Richard Carrier's Argument from Specified Complexity

Noted pseudo-philosopher Richard Carrier has an argument which, he thinks, demonstrates that "we should think the supernatural is impossible." Specifically, he wants to claim that "God's mind appears to be logically impossible." His line of reasoning goes (more-or-less) as follows:

1. (Assume for contradiction) God's mind is simple and immaterial.
2. God's mind must be able to store and process information.
3. Information storage and processing require specified complexity.
4. Such complexity requires some material on which information can be stored and circuitry stamped.
5. God's mind is complex and material (from 2-4).
6. Contradiction (from 1 and 5). 

Unfortunately, Carrier seems to have gotten himself tripped up on the nature of God's knowledge. For he writes:

A god has to know things (store information), and think things (process information). But there is a difference between correct and incorrect information, present and absent information; between conflation and distinction. A god has to be able to distinguish one person’s face, from another; and correctly connect each face, with other information about the corresponding person, like that Joe’s face goes with Joe’s job in sales and wife of eleven years, and Mark’s face goes with Mark’s service in the military and husband of eleven years. That information could be connected up differently—wires crossed, and Joe’s face gets incorrectly linked to Mark’s husband, producing the false information that Joe has a husband, and so on. And notice how many different ways connections can be crossed up: the more information, the more different connections are possible. And most of them (in fact, all but one of them; out of effectively infinitely many) will be false.

However, as the physicist Aron Wall pointed out in response to a near-identical objection (ironically put forward by a couple of conservative Mormons), "This is only an issue if you assume that God's knowledge is, like ours, representational, that is, that it proceeds by means of making something like an image or duplicate of the object known, in some other physical system (in our case, the brain)." But of course, classical theism does not make such an assumption; rather, it has always held that God knows all things via direct awareness, simply by knowing Himself as creator and sustainer of all things (hint: this is part of what CTs mean when we say that God's knowledge, creative act, etc. are really all one thing). Thomas Aquinas provides a useful summary of this concept, when he writes:

Now, it is not repugnant to the simplicity of the divine mind that it understand many things; though it would be repugnant to its simplicity were His understanding to be formed by a plurality of images. [...] Inasmuch as He knows His own essence perfectly, He knows it according to every mode in which it can be known. Now it can be known not only as it is in itself, but as it can be participated in by creatures according to some degree of likeness.  But every creature has its own proper species, according to which it participates in some degree in likeness to the divine essence. So far, therefore, as God knows His essence as capable of such imitation by any creature, He knows it as the particular type and idea of that creature; and in like manner as regards other creatures. So it is clear that God understands many particular types of things and these are many ideas. (ST I.15.2)

The idea that God's knowledge does not consist in stored-up beliefs or mental images may also be found outside of the Thomistic tradition. For example, William Alston (1986), a critic of divine simplicity, was nevertheless a major proponent of the idea that God has no beliefs whatsoever, but rather knows all things via direct awareness. To quote:

A creature in our condition needs inner representations in order to be able to think about absent states of affairs, since the facts are rarely if ever directly present to our consciousness. But since God enjoys the highest form of knowledge He is never in that position, and so He has no need for inner representations that He can ‘carry around with him’ for use when the facts are absent. The facts are never absent from His awareness; thus it would be fatuous to attribute to Him any such mental map. When we have arrived at our destination we can fold the map away.

In a recent paper defending Alston's view, Saeedimehr (2021) discusses two non-propositional accounts of God's knowledge, each of which would seemingly allow us to avoid Carrier's argument. To quote:

Since God is absolutely simple, He (His essence) is identical with his knowledge. Therefore, God’s knowledge is totally simple and hence it is beyond any kind of complexity, including the complexity due to having a propositional structure.

Since Alston finds the principle of Divine simplicity quite problematic, he seeks another basis for the non-propositional position. He argues that as human beings, our propositional knowledge stems from two of our limitations: first we ‘cannot grasp any concrete whole in its full concreteness’, and second ‘we need to isolate separate propositions in order to relate them logically’ and then ‘extend our knowledge inferentially’. But since God is obviously beyond these limitations, His knowledge is not required to be propositional.

It would seem, then, that a non-propositional account of God's knowledge allows us to reject premise (2) of Carrier's argument; namely, that God's mind stores and processes information. God does not store information at all (or to quote Alston, "carry [it] around with Him"); rather, at any one moment He has an infallible intuitive grasp of all facts. Similarly, God does not need to "process information" (or to quote Alston, "isolate separate propositions in order to relate them logically"). We need to do that, because our cognition is fallible and limited; God, on the other hand, is far beyond such things.

One hopes that Carrier himself never gets wind of this post, lest I be subjected to his, uh... scholarly rigor.

Do Theistic Arguments Support the Simulation Hypothesis?

Richard Brown believes that "the traditional arguments for God’s existence provide better support for the simulation hypothesis than they do for the traditional God of Theism." He basis this view on the following argument:

1. The traditional a posteriori arguments (cosmological, teleological, etc.) point, if one accepts their conclusions, to a creator, but not to what kind of creator.
2. The traditional theistic God (all-powerful, all-knowing, and morally perfect) is one candidate for being the Creator.
3. The Simulators are another candidate.
4. The traditional arguments do not distinguish between (2) and (3).
5. The problem of evil (evidential) suggests that (2) is not the creator.
6. Therefore, the traditional arguments for God’s existence provide better support for the simulation hypothesis than they do for the traditional God of Theism.

I think the theist can challenge almost every premise here. Let's go through them in order

While premise (1) might apply to some arguments for God's existence (such as the fine-tuning argument), it seems obvious that it does not apply to many others, including some of the most popular in the current literature. For example, Rasmussen's contingency argument tells us that the creator must be a metaphysically necessary being, while his various stage-two arguments (if they succeed) tell us that it must be eternal, unlimited, unsurpassably powerful, and possessing a supreme nature. Similarly, the Pruss-Koons argument from basic natural facts seeks to establish the existence of a "supernatural being," that is to say, "a simple being that is unbounded and wholly infinite in intrinsic measure."

Premise (2) is uncontroversial (especially amongst theists), and so it seems like we can skip over that one.

Premise (3) seems to fail for the same reasons as premise (1); namely, the most popular theistic arguments today (such as the contingency argument) would seem to rule out a simulator. After all, a simulator would presumably be a natural being, rather than a supernatural one. We also have no reason to assume that they would be necessary, rather than contingent. In addition, stage-two contingency arguments (such as those made by Rasmussen) are specifically designed to solve the so-called "gap problem," by showing that the necessary being in question must have some or all of the traditional divine attributes.

Premise (4) fails for the same reasons as premises (1) and (3).

Premise (5) only works if one agrees that the problem of evil really does provide evidence against theism. However, even if one does agree with this, it seems like this premise still fails to support the simulation hypothesis. This is because, if my criticisms of premises (1) and (3) succeed, the traditional theistic arguments rule out the idea of a natural contingent being as the cause of our universe. 

The conclusion (6) stands and falls with the rest of the argument, so if (as I've argued) the rest of the argument fails, then so does (6).

I think Brown has also neglected an important point, namely that theistic arguments must be approached in tandem, rather than one-by-one. For example, assume that the argument from contingency is correct, and the existence of a necessary being has been established. Then when we consider the fine-tuning argument, we must take into account the fact that a necessary being exists. It would be deeply strange for there to be a necessary being which explains contingent reality, and also a fine-tuner who fixed the laws of nature. Therefore, any evidence that we have for design should be interpreted as evidence for design by the necessary being. But surely the traditional simulation hypothesis does not regard the simulating beings (whoever or whatever they are) as necessary. So Brown's argument would seem to fall flat yet again.

There is a potential way that one could escape this last argument: namely, one could hold that our world really is a simulation, but that reality as a whole was created by God. This view is not unheard of in the literature; David Kyle Johnson (2012) has argued that some theists might be committed to this view, while theists Barry Dainton (2020) and Dustin Crummett (2021) have both approached it as a potential theodicy. That being said, I don't personally endorse this view (nor am I one of those whom Johnson argues are committed to it), and I'm not sure how important it is for my above argument (since it is ultimately still a theistic view).

Privation and Divine Hiddenness

J.L. Schellenberg insists that the problem of divine hiddenness should be viewed, not as a subspecies of the problem of evil, but as a unique problem in its own right. He supports this view by saying that the hiddenness argument is discussing something which only theists would view as "evil," whereas atheists would not. To quote:

Although a theist may indeed keenly feel the value of (what she takes to be) an existing relationship with God and may be inclined to view anything contributing to its absence, even for a time, as a bad thing, and although in debate an atheist may be tempted to take advantage of this, such moves only mislead in the present context. The atheist would properly be quite content were we all to recognize simply that, given certain definitional facts about ‘love’, the situation of hiddenness is in conflict with the idea that a God of fullest love exists, as opposed to feeling that hiddenness represents something bad that a benevolent or morally perfect God would resist.

However, it seems that once we adopt a privation account of evil (or something similar, such as Pruss' misalignment view), this argument simply collapses. After all, it seems to be a key premise of the hiddenness argument that, if God exists, then a relationship with Him would be a good thing (otherwise the lack of it could not impugn His perfect goodness). But then, hiddenness is simply the lack of a good thing (i.e. a privation), which, by our definition, would make it an evil. Therefore, the problem of divine hiddenness simply is a form of the problem of evil.

One might try and counter this by saying that an atheist doesn't regard their lack of relationship with God as an evil; they don't believe that God exists, and as such, a relationship with Him cannot be a due good that they are lacking. However, the hiddenness argument seems to be saying that if God exists, then a relationship with Him would be a due good, which some people are nonresistantly lacking. It seems, then, that we may regard it as an attempted reductio of theism, which tries to show that there is a specific gratuitous evil which would have to obtain if God exists, yet which would also (allegedly) render God impossible.

TL;DR: On a privation view of evil, divine hiddenness may be regarded as a specific form of the problem of evil. What makes it unique is the fact that the evil it posits (i.e. the lack of a due relationship with God) is one which can only obtain if theism is true, since if God does not exist, one cannot be said to lack a due relationship with Him. The problem of divine hiddenness therefore provides an interesting twist on the POE. It also seems that a solution to the POE more generally would also serve to solve the problem of divine hiddenness.

A New Paper on Physical Necessity

Alexander Roberts has published an interesting new paper in Mind, which argues for the claim that "those who believe in physical necessity should not harbour any scepticism towards merely metaphysical possibilities." How he reaches this result is quite complex, and I'll leave it to the full paper to provide an explanation; however, "the result requires those who believe in physical necessity to recognize merely metaphysical possibilities which are forbidden by our physical laws." The key line of argument in the paper revolves around the notion of lawless worlds (i.e. worlds in which no laws of nature, whether ours or any others, obtain). Roberts argues that such worlds are accessible from all other possible worlds by a finite chain of physical possibility.

The Feser-Ross Argument for the Immateriality of the Mind

In a lecture given for the Society of Catholic Scientists, Ed Feser lays out his argument for the immateriality of thought in simple, syllogistic form. Since he does not provide the actual syllogism in his (very good) paper on the topic, I thought I would jot it down here for future reference:

1. Nothing material can have an exact or unambiguous conceptual content.
2. Formal thought processes can have an exact or unambiguous conceptual content.
3. Therefore, formal thought processes are not material.

I think this is one of the more interesting arguments for dualism out there today; I wish it received more of the attention so often devoted to (for example) the Zombie argument.

Materialism, Open Individualism, and Eliminativism

I recently came across a weird argument for open individualism, i.e. the view that there is only one subject of experience. It goes basically like this: suppose my DNA were to be altered bit-by-bit, in such a way as to increase my fondness for Greek yogurt, or change the color of my eyes. Surely I would not think of this as my ceasing to exist; rather, it would simply be me who now had a greater fondness for Greek yogurt, or differently colored eyes. But if I do not expect that I would cease to exist in light of these minor changes, on what basis can I say that I would cease to exist given larger ones? Indeed, it seems that we can construct a Ship of Theseus dilemma for personal identity, where it is impossible to draw a principled line designating when exactly "I" would cease to exist. 

Now, suppose we infer from this that I would continue to exist no matter what changes occurred to my physical makeup. Even if my body were to be altered bit-by-bit until it was identical (right down to the brain chemistry) with that of Joe Biden, "I" would still be fully present. This fact must surely sever the link between my personal identity on the one hand, and any particular body and brain on the other. After all, if I would still be fully present in the experience of a future version of myself who had been rendered identical to Joe Biden, then on what basis can I say that I am not fully present in the experiences of Joe Biden right now? It seems, therefore, that I am already fully-present in the experiences of all conscious beings, and that therefore, there is only one subject of experience. This argument (or a very similar one) has also been made in print by Arnold Zuboff (1990).

It seems that there are only two ways to avoid the open individualist conclusion: (1) Deny that "I" would still be fully present in the Biden-shaped version of myself, or 2) Accept a further-fact view of personal identity, on which "I" am distinct from any particular facts about my biology and/or psychology. The first option would require us to draw some kind of principled line, i.e. a specific point in the DNA-swapping process at which "I" would cease to exist. However, this threatens to be tremendously arbitrary; is it really possible to find a point at which exactly one DNA base pair is what distinguishes whether or not "I" exist? What if the DNA were to be changed, and then changed back afterwards? Would "I" suddenly pop back into existence?

A less arbitrary route to (1) is to deny that "I" would be present in my Biden-form, because "I" am not present now. That is to say, we can read the above as an argument for eliminativism. I think eliminativism, as unintuitive as it is, is certainly more intuitive than the idea that there is only one self. I would find it easier to accept that the self is an illusion, rather than accept than Joe Biden and I are actually one self experiencing itself from two different perspectives in time and space. This seems to me to be incoherent; after all, what is the word "self," if not the thing that is supposed to distinguish me from others? It seems like a massive contortion of language to insist that two organisms, with no obvious way of accessing each other's experiences, can actually be one "self."

The other way out of the problem is (2). That is, we can accept a further fact view, on which there is something about me that does not change (and so would be unaffected by the DNA-swapping process) and maintains my identity through time. The obvious candidate here is an immaterial soul. The upshot, then, is this: either "I" have an immaterial soul, or "I" do not exist. I should note that similar arguments have been made by others in the past; for instance, Perry Hendricks (2016) has argued that substance dualism and eliminativism are our only real options. In light of the above, I think I am inclined to agree.

Contra Leon on Wave Function Realism

Felipe Leon thinks that wave-function realism should lead us to conclude that "ordinary perceptual experience is massively unreliable." He gives the following argument for this conclusion:

[It's] not at all clear how the ordinary three dimensions of our experience can be accounted for [given WFR]. In fact, some (e.g., Alyssa Ney) have argued that they probably can't, in which case there is non-trivial epistemic pressure to think the three dimensions of ordinary experience are, in an important sense, mirage-like.

Leon then argues that this leads to "troubling epistemic consequences for theism," because "if God exists, then God designed us in such a way as to ensure that our perceptual faculties reliably track the truth about the world." But if three-dimensional reality is illusory, then our perceptual faculties don't reliability track the truth, and as such, it is unlikely that God exists.

I think Leon is simply mistaken on this issue. To see why, take a look at this interview with philosopher of science Jill North (whom Leon also cites):

But ordinary 3-D space is not just an illusion, says North. “I think that 3-D space exists, and our talk about it is true. It’s just that this space is nonfundamental. Similarly, ordinary particles exist but are nonfundamental. They are more like tables and chairs: made up out of fundamental stuff, not themselves in the fundamental inventory.” 3-D space is a separate thing that is in some sense “made up out of” the higher-dimensional space, just as particles are ultimately “made up out of” the wave function.

Similarly, in a recent paper on wave-function realism and the place of 3D-space in a high-dimension world, Theodore Sider writes:

[High-dimensionalism] might suggest that rocks, trees, subatomic particles, and other three-dimensionalia are illusions, or intellectual mistakes, akin to phlogiston and phrenology, and should be purged from our cognitive lives. But high-dimensionalists cannot, and do not, take this hard line. In addition to being literally unbelievable, the view would be self-undermining. The empirical evidence for any scientific theory is three-dimensional, consisting of observations of pointer positions, computer readouts, and the like. If quantum mechanics implies that statements about pointer positions and the rest are all false, it does not imply any of our evidence, and thus it is incapable of empirical confirmation.

Accordingly, what high-dimensionalists say is not that three-dimensional matters are unreal, but merely that they are nonfundamental. High-dimensional fundamental reality “gives rise to” a nonfundamental three dimensional world. Thus high-dimensional quantum theories do, after all, imply facts about the three-dimensional evidence, and are therefore capable of confirmation.

Interestingly, Sider himself argues for a view on which high-dimensionalism is closer to what Leon supposes it to be (though he still accepts that our talk about 3D space is, in some sense, true). However, the point is that most defenders of higher-dimensionalism would reject the claim that 3D space is unreal.

As such, it seems that Leon is wrong to say that three-dimensional reality is "mirage-like." It may be nonfundamental, but it is not fictitious or unreal. This takes away most of the force from Leon's atheistic argument; after all, why should we expect God to give us accurate perception of fundamental reality? Isn't it enough that we perceive the level of reality on which we operate? One might as well say that our perceptions are misleading because we cannot see the individual atoms that make up the world around us! (NOTE: This is to say nothing of my own preferred view, on which reality is fundamentally an idea in the mind of God. What it would mean to "accurately perceive" this fact—and therefore. to have "reliable faculties" in Leon's preferred sense—is a mystery to me.)

On Luke Tracey's Logical Problem of Evil

A few years back, atheist blogger Luke Tracey formulated an ingenious new version of the logical problem of evil. The argument goes as follows: there are two types of properties, good-making properties (GMP) and evil-making properties (EMP). All EMPs are such that they are not entailed by any GMP, which is proven by the fact that God (who instantiates all GMPs) may exist alone, without His contingent creation. In this "alone world," all GMPs would exist (as instantiated by God), and no EMPs would exist. Thus, it is possible for all possible good-making properties to exist without any evil-making properties. Therefore, the existence of EMPs is innately superfluous, and since God would not allow superfluous evil, it follows that God does not exist.

It seems to me that the best response for the theist is to deny the existence of evil-making properties. The classical theist tradition (as epitomized by Augustine, Aquinas, etc.) has usually held that evil as-such does not exist; rather, evil is a privation, the absence of due goodness. Ben Page and Max Baker-Hytch (2020) explain this as follows:

Badness is a privation... because something is only ever ‘bad’ in virtue of its failure to exhibit (or to exhibit to a sufficient degree) a property that a member of a given kind ought to have.

On this view, so-called "evil-making properties" do not exist, and Tracey's argument loses all force. In addition, Tracey's argument relies on the idea that God would not allow any gratuitous evil to exist, a view which has been increasingly challenged by theistic philosophers (e.g. Rubio 2018, Murphy 2019). One could also adopt the view that God is free from moral obligations, as He is not a part of the moral community (see the aforementioned papers from Rubio and Murphy, as well as Davies 2006 and Feser 2021). 

Finally, I would draw attention to Kenneth Pearce's (2019) response to the logical problem of evil, in which he argues that "a certain way of thinking about the nature of mind—which is widely held by naturalists but might also reasonably be endorsed by theists—has the consequence that the existence of (non-divine) minds is impossible in the absence of evil." This would arguably serve to undercut Tracey's argument, which hinges on the notion that God could instantiate all good-making properties without this entailing any evil-making properties. If Pearce is correct, then Tracey's line of reasoning would lead us to conclude that the creation of any non-divine minds at all is impermissible for God, which is a highly implausible conclusion.

Causal Explanations Need Not Increase the Probability of Events

I recently came across this argument, which purports to refute the argument from contingency:

1. Suppose that some necessary proposition q causally explains a contingent proposition p.
2. A proposition q only causally explains a proposition p if q is true.
3. So, q is a necessary truth. (From 1 and 2)
4. The probability of a necessary truth is 1.
5. So, P(q) is equal to 1. (From 3 and 4)
6. Then, P(p|q) is equal to P(p). (From 2 and 5)
7. But, if q causally explains p, then P(p|q) > P(p).
8.  So, q does not causally explain p.
9. Then, q both does and does not causally explain p, which is absurd. (From 1 and 8)
10. Therefore, no necessary proposition causally explains a contingent proposition.

The essential premise here is (7), which the author summarizes thusly: "though causal explanations may neither entail nor make probable what they explain, it is at least true of causal explanations that their being true increases the probability of that which they explain." 

However, on closer examination, we see that this is flatly false. For it is well-known in philosophy of science that an explanation can reduce the probability of an event that it explains (thanks to Alexander Pruss for the following example). Suppose that Todd is a skilled assassin, who has been hired to kill Carl. When Todd fires his gun, there is a 99% chance that his target will die. As he is lining up his shot, Bob, a less effective assassin, also shows up. When Bob fires his gun, there is a 60% chance that his target will die. Bob, who compensates for his lack of precision with speed, gets his shot off first, and Todd flees the scene, never firing his gun. As it happens, Bob's shot kills Carl (though if he had missed, due to Todd's flight, Carl would have lived).

Here we have a case of a clear causal explanation, which nevertheless reduces the probability of the event that it explains. Bob's gunshot provides a causal explanation of Carl's death, despite the fact that it reduced Carl's chance of dying from 99% down to 60%. In other words, P(Carl's death | Bob's shot) is 60%, while P(Carl's death) without Bob's shot is 99%. So, by premise (7), we should say that Bob did not cause Carl's death, which is absurd.

At the end of the aforementioned "refutation," the author attempts to rebut these sorts of examples. He claims that, while the less effective assassin may reduce the target's chance of death relative to the more effective assassin, they nevertheless increase the probability simpliciter. I would argue that his objections fail; by premise (7), the probability of p occurring without q must be lower than it is with q in order for q to count as a causal explanation. Therefore, if the probability of p would be higher in the absence of q, premise (7) would tell us that q cannot be a causal explanation of p. This would require us to embrace the absurd conclusion that Bob did not cause Carl's death. The author of this supposed "refutation" should either revise premise (7), or acknowledge that his argument is a failure.

Just for the sake of argument, there are other examples we can give to illustrate this general issue. Suppose that there were an infinite series of snipers lined up to kill Carl, all firing one after another, and all with a non-zero chance of hitting their target. Here Carl's chance of death is 100%, and no individual sniper can affect this probability in any way (since even if he were to pack up his rifle and go home, there would be an infinite number of substitutes). But of course, one of the snipers must inevitably be the one to fire the fatal shot. From this, we can generate a problem for our interlocutor.

Suppose snipers one through thirty miss their target, and sniper thirty-one makes the kill. If he had missed, there would have been an infinite number of snipers after him, one of whom would have hit the mark; that is, the probability of Carl's death is 100%, whether sniper thirty-one is there or not. Therefore, P(Carl's death | Sniper Thirty-One) = P(Carl's death). But then, by premise (7) we should deny that sniper thirty-one caused Carl's death, which is absurd.

The conclusion, therefore, is that causal explanations need not increase the probability of the events that they explain. Thus, the supposed refutation of the argument from contingency fails.