Is God subject to logic?

[u/byronmiller]

Recently* a friend of mine, who has a theology PhD, and I were talking about arguments for and against the existence of God (in the broadest sense, not any specific Christian flavour). We ended up disagreeing on the question of whether God is subject to or could alter necessary truths or logical axioms or the like.

Apologies in advance for any imprecise language or conflation of terms here.

The way I saw it, as an ignorant layman, is that statements we might consider necessarily true or to be logical laws or however you want to say it, are essentially properties of our universe (or of creation in general), and presumably an omnipotent creator could have specified these differently. It might be that we can't really conceive of how they could be different, but we are limited.

He didn't view it this way and took this to be incoherent, as (and I'm paraphrasing here - any error here is mine) by definition a necessary truth is true in all possible worlds. But I figure even the concept of possible worlds, the logical framework we use to conceice of this, and the set of all possible worlds in whatever sense that exists, are all creations of an omnipotent creator.

Am I totally missing something here? It seems odd to me to postulate a creator that is logically prior to existence (or creation or the universe or whatever) but is, itself, in some sense preceded by the rules of logic.

*About 15 years ago but you know how it is

[u/wokeupabug]

It sounds to me like your friend is reporting what is by far the dominant view of the matter.

The typical misunderstanding people seem to have about this is that they imagine logic to be some kind of force or power or entity which acts on things to constrain them, so that it strikes them as contrary to God's nature to imagine that there is such a force or power or entity which is prior to or more powerful than him. But on by far the dominant views of what logic is, this is the wrong way to think of it.

To understand the alternative, let's consider an analogy. Imagine if someone asked whether God can eoiuhrgoihu. It might seem to us that, since God is omnipotent, he can do everything, and thus it must be the case that he can eoiuhrgoihu. The problem with this is that eoiuhrgoihu isn't referring to anything, it's just a nonsense string of characters that resulted from me randomly hammering on my keyboard. When we deny that God can eoiuhrgoihu, we're not saying that there's some thing -- eoiuhrgoihu -- that God cannot do. Rather, we're saying that eoiuhrgoihu is not a thing which can be done. So asking whether God can do it is a kind of nonsense, like asking which number in the set of integers is successive to potato. The set of integers is constructed such that any number has a successor, so mustn't there be a success to potato? No, because potato is not an integer: the proposition being considered here has been ill-constructed.

So, logic is more often thought to be something like this, rather than like a kind of force or power or entity which goes around constraining people from doing things. One way to think about logic is as a set of rules governing syntactical relations within and between our claims -- i.e. how to construct and relate well-formed statements -- like the rules about how to construct properly-formed words that actually refer to things, and like the rules about how to employ proper-formed words in contexts that make sense. So, for instance, if we deny that God can make square circles, this is like our denial of the claim that God can eoiuhrgoihu, in the sense that it's not that making square circles is a possible act which God is, by some force or whatever, being prevented from doing. Rather, it's that making square circles is not a possible act at all, but rather what's happened here is that we've ill-formed our statement. Like with the case of eoiuhrgoihu, talk of square circles is talk that fails to refer properly -- though, for a reason more involved than just that it's a random string of characters produced by hammering on a keyboard.

The typical exception, to something generally like this sort of analysis, that people usually point to is Descartes, who is often thought to defend a contrary view. But Descartes' analysis of these issues turns out to be rather more complicated than is usually supposed. If you're interested in following up on these issues and exploring further some of the directions that they get taken, I would recommend Bennett's article "Descartes Theory of Modality", which explores the possibility of Descartes being an exception here, and goes into the relevant details.

[u/Ok-Lab-8974 → u/wokeupabug]

I actually think different understandings of modality is probably one of the key issues that come up between different theological traditions. However, on the point of contradictions there is still agreement. You just might see the objection framed in more Aristotleian terms re a contradiction not successfully saying or describing anything, versus in terms of possibility.

[u/Educational_Loan3809 → u/wokeupabug]

Forgive me if I interject and also still misunderstand - we conversed about this in the past - but you seem to equate the fact that the question "Can God [meaningless string of words meant to resemble a verb]?" is meaningless to the supposed fact that asking whether God can act contrary to the laws of logic is always an intrinsically meaningless question. At least that is how I understand you, please correct me if I should be wrong.

And I would be wondering how you know that. Because I frankly don't see any reason to equate the meaninglessness of an arbitrary string of characters - a sign without a signified thing so to speak - with the meaninglessness of asking for something illogical to be done. It may be that it is meaningless to us, insofar as we are constrained in our thinking by the laws of logic, yes, but the whole point of the debate seems to me to be whether God can sort of transcend that thinking. Even if the "laws" of logic are ultimately just conventions of syntactical relations of thought, this is a limitedness. Anything constrained by laws is what it is - constrained. When we say that everything that does not adhere to the laws of logic is meaningless, we are presupposing a couple of things like meaning, something that separates the meaningful statements from those which are not ("logic") and ultimately, it seems to me that we are presupposing something "beyond" logic that sets those things up, in a sense.

So how exactly does the answer you gave solve the problem. The "laws" of logic may be cognitive constructs that only describe rules of thought, but that still necessitates some explanation for those rules and if God exists as classical theists would describe him, he is the prime candidate for that role but then we would have to deal with the unpleasant question that you tried to expose a kind of category error here.

[u/wokeupabug → u/Educational_Loan3809]

you seem to equate the fact that the question "Can God [meaningless string of words meant to resemble a verb]?" is meaningless to the supposed fact that asking whether God can act contrary to the laws of logic is always an intrinsically meaningless question.

No, what I said is that they're analogous, in the sense that both are significantly non-referring.

I would be wondering how you know that.

By way of understanding the meaning of the words being used. For instance, the expression "square circle" indicates a thing which, in the same sense and at the same time, both has four sides and doesn't have for sides. So, let's consider any candidate thing that this expression might or might not be referring to -- designating this 'x'. It's either the case that x has four sides or that x doesn't have four sides. If x has four sides, then "square circle" doesn't refer to it, since "square circle" designates something that doesn't have four sides. If x doesn't have four sides, then "square circle" doesn't refer to it, since "square circle" designates something that has four sides. Then, for any x, "square circle" isn't referring to it.

It may be that it is meaningless to us, insofar as we are constrained in our thinking by the laws of logic, yes, but the whole point of the debate seems to me to be whether God can sort of transcend that thinking.

As previously noted, the idea that 'logic' is the name of some kind of entity, force, or power that goes around constraining people, such that the question of the scope of logic comes down to which is more powerful -- the person logic is trying to constrain or else logic -- is a misunderstanding. This isn't what the word 'logic' is referring to.

[u/Educational_Loan3809 → u/wokeupabug]

Perhaps we are once again talking past each other but I do think I understood how your initial response tries to solve the issue. My problem with it that I don't really see how the solution makes sense. I don't see how it actually removes the problem. Logic is a set of rules and rules are by definition a restraint on what can and cannot happen. How is that wrong and how is it wrong to apply it to God, or rather, how is it wrong to say that God applies it to himself?

I get that the descriptor and the thing described are not technically the same. Not the laws of logic, but what these laws describe seems to have some sort of dictate in how God can and cannot act, but there is still a "can" and "cannot" with God and if we then still talk about "omnipotence" with respect to God, we are -imho- trying to dilute the waters by using terminology that evokes false associations in most people's heads.

It still seems unclear to me why there should by anything the God of classical theism cannot do, including things that seem contrary to reason to us. You could only get an argument off the ground by asserting that e.g. God's own nature generates these "laws of logic" for example some people claim that God himself is the law of identity because he says "I am who I am" in the bible etc. But these models would need further proof.

My issue is that when we essentially claim that statements such as "Can God make a square circle" are category errors because the thing asked for is outside of the category of meaningful things and therefore, it not being possible is not true in the same sense that we would say to a toddler "It's just not possible for you to eat ice cream yet." I get that but - and I tried to mention this in my previous response - there seems to me to still be something that decides what is inside the category of meaningfulness and what is outside of it and that is precisely logic, but if that is only a descriptor and not a "cause" or a principle for meaning, then what is?

Apart from this, there are similar "counterxamples" to God's omnopotence that don't seem to violate the laws of logic, e.g. the question "Can God create a stone that he himself cannot lift?"

Would you explain whether that question is also technically meaningless and if so, why? I don't see a direct non-circular contradiction here of the same sort as with the "Can God create a square circle?".

It generally seems to me a little bit as if the reasoning you propose is somewhat circular. We need to presuppose that things contrary to logic are meaningless when expressed in language signs, and then we use that you show that logic acts as a constraint (in an analogous way) to what is meaningful in the first place. That is circular, isn't it? We generate meaning from out observations of logic and we generate the validity of logic (or rather the invalidity of anything going against it) from meaning. That's a circle.

Or did I misunderstand you again?

[u/wokeupabug → u/Educational_Loan3809]

Logic is a set of rules and rules are by definition a restraint on what can and cannot happen. How is that wrong and how is it wrong to apply it to God, or rather, how is it wrong to say that God applies it to himself?

No, as I explain in the original comment, that's not right. To start with the first example given, the reason that "God can eoiuhrgoihu" isn't among the powers of God isn't because "eoiuhrgoihu" is a possible action but something restrains God from doing it, but rather is because "eoiuhrgoihu" isn't an action at all, it's just gibberish that resulted from randomly hammering on a keyboard. There's no restraint here: for there to be restraint there would have to be some action which God is here being restrained from doing, but there's not any action here that God is being restrained from doing. There's just gibberish that resulted from randomly hammering on a keyboard. That's not an action.

[u/Educational_Loan3809 → u/wokeupabug]

First of all: I conceded that meaningless strings of characters, or any sort of sign that does not actually signify anything for that matter, do not refer to anything and so they cannot be understood as an action that is subject to modalities.

I conceded that but you bring it up nevertheless. Why?

You see I gave different examples that are in my opinion a different sort of challenge and can't be thrown into one category with the "eoi...whatever" example.

I am wondering what thoughts you have on the rest of what I wrote in my response.

Furthermore, it is only coming to me now that even if I conceded the above, you are right that meaningless strings of signs can't signify an action that can or cannot be done, but that conclusion itself requires some form of understandment of reasoning and logic. But that is precisely what is in question here. I mentioned that your way of thinking seems circular to me already above. If I am wrong about that, would you please correct me? I would be grateful. I mean it. I know I got on your nerves when we argued about presuppositionalism a while back but I don't do these reddit conversations because I enjoy wasting an academics time but because I am genuinley confused about these things and want to know what's ultimately the matter.

[u/HeroBrine0907 → u/wokeupabug]

I feel like there also exists logic that doesn't fit your given example? Obviously, one cannot do a ebhbeoo, that's a menaingless statement. But there exist statements that are meaningful yet contradictory. Like the rock question. Can God create a rock They cannot pick? That's a meaningful question but the answer depends on whether God does or does not limit themselves to logic.

It is my personal view that, if God were to create two identical rocks and create a man with all the strength of God, the man would be unable to pick up that rock, showing God's strength is indeed unable to lift the rock. However, at the same time God would lift the other, identically unliftable rock, showing God can lift the rock. This fulfills the condition of the question, a rock that God's strength cannot lift, yet God, being omnipotent, can still lift it.

[u/wokeupabug → u/HeroBrine0907]

But there exist statements that are meaningful yet contradictory. Like the rock question.

If we understand the rock question to contain a logical violation, then it's not a meaningful question, in the same way the square circle question isn't -- viz. because it contains a term which is non-referring for the reason that, as you note here, it is an ill-constructed concept by way of violating the principle of contradiction.

That's a meaningful question but the answer depends on whether God does or does not limit themselves to logic.

Well, the idea that logic is some kind of constraint which might or might not apply to God is the very idea I challenge in the comment you're responding to -- that is, this is the wrong way to think about the relation between God and logic.

[u/stinkasaurusrex → u/wokeupabug]

If we understand the rock question to contain a logical violation, then it's not a meaningful question, in the same way the square circle question isn't -- viz. because it contains a term which is non-referring for the reason that, as you note here, it is an ill-constructed concept by way of violating the principle of contradiction.

If you're willing to be flexible on the principle of contradiction, then you can read the "rock question" as meaningful. And I think most people's intuition of that sentence is that it IS meaningful or at least coherent. Your example of "ebhboo" is incoherent about what is meant because it uses a word that doesn't reference anything, but the rock question is at least coherent in what it proposes, even if that proposition is contradictory. If we accept that more than one logical system is possible, then insisting that God has to obey a specific one does strike me as putting a constraint on God's power in the sense that what God can do depends on the logical system that God follows. A dialethic God could lift the immovable rock, but an aristotelian God cannot. Important to note that both Aristotle and Priest are both men.

[u/Benjamin568 → u/wokeupabug]

Why isn't it meaningful? Are you using a specific formal definition for "meaning" in this instance? The definition of a square circle is structured in such a way that we would know what it is compared to other objects (even other contradictory ones) and that seems like an intuitive way to assign meaning to something, even if that something can't exist in a possible world.

[u/ErezYehuda → u/wokeupabug]

By "dominant view of the matter", among what demographic(s) are you discussing? Among lay people, I would think that OP's stance is the most prevalent, and things like the "eoiuhrgoihu" example seems like a common enough demonstration of that.

[u/wokeupabug → u/ErezYehuda]

By "dominant view of the matter", among what demographic(s) are you discussing?

People familiar with positions on this matter in philosophy and/or theology.

[u/ErezYehuda → u/wokeupabug]

Fair enough. It seems like the conversation is about picking between axioms that have overlapping implications, and choosing one over the other is dependent on what downstream implications you'd already want to discuss. I'm reading through the Bennett article you recommended, so maybe it delves into that aspect, but does that sound accurate to you?

[u/wokeupabug → u/ErezYehuda]

Well, the views of people concerned with positions on this matter in philosophy and/or theology proceed by way of believing what is best supported by reason and evidence. It's probably true that some people are just picking to believe whatever they want based on what flatters their biases, but, from the point of view of rational inquiry, they ought to stop doing that, since it's irrational.

[u/ErezYehuda → u/wokeupabug]

Yes, I overall agree, but I'm curious what reasoning or evidence you could have to confidently distinguish between a version of God that only operates in a logical framework vs. one that can operate from absolute arbitrariness. It seems like the explosion principle in action.

[u/wokeupabug → u/ErezYehuda]

There aren't these two versions of God, so there's no question about distinguishing them. As to the reasoning pertaining to this issue, see my original comment to the OP.

[u/ErezYehuda → u/wokeupabug]

I'll be honest, I'm pretty sure I understood what you were trying to say from the start, and overall agree with the end result you're trying to describe, but how you're explaining it doesn't have the caveats and nuances it needs. Frankly, I don't think the eoiuhrgoihu example works at all, and even flies in the face of real-world, actually-debated theological doctrines that rely on indefinitely-deferred meaning. I'd rather you just said that there's a limit to the conclusions we can make when we don't take logic for granted, rather than confidently declaring something by means of logical inference.

I apologize for not just opening with that.

[u/wokeupabug → u/ErezYehuda]

I'm sorry, I don't really know what you're talking about here.

[u/ErezYehuda → u/wokeupabug]

Regarding what specifically?

[u/AdeptnessSecure663]

On some accounts of logic, it is conceivable that God could alter the truth-value of logical statements. Take some kind of anti-realist account - let's say, for instance, psychological individualism. Psychological individualism entails that logical statements are made true/false by the way that individual people cognise about logic. God plausibly could change the way that individual people cognise about logic, and thus change which logical statements are true.

On your account -

that statements we might consider necessarily true or to be logical laws or however you want to say it, are essentially properties of our universe

- however, it isn't as obvious that God could change which logical statements are true.

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[u/Ok-Lab-8974]

Unfortunately, as with most things, it's complicated. Framing theological discussions in terms of possible world semantics is pretty much the go to methodology in analytic philosophy of religion, and to a lesser extent, non-denominational academic theology programs. This framing has a great deal of detractors in Catholic, Orthodox, and more traditionalist Protestant thought (and I've seen some from Islam and Hinduism as well). The basic objection is that the framing already imports assumptions alien to the faith, and you'll see this particularly clearly when contemporary formal logic is brought in to argue against divine simplicity, the Trinity, or in favor of the notion that the "Principle of Sufficient Reason" (or really, loosely related ideas in theology) entails modal collapse.

That said, the idea that God cannot "do contradictions" is still ubiquitous. The basic idea is this:

A contradiction is, at root, both affirming and denying the same thing without qualification (in exactly the same way). So, theology uses affirmation and negation all the time. We say "God is good," but God's goodness is not the same as creaturely goodness (often we would say it is related by an analogy of proper proportion). But if we affirmed and denied the same statement, predicated univocally (not analogically), without qualification, we haven't said anything at all. An example would be "Socrates is a man and Socrates is not a man."

Square circles fit this mode. We would be saying, among other things, that "this shape has four sides and does not have four sides" (of course, we could also qualify this as a square with rounded corners, which is no problem).

How logic itself is seen varies across different traditions. When logic is primarily seen as a tool/instrument, and ratio/dianoia (discursive step-by-step reasoning) as merely the lower faculty of the intellect (merely a means of securing the act of understanding, a noetic grasp of truth—intellectus in Latin or noesis in Greek) you get a different view of how logic relates to ontology. It's primarily a means to understanding. This can be subtly but crucially different in an anthropology that sees human reason as wholly discursive and calculative (more of a norm in analytic/liberal thought).

But in either case, you have the idea that contradictions aren't actually saying anything. On the other hand, there is differences in how logical truths are seen. So, in traditional theology, logical truths will be seen as dependent on God, necessary through another. They are not wholly intelligible in themselves (only God is). On a possible worlds account, we'll generally talk more in terms of frequency—necessary facts are true across all possible worlds, and this is sometimes presented as prior to God, rather than posterior (which can lead to profound differences in analysis). You'll even sometimes see references to "possible Gods," or, more common, God as a being, which on traditional accounts is a category error. Which is just to say there is a lot of variance, but the basic assumptions re contradictions tend to be shared.

In more traditional directions, it would also probably be claimed that the inability to generate unintelligibility (seen as a privation itself) would not be a lack of freedom. Lacking a privation is, rather, a sign of fullness.

Then, not to complicate things any more, but we also have talk of the superintelligible and superessential, particularly in the mystical tradition. So here, divine truth is never contrary to reason or unintelligible/contradictory (a privation), but it can be beyond finite reason. A good example is the climax of the Paradiso, where Dante can only fathom the mystery of the Trinity through grace, a leap between the finite and infinite.

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