Note; This was originally a reddit post from nearly a year ago. I've made some edits to it and added some stuff.
Introduction
This is the second in a collection of posts I plan to make in arguing against orthodox theism. The first post was a defense of a logical problem of evil, originally conceived by Richard R. La Croix. In this post, I will be presenting and defending a set of arguments for the incoherence of orthodoxly conceived theism, known as incompatible properties arguments. What the heck is an incompatible properties argument, you ask? An incompatible properties argument is an argument that seeks to demonstrate the falsity of orthodox theism via proof by contradiction in how God is conceived. An argument of this sort will take a form which looks something like this;
1. If God exists then He exemplifies properties X and Y
2. It's not possible to jointly exemplify properties X and Y
3. Therefore God does not exist
It's important to point out here that not all theists will have the same commitments. As such, a real limitation of incompatible properties arguments is that they will target only certain conceptions of God. A theist might well avoid these kinds of arguments by affirming that God does not possess one or both of the properties in question. This would involve a denial of what would be premise 1. However, the theist must tread carefully here. For they may only be able to deny that God has a certain property on pain of giving up certain widely held religious beliefs about God, as well as a motivated conception of God. I take it that only God as conceived by classical or neo-classical theisms have philosophical justifications. Additionally, if the theist goes too far in jettisoning God's attributes, then God may no longer be a being that is apt to be worthy of worship. In that case, it's not clear that such a being would count as God at all.
However, most responses to incompatible properties arguments will involve a denial of what would be premise 2. It is objections of this kind that I will address in my presentation of the following arguments.
To close the introduction off, I will first note that the idea of this post is inspired by Theodore Drange's 1998 article[1]. I will not be including most of the arguments Drange presents in this discussion, and will include some not mentioned by Drange. Secondly, I will not be defending single attribute arguments against theism, such as the stone paradox and Patrick Grim's proofs for the incoherence of omniscience. I will only focus on arguments that purport to show that 2 or more of God's attributes are incompatible.
Argument 1 - Timelessness and Personhood
The God of classical theism is taken to be a timeless person, and indeed most religious conceptions see God as a timeless person. The following is an incompatible properties argument for the incoherence of a timeless person;
1. If God exists, then there is a timeless person
2. All persons have a succession of mental states in time
3. A timeless being cannot have a succession of mental states in time
4. Thus a timeless person does not exist (2, 3)
5. Thus God does not exist (1, 4)
As mentioned, premise 1 is analytically entailed given the classical theist conception of God. Importantly, some non-classical theists will not accept 1, in which case this argument will be ineffective for them. Premise 3 is just an analytical entailment from what it is to be timeless. So, premise 2 is the only premise that is up for dispute. But there is a case to be made that it seems overwhelmingly plausible. Upon reflecting on what it is to be like a person, it seems that it presupposes temporality, it is to have a sequence of phenomenological experiences.
For instance; at one moment, I am typing this paragraph and having that experience, and at another moment I am not and that experience becomes a memory. When I have thoughts, at a prior moment I think about some proposition or state of affairs, such as what I'll be eating tonight, and then at a later moment I think about some other proposition or state of affairs such as what my favorite video game is. Thinking inferentially, such as forming the line of inference "if P then Q, P therefore Q" seems to be a temporal sequence of mental events, we have the prior mental event of my thinking about the premises, and then we have a later mental event, where I derive the conclusion. I might change my beliefs as a result of inference-making, in which case there was a moment where I fail to believe P and a later moment where I believe P (P being a generic stand-in for some proposition or other). When I actualize my desires, that seems to be a temporal process, there is a moment when my desire is not realized, and then a later moment when I take some action to make it the case that my desire is realized. These are all features of my personhood which I take it are inextricably linked to temporality. While this may not be particularly convincing to theists, and while it might be argued that the premise may not be a necessary truth - I think my confidence in it is quite strong, as my understanding here stems from an introspection of my own internal phenomenology, and there isn't much I can be more sure of then that! Given how I understand my phenomenology on a very fundamental level, I literally cannot conceive of what it would be like to be a person with no sequence of phenomenal states in time. It is constitutive of my very understanding, and experiential knowledge of what it is, and what it's like to be a person. But perhaps I'm just being incredulous, perhaps you can conceive it, perhaps you have a very different internal phenomenology than I do. If so, please do let me know in the comments!
The common objection from the classical theist here will be to point out that God's being a person is merely an analogical predicate. That is, God is not a person in the same way we are persons He does not have a succession of mental states. When we refer to God as a person we are referring to him by the doctrine of analogy. The issue is that for something to be an analogy, there has to be common features. If I tell you that last night I had a burger, but then I tell you that it's not a burger in any sense you understand the term, but it was still a burger in an analogical sense. I have a feeling you would give me an odd look and rightly believe I was speaking gobbledygook. This is because for something to be analogical to a burger, while there may be some sense in which it is unlike a burger, there is also some sense in which it is like a burger. So, in the same way, in order for God's personhood to be an intelligible attribution, there has to be some feature it has in common with our human understanding of personhood. Yet, as mentioned, it seems that, constitutive of our human understanding of personhood, is a notion of temporal order and continuance of mental states through time, so it's not clear what that would be. If the theist wants to say that God is analogically a person, it's on them to intelligibly explain what common features it shares with the personhood humans possess, otherwise, they aren't really doing an analogy at all are they?
Argument 2 - Omnipresence and Personhood
Another incompatible properties argument that utilizes God's attribute of personhood, is one that pits it against God's attribute of omnipresence[2]. It can be formulated in the following way;
1. If God exists, then an omnipresent person exists
2. Necessarily, persons have intentionality
3. To have intentionality, is to be able to perceive external objects independent of the self
4. An omnipresent being, cannot perceive external objects independent of the self
5. Thus an omnipresent person does not exist (2, 3, 4)
6. Thus God does not exist (1, 5)
Premise 1 is an analytical entailment, 2 is also an analytic truth. So, what needs to be discussed is 3 and 4. The basic idea here is an appeal to content externalism, or related views. A feature of intentional states is that they are content-full mental states, they are representational, they are about things. We don't merely desire, we desire something, we don't merely have beliefs, we believe propositions. So there must be something external to our consciousness which furnishes mental content, but for an omnipresent being there is no external content. The theist may deny externalism and affirm that God's mental states can just be about other mental states in God's mind, but I think this seems insufficient for intentionality.
To see why, let's lay some groundwork by considering Kant's famous refutation of material idealism. Kant argues that we cannot doubt the external world without doubting the consciousness of our own existence in inner sense. The outer sense is how we represent things (e.g. empirical objects) as distinct from us in space, and the inner sense is where our mental states and representations reside such as thoughts and sensations. The idea here is that the way we distinguish ourselves from other objects is by comparing our experience to external objects outside of our consciousness. If there is no external content, then we could not in principle grasp that mental states are representations of something different from itself. So we must be able to make a conceptual distinction between the self and external objects or else we cannot form judgements about objects.
To put it another way, the thought is, higher order consciousness and intentionality includes the ability to form judgements about objects, and the ability to discern the difference between an object and our representation of it. For example I must recognize the difference between my mental representation of my keyboard, how I perceive it, and the keyboard itself, the properties it has etc. But this presupposes the ability to grasp a conceptual distinction between the self and the non-self, I could not judge the keyboard as an object with certain properties if I do not have an understanding of the keyboard independent of my mental representation of it. The issue being, an omnipresent being cannot make such a conceptual distinction, because for an omnipresent being there is no non-self. Now, it has been criticized that Kant's Transcendental argument goes too far here, and that all Kant establishes is that we must be able to conceive of our experiences as being related to external objects and events, not that they actually are. However, this more modest conclusion still threatens theism. God can not think of objects as external from Himself if they are not, as that would involve a false belief and God by definition cannot have false beliefs.
Once again the theist might object that God's having intentionality is merely analogical, but this runs into the same issue discussed in the previous section. If a being cannot form judgements about objects, it's very unclear that it would be right to say such a being is an intentional one at all. That's just how I understand intentionality. I leave it to the theist to give an intelligible account of God's supposed analogical intentionality.
The theist may object that even if God is everywhere He can still distinguish between parts of Himself, after-all, surely I can distinguish between my hands as parts of myself and recognize the distinction between my mental representation of my hands and my hands themselves. Firstly, it's unclear that God can be composed of parts, the traditional view is that God is purely simple. But more to the point, it seems that in order to make judgements about my hands, indeed in order to judge them as *my* hands, and not someone else's hands, I must be able to distinguish between them and other objects in the world which are not me. Further, I must be able to judge my hands as objects with properties, which are external to my consciousness, thus there is still an object-self distinction involved.
One last objection I will consider is that the theist could give a modified version of omnipresence, God is omnipresent not in virtue of being located everywhere and the whole of reality being in Him or part of Him, but perhaps He is co-present with everything in reality. Or perhaps He is omnipresent insofar as He can be anywhere at once. We are still able to run a similar argument without using omnipresence. For, another essential property of God is that He is the ex nihilo creator of the world, thus He existed prior to creation with no external world to constrain His mental contents, or for His thoughts to be directed at. We can formulate the argument like so;
1. If God exists, then there was a person prior to the creation of an external world.
2. Necessarily, persons have intentionality.
3. To have intentionality, is to be able to perceive external objects independent of the self.
4. Prior to the creation of the external world, it is not possible to perceive external objects independent of the self.
5. Thus there cannot be a person prior to the creation of an external world (2, 3, 4)
6. Thus God does not exist. (1, 5)
Argument 3 - Omniscience, Omnipotence and Personhood
One more incompatible properties argument that focus's on God's personhood is one that uses two of God's "omni" attributes, His omnipotence, and omniscience. It can be formalized as follows;
1. If God exists, then an omnipotent, omniscient person exists
2. Necessarily, persons are intentional agents
3. Intentional agency entails uncertainty and/or the possibility of failure
4. An omnipotent, omniscient being cannot be uncertain and/or fail
5. Thus an omnipotent, omniscient being cannot be an intentional agent (2, 3, 4)
6. Thus God does not exist (1, 5)
1, 2 and 4 are true by definition. 3 is the only controversial premise. There are a couple reasons to accept 3. One reason is, it seems intentional states are things one can be in or out of accord with (where out of accord with is what is meant by "failure"). This seems especially true in the case of desires, if there is a blizzard and I desire to not be cold, then I acknowledge that there is the possibility that I can be out of accord with this desire by experiencing cold sensations. We can say that if I go outside without the proper winter attire then I am failing to live up to my commitment as a rational agent. Indeed plausibly part of how we understand the concept of desires, is that they have possible conditions of satisfaction and dissatisfaction. If there is no possibility of being out of accord with one's desires, that is if some behavior is strictly governed by the fact that it could not have been out of accord with it's nature or something such like, then it seems to reduce to a mere causal tendency, such as a calculator following inputs, or a rock falling down a hill. At the very least, it's not without some plausibility that, part of what distinguishes intentional acts from mechanical events is that intentional acts involve responsiveness to normative reasons that one can be in or out of accord with. That is to say, intentional states are unlike dispositional states in that intentional states have a normative, or more precisely, rule-following component built in. (I also suspect that many if not most theists especially will be uncomfortable with reducing intentionality to mere causal tendencies, since theists tend to like libertarian free will). However, in the case of God, it doesn't make sense to speak of conditions of satisfaction, there is no possibility of being out of accord with His desires. In virtue of God's omnipotence His will is unfailingly efficacious, so God "desires" X, logically entails that X obtains or is the case. The theist can conceivably bite that bullet however, and accept that intentional states can reduce to mere causal tendencies or entailment relations, as bizarre as that initially seems. Perhaps more convincingly, then is it seems that in order to actualize our desires, we must pick out a state of affairs that is not currently in accord with our desires, and then take some action to make it the case that the state of affairs accords with our desire. For example, suppose I desire to lose weight, what that means is that I recognize that the current state of affairs is that I am more overweight then what I want to be, and so I must take some action, say exercise and diet, in order for the state of affairs to satisfy or to be in accord with my desire to weigh less. At the very least, I must be able to perceive that the state of affairs diverges from my goal/desire.
But God is omnipotent, so the only constraint on His power is logical possibility. God is omniscient, so I take it this means that God knows what He can achieve, and He cannot have non-rational desires, such as the desire to actualize logical impossibilities. Additionally, if God's desires are not in sync with what He can do, and if He can have conflicting desires, then it seems He has a less than perfect will which is surely not how God is conceived. Thus it seems, for any time t, and any possible state of affairs which is the object of God's desire S, God is omnipotent omniscient and desires S at t. So all the necessary and sufficient conditions for S's obtaining are met at t since God desires S, and God necessarily succeeds in actualizing His desires. But for any time when the necessary and sufficient conditions for S obtains, then S necessarily obtains, thus S necessarily obtains at t. So it seems there can be no state of affairs that fails to be in accord with God's desires, and in virtue of God's omniscience/infallibility He cannot falsely perceive states of affairs as out of accord with His desires. Thus it seems like, since there is no possibility of God being out of accord with His desires, God cannot act on His desires, since any object of desire He would have, necessarily, could not be unactualized at any point in which He has the desire and He cannot wrongly perceive states of affairs as being out of accord with His desires in virtue of His infallibility. If we take it, as is plausible, that acting towards ones desires is a necessary constitutive feature of agency, then this is a problem.
We can also argue for 3 on the grounds that intending requires that one is uncertain about the future[3]. Intending involves a process of deliberation, weighing normative reasons, reflecting on which of ones desires is a good reason to act. However, when one is deliberating their mind is not yet made up, they are in a state of uncertainty about what they are going to do, otherwise there would be no point in deliberating. But an omniscient being cannot be uncertain. Further, deliberating between options seems to entail at-least having a belief that both options remain open to you. In other words, we view the state-of-affairs of our Φ-ing or not Φ-ing at t as epistemically contingent. However, if an omniscient being knows that she will Φ at t, then she infallibly knows that not Φ-ing at t is not an open option for her. The theist might object by positing open theism and suggest that there is no truth value for future contingents, however there is a worry that open theism is incompatible with anselmian conceptions of God and undermines widely held views about God's absolute sovereignty, and, it by my lights seems obvious that propositions about future contingents are true or false (Although that's a whole other topic which we can put aside). The theist might object that God is timeless so God cannot believe that He Φ's at t. But this does not diffuse the argument, if 'God Φ's' is true, then it is true now that God Φ's. But if it is true that God Φ's now then it could be true that God Φ's at t. (These are all compatible with His being timeless).
Argument 4 - Omniscience and Timelessness
Next we have an incompatible properties argument which utilizes the divine attributes of omniscience and timelessness[5]. Here is the formulation;
1. If God exists, then an omniscient and timeless being exists
2. A being that is omniscient knows what time it is at present
3. A being that always knows what time it is at present cannot be timeless
4. Thus a timeless, omniscient being does not exist (2, 3)
5. Thus God does not exist (1, 4)
I think this is one of the weaker arguments, and in fact I think the argument can be safely diffused by rejecting presentism about time, as there would be no "what time it is at present". But for the theist committed to presentism, it seems both 1 and 2 are true. The thought behind 3 is, in order to know what time it is, or to know all time-indexed propositions, one must be situated in time, and must know different things at different times. But a timeless being, by definition, cannot be situated in time. Let's consider some objections the presentist theist might levy.
The theist might try to object that, God always knows what time it is, but there is only a changing succession of time in God's object of knowledge not God Himself. This is a mistake though, if God knows that it is such and such time, and the state of the universe changes such that it is no longer such and such time, then God must change His belief to be in accord with what the time is otherwise He will have a false belief.
The theist might object that God can have knowledge of all temporal states of the universe at once and not successively. However, given presentism, it seems that having knowledge of all temporal states is not sufficient for omniscience. God may know the time of the heat-death of the universe, when I will die, what I will do tomorrow, what you will do tomorrow, but on this view God cannot know what it is I or you are doing presently, because what I or you are doing presently constantly changes. That is, He cannot know, as I do, that in the present I am typing this paragraph, or as you know, that you are reading it now, for all He knows the present is thousands of years in the future far past both our deaths. Thus it seems an omniscient being cannot merely know the entirety of the universes temporal states, He must also know what time it is presently, otherwise we would be admitting that I, a non-omniscient knower, can know something an omniscient being cannot, but this seems absurd.
The theist might take omniscience to be knowing everything that is logically possible for God to know, and since it is logically impossible for God to know what time it is in virtue of His timelessness, God cannot know what time it is and still be omniscient. The problem is this runs into reductios such as Michael Martin's McNose objection[4], suppose I define a McNose as a being that logically necessarily can only know how to scratch it's nose, and I further stipulate that the McNose has perfect knowledge of how to scratch it's nose. Since a McNose knows everything that is logically possible for it to know, it follows that the McNose is omniscient despite only knowing how to scratch it's nose, but surely that is absurd. The theist might then modify there conception of God's omniscience to knowing everything which does not otherwise decrease God's perfection. Since timelessness is a perfection, God cannot know what time it is. However, this seems like an ad hoc move designed to avoid the objection, there doesn't seem to be any independent motivation for such a conception of omniscience. Further, the condition "which does not otherwise decrease God's perfection" is not one that is necessary for maintaining the coherence of omniscience. Thus, absurdly, it seems this entails that we can conceive of a more knowledgeable being, than an omniscient being.
Argument 5 - Omnipotence and Essential Moral Perfection
The final incompatible properties argument that I will present will be one that argues for the incompatibility of omnipotence and moral perfection. Specifically, necessary moral perfection, which is the attribute of being morally perfect in all possible worlds. This attribute is essential to the MGB (Maximally Great Being) conception of God which entails God's having maximal excellence (which includes moral perfection) in every possible world. Following Wes Morriston[6] the argument can be formulated in the following way, let E be some all-things-considered evil state of affairs such that a morally perfect being would not actualize it;
1. If God exists then God is necessarily morally perfect and omnipotent.
2. If God is necessarily morally perfect, then there is no possible world in which He actualizes E.
3. If God is omnipotent, He has the power to actualize E.
4. If God has the power to actualize E, then there is a possible world in which God actualizes E.
5. Therefore God cannot be necessarily morally perfect and omnipotent. (2, 3, 4)
6. Therefore God does not exist. (1, 5)
The theist may object to 2 on the grounds that while God may not be able to strongly actualize E, He can still weakly actualize E. Strong actualization means God directly causes some state of affairs to obtain with His actions. Weak actualization is a bit more complicated if you are not familiar with Plantinga, but the basic idea is that God indirectly causes some state of affairs to obtain by actualizing a state of affairs where a contracausally free creature is in a situation where she freely chooses to cause some other event. In any case, as Morriston points out, we can revise the premise to "If God is necessarily morally perfect, then there is no possible world in which He strongly actualizes E." and the worry remains. If I tell you to lift a box for me because I am not strong enough to lift the box, and this causes you to lift the box, I weakly actualize the state of affairs of you lifting the box, but it's still the case that you have superior box-lifting power than me. So it's clear weak actualization in this case, is not sufficient for omnipotence.
A theist might deny 3 and construct a conception of omnipotence that is such that a being is omnipotent if they are able to actualize any logically possible state of affairs that is consistent with it's nature. The problem is that this runs afoul of the famous McEar objection (Similar to the McNose objection above), suppose we have a being that is so defined such that it's nature is that it can only scratch it's ear, it cannot tie it's shoes, it cannot lift a feather, it can do only one thing namely scratch it's ear. Yet it can do anything that is logically compatible with it's nature, thus it follows, absurdly, that the McEar is omnipotent. There have been replies to the McEar objection most notably, "But it might be replied that an agent such as McEar is impossible. It can be cogently argued that, necessarily, if McEar has the power to scratch his ear, then he also has the power to move a part of his body to scratch his ear, for instance, his arm (Wierenga 1989, pp. 28–29)". But this doesn't seem particularly convincing, one can reconstruct the problem by adding that the McEar can necessarily only scratch it's ear and whatever necessary and sufficient conditions must obtain for scratching it's ear. Further it doesn't seem to engage with the heart of the issue. The problem that the McEar objection underlies is that just because something is impossible for you, doesn't mean that it is impossible tout court. It seems like an omnipotent being must be able to do anything that is logically possible for someone or other to do. A case can be made that omnipotence at time t requires being able to actualize any logically actualizable state of affairs at t.
Finally, the theist can dispute 4 on the basis that, God cannot actualize E but not by any lack of power on His part. If He (per impossible) wanted to actualize E He would succeed. But in virtue of Him being morally perfect across all possible worlds, there is no possible world where He would ever bring Himself to actualize E. This view still lends itself to reductio's. Suppose we imagine a being, let's call it a McCheese, a McCheese is extraordinarily powerful, so powerful such that if it decided to actualize some state of affairs, it will always succeed (Morriston calls this conditional power). However, the McCheese is in a state of mental paralysis, such that it can only choose one thing, to eat cheese. It seems clearly that the McCheese is not omnipotent, yet absurdly, since it has maximal conditional power, there is nothing to suggest it is not on this analysis. Thus it seems, the theists objections all seem to make us view beings as omnipotent that we wouldn't otherwise take to be omnipotent.
Conclusion
These are 5 of among, I think, the strongest incompatible properties arguments against orthodox theism. There are many other incompatible properties arguments that I did not cover here, for instance there are worries of omniscience being incompatible with moral perfection, after-all it seems an omniscient being would know what it's like to sin, or to have perverted thoughts, or to be envious. There are worries that God cannot be timeless and the efficient cause of the universe, since it seems causation is a temporal notion. These too, are concerns I have some sympathies with. Overall, I think a priori deductive arguments such as these aren't going to tend to be the most convincing for theists, however, they succeed at least in raising my credence in atheism. They may serve as a symmetry breaker for the possibility premise in modal ontological arguments, since if we have a reason to think God's attributes are contradictory then we have a reason to think the possibility premise is false. They also might be effective in terms of blocking stage 2 cosmological argument inferences, as we'd always have a strong a priori reason to favor a necessary being that isn't incoherent, or against Bayesian fine-tuning arguments, since if one's prior probability for theism is 0 then Bayesian fine-tuning arguments are dead on arrival.I
Inspirations & Further Reading
[1] Theodore Drange - Incompatible-Properties Arguments: A Survey
[2] Matthew Mccormick - Why God Cannot Think: Kant, Omnipresence, & Consciousness
[3] Tomis Kapitan - Agency and Omniscience
[4] Michael Martin - Atheism: A Philosophical Justification
[5] Norman Kretzmann - Omniscience and Immutability
[6] Wes Morriston - Omnipotence and necessary moral perfection: are they compatible?
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