depends on. (8) also seems to be quite plausible. It seems that mathematical objects must necessarily exist in order to provide a stable ontological ground for the practice. Many philosophers have also thought that propositions, states of affairs, and properties are other things that are necessary existents. It seems that if one wants to have an ersatz take on possible worlds we must hold that some of these things necessarily exist. So it seems that we have plenty of reason to hold that (8) is quite plausible.

13 Comments leave one →
  1. Knockgoats permalink
    April 24, 2010 9:19 am

    This post has been removed

  2. April 25, 2010 10:56 pm

    Hey KG,

    Good to hear from you. Things have been kind of boring around here without you.

    Finals went well now on to a new quarter.

    You asked: First, what does it mean to say “Possibly, ST is true”. Does it mean “In some logically possible world, ST is true”, i.e. “ST is not necessarily false”? If not, what does it mean?

    Something is possible if there is at least one possible world in which it is true. This is equivalent to saying that it is not necessarily false. So the contraries here are possible and impossible. among what is possible are what is contingent and what is necessary. The necessary is true (or exists, obtains, etc) in all possible worlds, the contingent in some but not all possible worlds.

    Here are some equivalences:

    It is impossible that____ = Necessarily not ____ = Not possibly/ it is not possible that ____

    It is contingent that ______ = Not necessarily but possibly ______ = It is not impossible but not necessary that ______

    It is possible that ______ = it is not necessary that not _____ = it is not impossible that ______

    It is necessary that _______ = it is not possible that not _____ = it is impossible that not ______

    I hope that helps answer your question.

    So I take it that you have two main points. I’ll deal with the second point first:

    (E) Either the Sovereign being is (i) a Necessary thing or is (ii) not a necessary being.

    The truth of (E) follows from the law of the excluded middle, making it a logical truth.

    (E’) The present King of France is (i) bald or (ii) not bald.
    (E”) Unicorns’ horns are (i) made of gold or (ii) not made of gold.

    Your (E) assumes the existence of the Sovereign being – or are you going to insist that in E’ and E”, one disjunct or the other must be true?

    Actually my (E) does not assume the existence of the sovereign being. If you take it as if I am talking about the P.W. where the ST obtains as if it were actual then I can make de re claims about the Sovereign. But I think the claim I was making can be cashed out in a more formal matter as so:

    (E’) Either it is necessarily there is an X such that X is the sovereign being or it is not necessary that there is an X such that X is sovereign being.

    Since the modal operators are outside the scope of the existential quantifier, it does not commit me to that beings existence, whereas if they were inside the scope of the quantifier it would.

    Further this claim is inessential to my argument. I could set the argument not as a disjunctive syllogism, actually looking back over the argument, I’m not sure why I did.

    Y must, presumably, range over mathematical and logical objects as well as cauliflowers and cuttlefish. If so, the ST claims that every mathematical and logical object “depends on X [the “sovereign being”] for its existence. (This would extend, presumably, inter alia, to the truthvalues “true” and “false” themselves, which rather makes my head spin.) Is this claim really a tenet of standard theism?

    Yes, indeed it is a standard tenant of theism. The inverse of this thesis is the thesis that God exists independently of everything else (the aseity theses). I would like to know what confuses you about the truth values being dependent entities. First off I’m not sure that there are properties true and false. But if there are, most any view of truth that I am aware of would make them dependent on something. Theists hold the following truth equivalence:

    (TETE): P is true iff God believes P.

    It seems here that something cannot be true if God does not believe it, and how can God believe something if He does not exist? This seems to suggest that what is true would depend on God for its existence.

    What does it mean for Y to depend on X for its existence in this case?

    There are many different accounts of what dependence amounts to, whether or not it should be taken to be a primitive, etc. I don’t need to choose one in order to for the argument to go through all I need is the conditional true:

    (7) For any X and Y: If X depends on Y for its existence, then if X exists so does Y.

    The consequence of (7) need not be taken to be what dependence amounts to, but just what is entailed when one thing depends on another.

    Mathematical and logical objects surely exist (if they are held to exist at all) in all logically possible worlds – i.e., are “necessary beings”. If we admit the existence of a plurality of necessary beings (e.g., the natural numbers), and interpret “Y depends on X” as “There are no logically possible worlds in which Y exists and X does not”, then the ST is true, but there are an infinite number of “Sovereign Beings”.

    Indeed this would be the case if it we were understanding dependence in the way that you mentioned. That is that “There are no logically possible worlds in which Y exists and X does not” is what “Y depends on X” amounts to. But, this is not something I am committed to with (7). I avoid the issue of whether or not this analysis of dependence is adequate or not. I personally think that it is extremely inadequte. But for now that is neither here nor there.

    However, does it make sense to assert that the existence of a necessary being depends on anything at all?

    Yes I believe it does. So we’ve established that if “There are no logically possible worlds in which Y exists and X does not” is what dependence amounts to then all necessary beings depend on all other necessary beings for their existence. From what I understand sets are taken to depend on their members. If this is the case then we have a prime example of necessary beings depending on one another: The singleton empty set depends on the empty set, the set which contains the empty set and the singleton empty set depends on the empty set and the singleton empty set for its existence etc. Other examples can be made. A broader version of the question is whether or not two beings which exist in all the same possible worlds as each other can be such that one depends on the other. I think that any adequate account of dependence must be able to allow for this to be a possibility.

    Surely it is reasonable to interpret “necessary being” precisely as one whose existence does not depend on anything? If we do that, ST is necessarily false, because in any logically possible world there will be the same, infinite set of necessary mathematical and logical objects that do not depend on any jumped-up, self-styled “Sovereign Being”!

    Maybe in some context we can understand necessary being this way, but in the context in which we are talking a necessary being is one that just exists in all possible worlds. So as far as this argument goes I would deny the first premise, because that sense of necessary being is not the sense I am interested in with my argument, I am just curious about those beings which exist in all possible worlds. But I take it you mean that if a being exists in all possible worlds then it does not depend on anything else. I would like to see an argument for this or at least some motivation for this view, because it seems like an arbitrary judgment to me that all necessary beings do not depend on anything, without any further reasoning.

    If we take the counterfactual analysis of dependence to be true then no necessary being exists independently of everything else, it depends on every other necessary being for its existence, they certainly are not independent entities. The other accounts don’t rule it being the case that some necessary beings depend on other things. So I find it hard to believe that a sovereign being is impossible based on these grounds.

    I definitely agree that the argument if it is not equivocating on the term ‘necessary being’ then it is valid. It just isn’t sound.

    Thanks for the critique.

  3. Knockgoats permalink
    May 1, 2010 5:08 pm

    This post has been removed.

  4. May 2, 2010 10:09 pm


    All this means is that two sets cannot be identical unless their members are: it’s part of a definition of what is meant by “set”.

    Hardly. I think what you meant to say is that Necessarily for any sets ∂ and µ if the set ∂ and the set µ have all and only the same members then they are identical. In other words if ∂ and µ have the same extensions they are the same set. That is a claim about what determines the identity of the set and not one that makes any sort of claim on what the set depends on. For all we know ∂ could have different members in different possible worlds. If ∂ is {x,y,z} in @ what we have said about the relations of sets and their extensions has not determined that ∂ could not be {p,q,r} in W*. The claim about sets depending on their members is more substantial than this.

    You can’t just take the word “depend” and assume it means the same in all contexts: I depend upon my parents for my existence, I also depend upon water for my existence, I depend upon my organs for my existence, I depend on all the people and animals who have not killed me when they had the chance for my existence – and in all these cases, “depends” means different things. Unless you are willing to say what you mean by “depend” in the context of your argument, there seems no point taking this any further.

    (1) The word depends has a general enough use that it can be used in very many different contexts without equivocating. There are different species of dependence, but the fact that x depends on y still amounts to the same thing across all of the specific cases. Just as there are different shades of red and different orders of mammalia there are different species of dependence. The truth conditions for what is to be red are the same no matter what shade and are the same for something being a mammal no matter what order it is in. The same holds for the truth conditions of a true statement of the sort X depends on Y no matter what species of dependence. Every example you give pick out different species of dependence but no different genus, and it is the genus I am working with not the species. The use of the general notion of dependence instead of some specific one is actually a virtue of this argument.

    (2) I do not need to give any sort of analysis of the dependence relation. There is much discussion on whether of not this term can in fact be analyzed. Most think that it can’t be defined see Jonathan Schaffer for more of a discussion on taking dependence as a primitive. Kit Fine offers an analysis of dependence in his paper on ontological dependence. I think we do have enough of a grasp of this notion to not need to offer an analysis of the notion, even if we could. So I really do not see any sort of obligation to meet your demand.

    If we take “Y depends on X” simply to mean that there is no possible world in which Y exists and X does not, then the ST is equivalent to the proposition that there is at least one necessary being, and all necessary beings are sovereign beings. So clearly, that won’t do for your purposes. However, unless and until you are able and willing to specify what more “Y depends on X” means, we are in no position to judge whether your:

    (6) Possibly the sovereignty thesis holds.

    is true.

    So that analysis of dependence is one that I definitely do not hold to be true, but if I did the conclusion of the argument would indeed be trivially true. Maybe thats what you mean by ‘that won’t do’ for my purposes. But as I said, the counterfactual analysis of dependence is not one that I hold to be true and is inadequate to capture the phenomena of dependence.

    I find it hard to believe that you do not have some sort of grasp of the notion of dependence. But, even if you don’t have a grasp on the notion all the information needed is in the premises.

    As far as dependence goes I understand it to be an asymmetrical (maybe antisymmetrical) irreflexive transitive relation I think it can be defined as something along the following lines:

    (†)For any X and Y, X depends on Y if and only if if X is grounded in any set of facts Z then Y is necessarily a member of Z.

    There’s really no point in constructing arguments in which the premises are so vague – it’s pseudo-intellectual wankery of the most absurd sort.

    This is plain unnecessary. What reason do you really have to post that here other than feeling the desire to puff up your reply by posting some fallacious rhetoric that is by no means constructive to this dialogue. Not only is it not constructive and serves no real purpose but it is totally obnoxious and makes me opposed to even trying to further this conversation.

  5. May 3, 2010 2:06 am

    (†) can also be stated:

    (†*) X depends on Y iff Necessarily, X is partially grounded in Y.

  6. Knockgoats permalink
    May 3, 2010 11:48 am

    This post has been removed

  7. Knockgoats permalink
    May 3, 2010 11:50 am

    This post has been removed

  8. May 3, 2010 12:03 pm


    You are now being removed from the post.

    You have shown me that you are incapable of being respectful in your posting. Jon has given me control over my posts and I have a very strict policy on being respectful. If you wish to post on this entry you can come back and do it respectfully. Otherwise this conversation is over.

  9. Knockgoats permalink
    May 3, 2010 12:23 pm

    This post has been removed

  10. Knick Gaughts permalink
    May 3, 2010 1:37 pm

    Oh, Real Nick Gotts, how far you\’ve fallen.

  11. Knockgoats permalink
    May 3, 2010 2:03 pm

    This post has been removed due to lack of philosophical content.

  12. thomas2026 permalink*
    May 3, 2010 2:44 pm

    Knick Gaughts,

    I would prefer if you showed Knockgoats some respect. There is no need to play a similar game by posting backhanded comments on this post.

    If you do not comply you will be removed also. This is a post for philosophical discussion and no insults and name-calling. If you have arguments and questions about previous arguments then I will be happy to reply. But if those include disrespectful and non philosophical behavior the comments will be deleted.

    We are all adults, so let’s behave as adults.

  13. May 3, 2010 3:21 pm

    Sorry, that last post was from me and not Jonathan.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: