Here's an admittedly crude formulation of a modal cosmological argument that has been bouncing around in my head for a while. I'd like to know what y'all think of it.
Consider the following statement:
There is a mountain of gold in my backyard.
As I'm sure you already suppose, this statement is false. In actual fact, there is no mountain made of gold in my backyard. But still, the statement makes sense to you. It seems to be perfectly coherent. You can easily conceptualize things like backyards, mountains, and objects that are made out of gold. Moreover, there seems to be no conceptual difficulty combining these things so that it does indeed seem that there might actually be (or have been, or be at some time in the future) a mountain that is made out of gold in a backyard somewhere. Perhaps it might even be that everyone in the entire world will suddenly decide to give me all their gold and I will choose to have it made into a mountain in my backyard. Okay, so that's highly unlikely to ever happen, but technically it does have a non-zero probability. (Hey, a guy can dream, can't he?
) So in order to make the above statement true, it seems we should change it to the following:
Possibly, there is a mountain of gold in my backyard.
Now consider this statement:
There is a Bradford pear tree in my backyard.
Unlike the first statement about my fictitious mountain of gold, this statement is true. If you were to come over to my house and look into my backyard, you would see that therein does indeed grow a real, living Bradford pear tree. You would be able to reach out and touch its trunk and feel the roughness of its bark. Were you to come in early March, you would be able to see its lovely white blossoms and smell their rather noxious odor. It's actually there. But it doesn't have to be there. I could remove it, so that it would no longer be there. Instead of a Bradford pear tree, whoever planted it might have decided that a maple would be preferable, or a pecan, or no tree at all. In fact, it seems to make perfect sense that there might not ever have been any Bradford pear trees, or any trees, or even any plants at all. We can go even further and say that there seems to be no trouble conceiving that there might never have been any plots of land that might be called backyards, or any human persons who might call them such. Indeed, it seems perfectly coherent to say that there might not ever have been any physical objects at all! For it seems that for any physical object whatsoever (and for argument's sake we may treat humans, animals, and any ETs there might be as purely physical objects as well; whether or not they really are is immaterial for our purposes [pun intended
]), we could, in principle, say of it that that object does not exist, and, though our statement would be false, it would make perfect sense. But if it makes sense to say of any physical object whatsoever that it doesn't exist, then what should prevent us from going ahead and making the stronger claim that:
Possibly, no physical objects exist.
So now we have that, while it is not actually the case that there is a mountain of gold in my backyard, it is possibly the case that there may be. And while it is in fact actually the case that there's a Bradford pear in my backyard, there doesn't have to be; it is possibly the case that that it isn't really there. Not only is it possible that the Bradford pear isn't there, but, as we've seen, it also seems to be possible that there aren't any physical objects at all.
Now, when we make existential statements, whether positive or negative, the truth conditions of these statements seem to be dependent upon whether or not there actually exist grounds that make them true. What I mean is that, e.g., for the statement there is a Bradford pear tree in my backyard to be true, it seems there must actually exist some state of affairs that satisfies the content of my claim. And when I say that there is a mountain of gold in my backyard, it seems the falsehood of my claim must depend on there not actually existing any such satisfying conditions. Satisfying conditions such as these that serve as the grounds for true existential statements are called truthmakers. But what about other types of statements? More specifically, what about modal claims, such as that it is possible that [such and such] is the case? I would say that these too must have truthmakers if they are to be true, and indeed, I think that for there to be any true proposition at all, then there must needs be a truthmaker for it. But if it is true, as I said above, that it is possible that there are no physical objects at all, then what might there be left over that would make such a statement true? Well, as we saw with our fictitious golden mountain, we can conceptualize things like backyards, mountains, and items of gold. We understand that these things have certain properties, like spatial and temporal extension, quantifiable relations to units of measure, or chemical properties (in the case of gold, anyway), but what all of these properties--and all properties, characteristics, or other attributes whatsoever, I would say--have in common is their abstract nature.
Now, what we abstract from in forming our concepts are physical objects. And when we say that a certain physical object exists, the truthmaker for our claim is just that physical object. But I would say that when we turn to alethic modal claims (i.e. that possibly or necessarily something or other is the case) regarding physical objects, we cease to talk about the physical objects by themselves (i.e. as concrete states of affairs) and begin to talk in abstraction about immaterial natures or essences that might or might not be concretely realized in actual, corporeal physical substance. So when we say that, possibly, it is the case that no physical objects exist, the truthmaker for our true claim would seemingly have to be an object that is not of a physical nature, but that is more closely related to our abstract conceptualizations.
But what of the modal status of this object? As I've tried to show, physical objects are modally contingent beings, meaning that it is possibly the case that they exist, but it is not necessarily the case that they exist (whether or not they actually exist is beside the point). But what of the modality of our truthmaker(s) for such modal claims? Might it (they) possibly not exist, just as physical objects might not exist? I think not. For by modal axiom 5 we can say that:
For any proposition p, if it is possibly the case that p, then it is necessarily possibly the case that p.
Assuming S5 modality, which allows mutual accessibility among all possible worlds, and applying this to our alethic modal claims regarding physical objects, we can see that in order for it to be true that it is possibly the case that no physical objects exist, it would have to be necessarily true (i.e. true in every possible world) that it is possibly the case that no physical objects exist. But if the latter statement is true, and if it is the case that this truth needs a truthmaker, then its truthmaker would seem to have to be a necessary being. For if it weren't a necessary being, then it could not serve as the truthmaker for this necessary truth in worlds where it does not exist, and it doesn't seem very plausible that non-indexical propositions can shift truthmakers.
To put this in syllogistic form, then:
1) Possibly, there are no physical objects. (premise)
2) For any proposition p, if it is possibly the case that p, then it is necessarily possibly the case that p. (premise, modal axiom 5)
3) It is necessarily possibly the case that there are no physical objects (by 1 and 2)
4) For any propostion q, if q is true, then q has a truthmaker. (premise)
5) 3 has a truthmaker. (by 3 and 4)
6) For any truthmaker t, if t is a truthmaker for a modally necessary proposition, then t is a modally necessary being. (premise)
Therefore,
7) The truthmaker for 3 is a modally necessary being. (by 3, 5, and 6)
So what are the implications of all this for theism?
Well, according to orthodox Christian theism, God is (among other things) 1) a necessarily existent being, 2) a necessarily omniscient being, and 3) is necessarily the creative cause of the physical (and otherwise contingent) order in this or any other possible world.
If the above argument is correct, then it shows that there exists at least one necessary being (i.e. a being that can't possibly not exist) that serves as the truthmaker for the proposition that possibly, there are no physical objects, and that this truthmaker must be non-physical (another characteristic I would say God necessarily has, in his essence at least). So item 1 is proven to exist.
Furthermore, as I briefly touched on earlier, it seems that this being (or perhaps beings [plural]) would need to have something very much like an abstract existence, since it seems that for an object to be concretely realized in physical substance, it must be coherently conceivable. It appears to be possible, for example, for a cube-shaped object to suddenly appear on my desk, but it does not appear to be possible for an object that is both cube-shaped and spherical at the same time to suddenly appear on my desk. I would say that this is largely (if not entirely) because such an object is not coherently conceivable. The close relationship there seems to be between pure possibilia and the abstractions we invoke in our alethic modal claims seems to suggest that these possibilia have something very much like a mental existence, themselves. Perhaps we might say that these are objects within the Divine Intellect, or perhaps they are just snapshots, as it were, of the Divine Intellect itself, as examined piecemeal by our own discursive, propositional, finite intellects. So while not proven in the strict sense, item 2 seems very plausible.
Item 3, however, is where things get a bit sticky. While it does seem that what we have here are either necessarily existent mental objects within the Divine Intellect or simply finite perspectives on the Divine Intellect itself, and while it is reasonably clear these objects are enfleshed, as it were, in physical substance, it is not quite so clear on the above argument that an act or acts of divine volition are what make up the difference. Still, I think a fairly strong analogy can be drawn from our own experience with volition. For example, it is actually the case that there is a book sitting on the floor to my right as I type this, and it is also true that, possibly, said book will be sitting on my desk at some time in the future by an act of my volition. Now, I know that in order for there to be an act of my own volition it is necessary for me to be able to understand, in abstracto, as possible the state of affairs I wish to accomplish and to understand that said state of affairs is actualizable in concreto. Now say that tomorrow it will happen that a huge mound of gold will suddenly pop into existence in my backyard, apparently ex nihilo. We already know that that mound of gold is possible, and now we know that tomorrow it will be actual. So far, the analogy holds. But in order for an act of my own volition to occur, another ingredient is required--the willful act itself, which is the (efficiently) causal principle of the book's finding its way onto my desk. And while I think it is quite plausible to believe (and in fact I do believe) that neither the mound of gold nor anything else can just pop into existence uncaused, further argumentation is required to show that this must be the case. So although I don't think that item 3 is quite as plausible as 2 (on the present argument, anyway), I still think it's pretty plausible, given the analogical argument. Still, however, I think the atheist might be within his rights to insist that stronger argumentation be given in support of it.
Thoughts?
Consider the following statement:
There is a mountain of gold in my backyard.
As I'm sure you already suppose, this statement is false. In actual fact, there is no mountain made of gold in my backyard. But still, the statement makes sense to you. It seems to be perfectly coherent. You can easily conceptualize things like backyards, mountains, and objects that are made out of gold. Moreover, there seems to be no conceptual difficulty combining these things so that it does indeed seem that there might actually be (or have been, or be at some time in the future) a mountain that is made out of gold in a backyard somewhere. Perhaps it might even be that everyone in the entire world will suddenly decide to give me all their gold and I will choose to have it made into a mountain in my backyard. Okay, so that's highly unlikely to ever happen, but technically it does have a non-zero probability. (Hey, a guy can dream, can't he?
Possibly, there is a mountain of gold in my backyard.
Now consider this statement:
There is a Bradford pear tree in my backyard.
Unlike the first statement about my fictitious mountain of gold, this statement is true. If you were to come over to my house and look into my backyard, you would see that therein does indeed grow a real, living Bradford pear tree. You would be able to reach out and touch its trunk and feel the roughness of its bark. Were you to come in early March, you would be able to see its lovely white blossoms and smell their rather noxious odor. It's actually there. But it doesn't have to be there. I could remove it, so that it would no longer be there. Instead of a Bradford pear tree, whoever planted it might have decided that a maple would be preferable, or a pecan, or no tree at all. In fact, it seems to make perfect sense that there might not ever have been any Bradford pear trees, or any trees, or even any plants at all. We can go even further and say that there seems to be no trouble conceiving that there might never have been any plots of land that might be called backyards, or any human persons who might call them such. Indeed, it seems perfectly coherent to say that there might not ever have been any physical objects at all! For it seems that for any physical object whatsoever (and for argument's sake we may treat humans, animals, and any ETs there might be as purely physical objects as well; whether or not they really are is immaterial for our purposes [pun intended
Possibly, no physical objects exist.
So now we have that, while it is not actually the case that there is a mountain of gold in my backyard, it is possibly the case that there may be. And while it is in fact actually the case that there's a Bradford pear in my backyard, there doesn't have to be; it is possibly the case that that it isn't really there. Not only is it possible that the Bradford pear isn't there, but, as we've seen, it also seems to be possible that there aren't any physical objects at all.
Now, when we make existential statements, whether positive or negative, the truth conditions of these statements seem to be dependent upon whether or not there actually exist grounds that make them true. What I mean is that, e.g., for the statement there is a Bradford pear tree in my backyard to be true, it seems there must actually exist some state of affairs that satisfies the content of my claim. And when I say that there is a mountain of gold in my backyard, it seems the falsehood of my claim must depend on there not actually existing any such satisfying conditions. Satisfying conditions such as these that serve as the grounds for true existential statements are called truthmakers. But what about other types of statements? More specifically, what about modal claims, such as that it is possible that [such and such] is the case? I would say that these too must have truthmakers if they are to be true, and indeed, I think that for there to be any true proposition at all, then there must needs be a truthmaker for it. But if it is true, as I said above, that it is possible that there are no physical objects at all, then what might there be left over that would make such a statement true? Well, as we saw with our fictitious golden mountain, we can conceptualize things like backyards, mountains, and items of gold. We understand that these things have certain properties, like spatial and temporal extension, quantifiable relations to units of measure, or chemical properties (in the case of gold, anyway), but what all of these properties--and all properties, characteristics, or other attributes whatsoever, I would say--have in common is their abstract nature.
Now, what we abstract from in forming our concepts are physical objects. And when we say that a certain physical object exists, the truthmaker for our claim is just that physical object. But I would say that when we turn to alethic modal claims (i.e. that possibly or necessarily something or other is the case) regarding physical objects, we cease to talk about the physical objects by themselves (i.e. as concrete states of affairs) and begin to talk in abstraction about immaterial natures or essences that might or might not be concretely realized in actual, corporeal physical substance. So when we say that, possibly, it is the case that no physical objects exist, the truthmaker for our true claim would seemingly have to be an object that is not of a physical nature, but that is more closely related to our abstract conceptualizations.
But what of the modal status of this object? As I've tried to show, physical objects are modally contingent beings, meaning that it is possibly the case that they exist, but it is not necessarily the case that they exist (whether or not they actually exist is beside the point). But what of the modality of our truthmaker(s) for such modal claims? Might it (they) possibly not exist, just as physical objects might not exist? I think not. For by modal axiom 5 we can say that:
For any proposition p, if it is possibly the case that p, then it is necessarily possibly the case that p.
Assuming S5 modality, which allows mutual accessibility among all possible worlds, and applying this to our alethic modal claims regarding physical objects, we can see that in order for it to be true that it is possibly the case that no physical objects exist, it would have to be necessarily true (i.e. true in every possible world) that it is possibly the case that no physical objects exist. But if the latter statement is true, and if it is the case that this truth needs a truthmaker, then its truthmaker would seem to have to be a necessary being. For if it weren't a necessary being, then it could not serve as the truthmaker for this necessary truth in worlds where it does not exist, and it doesn't seem very plausible that non-indexical propositions can shift truthmakers.
To put this in syllogistic form, then:
1) Possibly, there are no physical objects. (premise)
2) For any proposition p, if it is possibly the case that p, then it is necessarily possibly the case that p. (premise, modal axiom 5)
3) It is necessarily possibly the case that there are no physical objects (by 1 and 2)
4) For any propostion q, if q is true, then q has a truthmaker. (premise)
5) 3 has a truthmaker. (by 3 and 4)
6) For any truthmaker t, if t is a truthmaker for a modally necessary proposition, then t is a modally necessary being. (premise)
Therefore,
7) The truthmaker for 3 is a modally necessary being. (by 3, 5, and 6)
So what are the implications of all this for theism?
Well, according to orthodox Christian theism, God is (among other things) 1) a necessarily existent being, 2) a necessarily omniscient being, and 3) is necessarily the creative cause of the physical (and otherwise contingent) order in this or any other possible world.
If the above argument is correct, then it shows that there exists at least one necessary being (i.e. a being that can't possibly not exist) that serves as the truthmaker for the proposition that possibly, there are no physical objects, and that this truthmaker must be non-physical (another characteristic I would say God necessarily has, in his essence at least). So item 1 is proven to exist.
Furthermore, as I briefly touched on earlier, it seems that this being (or perhaps beings [plural]) would need to have something very much like an abstract existence, since it seems that for an object to be concretely realized in physical substance, it must be coherently conceivable. It appears to be possible, for example, for a cube-shaped object to suddenly appear on my desk, but it does not appear to be possible for an object that is both cube-shaped and spherical at the same time to suddenly appear on my desk. I would say that this is largely (if not entirely) because such an object is not coherently conceivable. The close relationship there seems to be between pure possibilia and the abstractions we invoke in our alethic modal claims seems to suggest that these possibilia have something very much like a mental existence, themselves. Perhaps we might say that these are objects within the Divine Intellect, or perhaps they are just snapshots, as it were, of the Divine Intellect itself, as examined piecemeal by our own discursive, propositional, finite intellects. So while not proven in the strict sense, item 2 seems very plausible.
Item 3, however, is where things get a bit sticky. While it does seem that what we have here are either necessarily existent mental objects within the Divine Intellect or simply finite perspectives on the Divine Intellect itself, and while it is reasonably clear these objects are enfleshed, as it were, in physical substance, it is not quite so clear on the above argument that an act or acts of divine volition are what make up the difference. Still, I think a fairly strong analogy can be drawn from our own experience with volition. For example, it is actually the case that there is a book sitting on the floor to my right as I type this, and it is also true that, possibly, said book will be sitting on my desk at some time in the future by an act of my volition. Now, I know that in order for there to be an act of my own volition it is necessary for me to be able to understand, in abstracto, as possible the state of affairs I wish to accomplish and to understand that said state of affairs is actualizable in concreto. Now say that tomorrow it will happen that a huge mound of gold will suddenly pop into existence in my backyard, apparently ex nihilo. We already know that that mound of gold is possible, and now we know that tomorrow it will be actual. So far, the analogy holds. But in order for an act of my own volition to occur, another ingredient is required--the willful act itself, which is the (efficiently) causal principle of the book's finding its way onto my desk. And while I think it is quite plausible to believe (and in fact I do believe) that neither the mound of gold nor anything else can just pop into existence uncaused, further argumentation is required to show that this must be the case. So although I don't think that item 3 is quite as plausible as 2 (on the present argument, anyway), I still think it's pretty plausible, given the analogical argument. Still, however, I think the atheist might be within his rights to insist that stronger argumentation be given in support of it.
Thoughts?