Note, this question doesn't require belief in God, but it helps me formulate the question.

Is the following statement a possible truth:

He decided that 2 + 2 = 4*. He could have made it so that 2 + 2 = 5, without modifying the meaning of "2" or "+" or "=" or "4" or "5" (i.e. keeping all of that exactly the same).

In His omnipotence/lack-of-definition, He just as easily could have said "Let 2 plus 2 be equal to 5", and so it would have verily been and we wouldn't have been able to fathom 2 + 2 = 4 in the same way that we can't fathom 2 + 2 = 5 now.

If you had 2 things and I had 2 things, we'd have 5 things between us and that would be obvious.

The question of whether God created logic or not is covered, but I can't see if there is one on whether He also designed it.

* do not misunderstand and open a discussion about convention, such as counting systems. I mean this in the most fundamental sense possible

EDIT: Now that this is HNQ, I just want to mention something clarified in the comments: the question is ill formed. It seems I didn't mean "logic", but I am still trying to get to the root of what I mean, and how to formulate the question along my original intentions (I am considering re-asking, but regarding the Platonic Mathematical World, rather than logic). Either way, the question stands as is.

  • Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Philosophy Meta, or in Philosophy Chat. Comments continuing discussion may be removed.
    – Geoffrey Thomas
    Commented Apr 28 at 11:25
  • Regarding the edit, if anyone thinks they sort of know what I am asking and know how to express it better, please feel free to suggest in the chat above ^ (there has been quite a bit of misunderstanding - and I am happy to change the "Accepted" checkmark to a better answer if one comes along). I have asked this to my Professor in the past, and he has said that this is an old question that is very hard and has seemingly no ways to tackle it... so I do know I once was able to express it properly and it is a real question.
    – Rabbi Kaii
    Commented Apr 28 at 15:37

7 Answers 7


One characterization of logic is as "topic neutral" (though heed the caveats in the SEP entry!), so logic is, or there would be a logic that is, about God as much as anything else. If God created every logic, even that one, though, then would this be as much as to say that God had created Itself?

But, if we focus on that word "design," not just "creation": logic, even a logic (any given sample), seems to have a great many variables. How many basic quantifiers? Parentheses or no? How does the substructure unfold? How many truth values does it have? And so on and on. From what standpoint can we reason about reasoning so as to decide if a given attempt to reason is successful or not? So it is hard to say that this variability can be resolved in a non-circular manner. Hence, the abyss of epistemology (e.g. epistemic logic); and then here, the question as to the contingency of some evaluations of logical variables. For example, if we held fast to noncontradiction, yet acknowledged paracompleteness as a logical phenomenon, we might think that the Aristotelian tertium non datur is not "logically necessary" (even if "logically actual"). This would seem to be the kind of thing that intuitionism about logic would allow for, except we should note that per Cantor's account of divine infinity, a divine intuition of the facts would be able to uphold the excluded middle even in cases where intuitionism would say that even the Freely Creating Subject might not do so. At any rate, the contingency of some logical factoid would be a kind of thing that a logic-designing God would have to work with, to do such work.

But again, God seemingly cannot have designed whatever logic might be applicable to Itself as such, at least not insofar as this logic applies to God's existence (or we should have self-creation by self-design). If the "fact" that there is only one God, or that only one God can be quantified over, in the given system, depended on God designing the quantifier part of Its logic to that effect, well... And so by contrast, the traditional claim is that God's existence is necessary, even in some especially absolute way, and uniquely so to boot, so the traditionalist about God's being uncreated (if not outright uncreatable) will be motivated to severely limit or omit from the domain of contingency those aspects of (a) logic that pertain to the ultimate necessity of God.

Confession: we have proceeded in the above as if the intersection of logic and ontology is a matter of logical and metaphysical structures being echoes of each other. The idea is that the world is metaphysically composed from, in Quine's unbeatable (if critical) phrase, "sentence-like slices of reality" that are related to each other like "actual" sentences in languages subjected to logic; ergo, there is some pattern to the facts that "looks like" the patterns of language and logic; hence... But such a picture of things might sound naive, or outlandish, too, and so one might very well say, "God is no more 'subject to logic' than anything else is, metaphysically-speaking; God is not a mere language, not even a mere 'language of thought'." (Yet ironically, the most ardently maniacal of all theologians, the divine illuminationist on the level of the epistemology of logic (e.g. Cornelius van Til), must instead confess that God is indeed the intended language of our thoughts in the sense that we are morally expected to use the concept of God at the analytical foundations of our philosophical reflection.E)

ENot to define the concept of God in terms of axioms, then, but to define the concept of axioms in terms of God. Determining the possible insanity (or poetry) of this notion will be left as an exercise for the reader.

  • Thank you. I think my question is very ill formed, but I believe you've gotten the closest to my original intention. I do plan to yet ask again in a better way but I've learned a lot from this and find it fascinating how much this resounds with my own theology.
    – Rabbi Kaii
    Commented Apr 28 at 9:39
  • From, the little that I know, classical logic, up to a point, is both internally and externally consistent. It doesn't permit contradictions and there's a 90% match with what we know as reality. Is it possible to design a system of reasoning that is, let's stretch this to the limit, the mirror image of classical logic and is, at a minimum, internally consistent. So, e.g. in such a system, the conditional would be true iff the antecedent is true and the consequent false.
    – Hudjefa
    Commented Apr 28 at 11:42

He could have made it so that 2 + 2 = 5, without modifying the meaning of "2" or "+" or "=" or "4" or "5" (i.e. keeping all of that exactly the same).

What do we mean, when we talk about the meaning of "2" or "+" or "=" or "4" or "5"? What would it mean to leave the meaning unchanged?

Normally we understand the meaning of a term in logic to be the way the term is used. The meaning of 2 consists of where we may use this term 2. If we altered our logic so that we use the symbol 2 everywhere we previously used a left parentheses "(", then we would alter the meaning of 2 so it would be what previously was a left parentheses.

So by adding the proposition 2+2=5, and removing the proposition 2+2=4, you are automatically changing the meaning of the component symbols, because you are adding a new place to use them where previously you could not have used them. By changing the use you change the meaning.

  • I'll need to think about this one. My initial reaction is you have misunderstood the question (if so, 100% my fault). My intention in the quoted statement is to demonstrate that this is not the "can He make a square circle" question, and to avoid silly answers like "yeah, He could just make it that 5 is actually 4"
    – Rabbi Kaii
    Commented Apr 28 at 1:13
  • If you had 2 things and I had 2 things, we'd have 5 things between us and that would be obvious. Is it possible that that paradigm could exist? Is it equally possible from the point of view of "outside all paradigms and definition"? Are we biased on this, or is 2 + 2 = 4 fixed and inevitable from all points of view
    – Rabbi Kaii
    Commented Apr 28 at 1:28
  • 2
    @RabbiKaii "We'd have 5 things between us and that would be obvious." What is the meaning of 5? What is the meaning of 2? If you are concluding that two objects and two objects makes five objects, something has to be different about your reasoning process. Somewhere in your chain of reasoning you "zag" instead of "zig." The symbols are being used in different ways, which would give at least some of them different meanings, assuming meaning is based on use.
    – causative
    Commented Apr 28 at 2:54
  • For instance, part of the meaning of 2 is, "that which, when added to itself, makes 4." That would no longer be part of the meaning of 2 in your hypothetical world. So the meaning would be at least partially different.
    – causative
    Commented Apr 28 at 3:00
  • Thanks for taking the time. It's clear the question is ill formed. I am sorry for having wasted your time if so. I will try to reformulate another day. It's 4am
    – Rabbi Kaii
    Commented Apr 28 at 3:01

There seems to be more than one question here.

  1. What is the origin of logic: is it the product of human design, or a natural feature of human thought, or is it supernatural in some way?

  2. What is the metaphysical or epistemological status of logic: could it be other than what it is?

  3. Could an omnipotent being make logic different from what it actually is, even if that seems to us to be impossible?

As to the first, the word 'logic' is used in several different ways. At its narrowest, it refers to formal systems that exhibit how propositions can be deduced from other propositions. In a broader sense it is concerned with the principles of good reasoning. In a broader sense still, it is concerned with rationality and what distinguishes rational behaviour and decisions from irrational ones.

In the narrow sense, obviously God did not create logic. Formal systems of logic are human inventions. In the broadest sense, logic reflects what humans consider to be rational; maybe other beings would see things differently. It is questionable as to how rational human beings are anyway. Unless you believe that God created humans and endowed them with the capacity for rational thought, then logic in this sense is also of human origin.

The middle sense is perhaps more interesting. Are there general principles of good reasoning that would command the assent of any rational agent, human or otherwise? Maybe there are, but there still does not appear to be any path to inferring a divine origin. A more naturalistic explanation would be to say that agents who reason badly are less likely to be successful in surviving and reproducing. Though again, judging by the history of the human race, this is dubious to say the least.

As to the status of logic, this is a matter of dispute within the philosophy of logic. Some hold to logical monism, i.e. that there is one and only one correct logic. The alternative, logical pluralism, has become more common in recent years. There are certainly many different systems of logic, and these differ materially. Claiming that only one can be correct and identifying which one is difficult to justify. If one of the many systems of logic is of divine origin, it certainly isn't obvious which.

As to whether an omnipotent being could design a logic that appears to us to be impossible, there is disagreement. Descartes held that God could create true contradictions, but if God did so we would not be able to understand them. A more common view is that it does not make sense to speak of true contradictions, so their impossibility does not conflict with omnipotence.

Another position is that logic, being a human creation, is the product of our best endeavours to make sense of the world around us. The fact that we consider contradictions and claims that 2+2=5 to be false is not because logical truths have some grand transcendental or metaphysical status. We hold them because they form part of our best understanding of how things are. Maybe there are universes where it is useful to believe in contradictions and weird arithmetic. Ours is not one of them. (Though there are dialetheists who maintain that some contradictions are true.)

  • Before I deeply contemplate your answer, would it change if I replaced "logic" with "platonic mathematical world"?
    – Rabbi Kaii
    Commented Apr 28 at 2:24
  • 1
    Yes, that would be different. Logical and mathematical platonism is a particular philosophical position and is much less popular than it used to be. The position I describe in the last paragraph is sometimes called 'anti-exceptionalism'. It regards logical and mathematical propositions as being similar to things like statements of laws of nature. On this view, such propositions exhibit a great deal of abstraction and apply very broadly but they are not different in kind from other features of our scientific knowledge.
    – Bumble
    Commented Apr 28 at 2:35
  • Further reading for your last paragraph?
    – Rabbi Kaii
    Commented Apr 28 at 4:19
  • 1
    There are articles about anti-exceptionalism here, also here and here. There is an article about dialetheism in the Stanford Encyclopedia.
    – Bumble
    Commented Apr 28 at 19:26

2 + 2 = 4 by definition. It's not that we can't fathom 2 + 2 = 5, it's that that's not what we defined 2 + 2 to be. We can fathom much stranger things, like i*i = -1

The is no world, where the fourth successor of 0 is also the fifth successor of 0, if we have a consistent worldview, and we are keeping our definitions constant. This isnt about logic, its about definitions.

You may as well ask if its possible to imagine a world where words mean different things.

Now, I think you are asking a different question. I interpret your question as, is there a context where 2 apples plus 2 apples makes 5 apples?

I don't see why not.

A standard meaning of "add" is to combine, and so adding one droplet of water to another- does not mean one has 2 water droplets.

They have one ( larger by volume) droplet of water.

Similarly, if we have one particle, and we add it's anti-particle - we dont get 2 particles we get zero particles.

All we need to do is imagine a system without conservation laws with respect to what quantity a number is measuring, and we can produce a situation where "adding" produces nonstandard results.

Note: As far as clocks are concerned, 12 + 24 = 12

Amendment In response to the Change in the OP

I will respond with two different interpretations of your question.

  1. Could it be the case that a world admits absurdity, i.e. 0 = 1, 4 = 5 etc...

I would say yes, such a world is imaginable. Although, it is hard to give any specificity as to how it would function.

In such a world, people would accept absurdity as "normal" and so would see it as normal- but it would be a completely alien world to our own.

I imagine such a place to function similar to a dream, where events can take fold, seemingly randomly.

  1. Is there a possibility without changing the meaning of the terms, for 2 + 2 = 5 to not be an absurdity.

I would say that this is a definite No. 1+1+1+1 < 1+1+1+1+1 is a feature of definition, which includes the logic it is embedded in.If we change the logic to make it work, we necessarily change the definition, which breaks the premise of the question that we keep the same meaning of terms.

  • Please review the asterisk footnote in the OP
    – Rabbi Kaii
    Commented Apr 28 at 14:25
  • Okay, sure. But what if apples were really roses by a different name, and you were adding them together? Then could 2+2=5? Asking for my friend Bill. Commented Apr 28 at 17:36
  • @AlistairRiddoch Would we then have multiple Roses or a Singular Bouquet Of Roses? Commented Apr 28 at 19:02
  • @RabbiKaii I have amended my comment in response to the Footnote.Hopefully, it is helpful. Commented Apr 28 at 19:02
  • For clocks, 12 = 0 mod 12. Start counting at 1? Or zero? NO! 12! ha ha ha ha ha!
    – Scott Rowe
    Commented May 8 at 13:26

Let's start with an answer to your comment on the question itself @RabbiKaii.

Yes, logic itself is an effect of a cause, that cause being design. In fact, we can even argue that logic itself is a fundamental guide to creation. Perhaps this is proof that God himself, or even the concept of God itself is nothing but ordered, similar to the understanding that the cosmos is a well ordered whole by definition.

For a moment, let's get "deep":

*Let us "assume" that God is not a singular man, rather, equivalent to the big bang. In this situation, let us say that God is expressed in a mammalian sense. Since we mammals need the masculine and feminine to express creation in regard to biology at the least, let us say that God is the dualistic expression of the masculine and feminine in regard to energy perhaps at the foundational level. This point itself puts any theological connections into question since theology is in and of itself monistic, whereas this point requires dualism.

*Let us say that this dualistic source, of both masculinity and femininity, is in and of itself designed via laws such as the law of attraction and even the law of cause and effect. The law of attraction dictates that opposites can pose a cohesion, whereas the law of cause and effect can be used before and after. The existence of opposites allows for the effect that is the law of attraction, whereas the existence of the law of attraction allows for the effect that is creation via opposites. This of course suggests some sort of cosmic truth in accord with biology on an energetic scale. Surely to be debated.

*If we can fathom that existence itself retains innate design, perhaps we can say energy is the designer. If energy is the designer, it would truly require the law of attraction and even the law of cause and effect to even be fathomable.

*Once we accept the above, even if for a mere thought experiment, we can move forward with the potential understanding of how God designed logic.

*If God designed logic, it must have been within its own image. "its" is used solely to quantify both the masculine and feminine role in creation.

*The formulation of logic in accord with innateness of what God is, is nothing but a metaphorical "glance into the mirror". The quantification itself must be accepted by all, in order to truly be logical. If it is not, it will be logic that is opinionated, thus being what I call "masqueraded logic". Why? Because logic itself is meant to provide clarity. Opinions themselves do nothing but cause muddy notions.

Thus, we can argue that logic is designed, or even a quantification that allows for a concise description of that which is designed itself. While some would argue that creation and design are different things, let us take the following into account:

  1. Creation implies a "from nothing" or "from scratch" notion, saying that we took multiple things and made it something "new", or made something that never could or would exist. The former is more appealing than the latter.

  2. Design implies a "manipulation" or intended order of something that had to be created... perhaps. If something had to be created, then we must reference the former and attend to "design" with reverence to such. If not, then we can say that creation happens because "something" always is. Perhaps this something is energy, and perhaps energy itself can concentrate to the point of something "significant" happening.

Taking all of this into account, yes, we can argue that logic was designed via God, even if we manipulate the definition of God itself. In fact, this notion would suggest that we are at the least exercising a trait of God via ourselves. Perhaps a damning notion but regardless, it seems as if though it is truth, regardless of opinion.

To correlate back to the question itself, in regard to mathematics, we must understand that math itself is seemingly a principle of all existence. Thus, it would be probable that 2 + 2 = 4 is unchangeable. For instance, if there was one concentrated masculine force and one concentrated feminine force, that we could argue is the reason all things, all life exists, we could go further to understand that 1 + 1 = 2 is a foundational truth that allows for the initial two forces of all existence to "look in the mirror" and see themselves as what they are. That simply would be individuals expressing as opposites that are compatible, to simplify it incredibly.

We see that 2 + 2 cannot = 5 because it is laughable, truly. Why? This could be due to the nature of numbers themselves, or creation itself. Biologically, we understand that 1 + 1 = 2 and can even create situations where 1 + 1 + (specific act) = 3. This itself is a numerical equation for creation biologically, perhaps specifically in the mammalian sense. Thus, if energy follows similar laws to mammalian laws, we can see that 1 + 1 + (specific act) = 3 translates to 1 + 1 + 1 = 3. Even further, 1 + 1 + (effect of specific act) + (engagement of specific act again) = 4. Via this "model" it is true that 2 + 2 = 4 total, not even showing the potential for 2 + 2 = 5.

  • 1
    I tried to follow your steps but couldn't get through them, I will keep trying because this seems like a very sincere answer that is genuinely deep and not just "stoner deep". I just need time to process it. +1 for taking the time
    – Rabbi Kaii
    Commented Apr 28 at 9:48
  • HaHa sound good! I'll be honest there's truly no way to consider it stoner deep as I don't smoke marijuana anymore. If you had caught me a couple years ago, this would have been so, lol. Regardless, let me know if you have any questions. The simplest thing I can say at this moment, is that it can be viewed as a hypothetical or "theory", thus, you simply ,must take such a view into consideration and the text will make more sense. Commented Apr 28 at 13:20
  • 1
    Great that you gave it up, you clearly don't need it to be deep!
    – Rabbi Kaii
    Commented Apr 28 at 13:49

Leaving the question of God aside as irrelevant, we can sum up the question as follows:

Could logic be different so that 2 + 2 = 4 be false and 2 + 2 = 5 true

The answer is terribly simple: If we don't equivocate, no, at least not for normal human beings, and (of course) only far as we know.

If 5 was equal to 2 + 2, then either '5' would denote 4, or '2' would denote 2.5, or else '+' wouldn't denote the addition as we know it.

The limiting factor isn't with 4 and 5, it is with us human beings. We look at four things, and we also see two plus two things. Whether this could at all be different is as cogent as asking whether if reality as it is didn't exist, then there would be another one, and if so what it would be. Nobody knows the answer to that, and presumably nobody will ever know. As we presumably all understand.

Thus, '4' and '5' are just the names we give to things as they are and there is nothing we can do about how they are in this instance. It seems to be our nature that we look at four things and also see two plus two things, or one plus three etc. It normally doesn't work if we look at five things. We can see two plus three, not two plus two. Blame our nature.

Could we be different. Presumably some people are born different in this respect, but if they are, they don't seem to survive and prosper. This is not our nature for nothing.

Could our logic be different, though?

Might be, as our imagination is the only limiting factor here.

However, if it was any different, it would better have to be such that 2 + 2 = 4. Any entity with a logic such that 2 + 2 = 5 would similarly not survive very long, at least not in this our universe.

Could reality have been any different from what it is? I don't know and I am confident that nobody does, but if we assume that it could have been, then the problem is that we ourselves are in this one reality, and therefore with our nature as it is, and we simply cannot seem to be able to even conceive of a different logic, or of 2 + 2 = 5 being true. Any theory that we could imagine saying that 2 + 2 = 5 would be easily falsifiable. Any theory of a different logic would be easily proved illogical according to the only logic that we have, which is the one that we happen to have.

As it happens, there is such a theory. It is based on the idea that "A implies B" is logically equivalent to "not A or B". This is of course terribly circular, but also totally false. It doesn't even make sense. It is not even logical. The same conclusion would presumably apply to any logic not our own, not because it wouldn't be logical, only because such is our nature that no human being would be able to think logically using it.

We are perfectly able to reason illogically, though. This is something that we do, although most of the time it is probably for a good reason.

The logic that we have we have it because we inherit it from our genitors and ultimately from our ancestors, including other species, and it is this particular logic because it turns out that it works in the natural environment that we have on planet earth. If it didn't work, humanity wouldn't have survived, and it has. So our logic helps us survive. Could another logic do the trick? Possibly, we'll see when we met with Aliens from a different galaxy, but for now we certainly haven't been able to conceive of a different logic (something that we could effectively deem logical). We can't even explain exactly how this one works!

  • Could reality have been any different from what it is? I don't know and I am confident that nobody does, but if we assume that it could have been, then the problem is that we ourselves are in this one reality, and therefore with our nature as it is, and we simply cannot seem to be able to even conceive of a different logic, or of 2 + 2 = 5 being true. This indeed is my very problem.
    – Rabbi Kaii
    Commented Apr 28 at 10:48

If there is a god (I suspect not), then I would think that even it is beholden to the laws of logic and mathematics. It might be able to create clever worlds where certain logical or mathematical truths seem broken... but then again, so can we.

  • I've gotta side against god on this one. (Still friends?) Math simply observes the phenomenon of countable being. I saw a great rant where someone proclaimed math is fake. Ultimately someone said: It solves problems - it's working.
    – Dor1000
    Commented Apr 28 at 8:52
  • This doesn't even attempt to answer the question
    – Rabbi Kaii
    Commented Apr 28 at 9:45
  • @RabbiKaii yes it does. If god is beholden to the laws of logic, that means it didn't invent them. You're not being very charitable in your reading if you don't see that.
    – TKoL
    Commented Apr 28 at 10:38
  • The question clearly stated that the invocation of God is just a tool to clarify the question of whether logic is designable or not. So even if God is bound by the rules of logic, that still doesn't answer the question.
    – Rabbi Kaii
    Commented Apr 28 at 10:45
  • @Dor1000 once there is multiplicity, is its form inevitable?
    – Rabbi Kaii
    Commented Apr 28 at 10:47

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