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This thought started off as 'If we are in a simulation, or if there exist a God/omnipotent being that can change the laws of physics (and everything) as we know it - is it possible for a change to defy reality as we know it?"

The most dramatic example I could think of is 1+1=3.

Ex: One shoe, another shoe, bam - 3 shoes.

This concept of a world where 1+1=3 is really hard to conceptualize for me because it changes everything that I understand the world as - which creates a picture for my original thought process:

Are there rules that even God(s) have to follow when formulating a world? Is it possible for us to be completely sure that 1+1=2 and there's no other way around it? Or, am I having a trouble conceptualizing this simply because I've lived my whole life in a world where 1+1=2 and laws of the universe are possibly more fluid than I had originally imagined?

(Note: Although I am indeed curious if 1+1=3 is possible in a theoretical world, please note that this is just an example for a bigger question)

Jett
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  • One position is at least is that you must distinguish types of knowledge. There is science tific knowledge which most of humanity relies on.There is something else referred to as OBJECTIVE KNOWLEDGE . Now in the case of science nothing is absolute. That is every theory must be falsifiable by definition. Objective knowledge is absolute. The truth value will never change by definition. So what is true must remain true forever. No false today & true 50 years later stuff. So in the case of objective knowledge GOD would not be able to change it by definition. Nothing can change the objective kind. – Logikal Mar 16 '20 at 15:52
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    "Could an omnipotent being draw a square circle? Descartes notoriously answered “yes.” However, the Western philosophical and theological traditions have, at least since Aquinas, almost universally given the opposite answer. The view that an omnipotent being could do absolutely anything, even the logically absurd, is known as voluntarism." – Mauro ALLEGRANZA Mar 16 '20 at 16:01
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    Seems like there might be two aspects to this question, one about whether "a world where 1+1=3" is actually a possible world, or even expresses a coherent or conceivable concept (some philosophers do discuss impossible worlds), and second about whether philosophical views about God's omnipotence say that God can change the "laws" of mathematics or logic. Might be a good idea to edit the question a bit to focus on which question you're more interested in, or if you're interested in both split it up into two more focused questions. – Hypnosifl Mar 16 '20 at 18:30
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    1+1=3 is not something that can be in the world or even about the world, it is a mathematical abstraction. So the title question does not really make sense. But we can easily make it true "in" our world by swapping the use of symbols "2" and "3". Even without that there can be a world where putting two things together makes a third thing pop up. There can even be a world where this happens often enough for its intelligent inhabitants to incorporate it into their rules of arithmetic. It doesn't even take omnipotence. But it is a postulated rule, not something to be sure or unsure about. – Conifold Mar 17 '20 at 04:49
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    @Conifold - Even in that hypothetical world, ppl would likely have notions of arithmetic matching ours for conceptual groupings (such groupings may be the intuition behind sets in set theory). For example if you pick some volume of space at a single instant of time and divide it conceptually into two halves, then ask "how many people are in the left half" and "how many people are in the right half" and the answer in each case is "1", then they would presumably agree this implies that the whole volume contains 2 ppl at that instant, even if a 3rd would appear if they later moved closer. – Hypnosifl Mar 17 '20 at 06:15
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    @Hypnosifl Perhaps, or perhaps they'll have no arithmetic or concepts, those are our devices. We or they decide what the rules are for them, if any, not the world. The question confuses linguistic conventions with what they are used to express. – Conifold Mar 17 '20 at 07:34
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    Welcome to SE Philosophy! Thanks for your contribution. Please take a quick moment to take the tour or find help. You can perform searches here or seek additional clarification at the meta site. Don't forget, when someone has answered your question, you can click on the checkmark to reward the contributor. – J D Mar 18 '20 at 03:58
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    When you say 2+2=3, are you using or mentioning? Food for thought. – J D Mar 18 '20 at 03:58
  • Does this answer your question? Can there be a universe with different mathematics? – viuser Mar 21 '20 at 03:59
  • https://mathworld.wolfram.com/PeanosAxioms.html Can an omnipotent being make Successor(Successor(0)) = Successor(Successor(Successor(0))) ? No. – polcott Apr 19 '20 at 15:33
  • No. Take a look at the points raised here. (Unless your definition of "3" is not the same as mine.) – user21820 Apr 23 '20 at 19:35
  • Easy-peasy! Then "+" means "+1+"... Then you can get 1+ 0 = 2 (but isn't there enough confusion in "the people"?) – xerx593 Jan 03 '24 at 09:31
  • Yes, absolutely. But the kind of reason that human beings possess would be considered madness there. – pureprimitive Jan 06 '24 at 13:10
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    @MauroALLEGRANZA Your link to ‘voluntarism’ returns Page Not Found, just a heads up. Could you double-check and re-link? – Julius Hamilton Jan 07 '24 at 07:45
  • It seems it has been rewritten here – Mauro ALLEGRANZA Jan 07 '24 at 10:48
  • Nut we must take care about changing the definition of sum Vs performing a miracle: we put on egg on the table, then a second one.. and suddenly a third egg pops up from nihil. – Mauro ALLEGRANZA Jan 07 '24 at 10:51

18 Answers18

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Can an omnipotent being make:
Successor(Successor(0)) = Successor(Successor(Successor(0)))? --No. https://mathworld.wolfram.com/PeanosAxioms.html

Can an omnipotent being assign the semantic meaning of {2} to the numeric symbol "3", --Yes.

polcott
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  • easy-peasy: just declare: 0 := +infinity + 1 resp. 0 := -infinity - 1 (and i feel/think: this is not "fiction", this is reality/truth) – xerx593 Jan 04 '24 at 14:20
  • But then 1+1 does not necessarily have to be equal to Successor(Successor(0)), outside of PA. – rus9384 Jan 06 '24 at 14:51
  • @rus9384 There is nothing that exists anywhere in the world that defines the meaning of Successor(Successor(0)) thus the ambiguity that you refer to does not exist. – polcott Jan 06 '24 at 15:39
  • The notion of Successor itself is a human invention that attempts to describe the world around us, not some hypothetical world with different laws of physics (and even logic). We have noticed that if you put an apple near a single apple, then you have two apples in a pack. Repeat and it is 3, then 4, etc. That is what Successor is, and in the hypothetical world we assume that if you put an apple near a single apple, you somehow have 3 apples together. And then Successor does not describe that hypohetical world. – rus9384 Jan 06 '24 at 15:46
  • @rus9384 There is a difference between {analytic} expressions that can be verified as completely true entirely based on their meaning and expressions that require sense data from the sense organs to verify their truth. {1+1=3} is stipulated to be false on the basis of its meaning. This remains true no matter how the semantic meaning is {1+1=3} is encoded. – polcott Jan 07 '24 at 22:41
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1 + 1 in exponential math can equal three, so this is not actually a good way to phrase the question. Some aspects of our world sum arithmetically, some sum exponentially, some sum logarithmically, some statistically, and some sum in the frequency domain. I think we all get the point, which is to ask about logical impossibilities, but the answer when one just considers the math actually suggests an answer.

We humans tend to think that what we experience on a daily basis is a logical necessity. In math terms, this was exemplified by the belief that Euclidean Geometry couldn't NOT be true -- everywhere and for everything. This was actually the example Kant used. Of course, less than a half century later, non-Euclidean geometries were developed that were self-consistent, demonstrating Kant was entirely wrong about the "logical necessity" of any form of math. And then our universe ended up following non-euclidean geometry, just rubbing the noses of necessitarians in their error. (Note that in a space of varying non-euclidean curvature, angles do not sum arithmetically either, for yet another example from our world.)

MATH, it turns out, can be done in all sorts of exotic and unique ways. Which of them are instantiated in the world -- is CONTINGENT, not necessary. And yes, a world could exist where exponential summing was common rather than an unusual exotica, and 1+1 = 3 on a pretty regular basis.

Your bigger question has to do with logic, and whether logic is necessary, even if math is not. And if logic IS necessary, would it then precede and constrain a creator deity? Alternatively, of a deity created everything, a PantoKrator, why would that everything not include logic?

Well -- it took a century and a half after showing that math is purely discretionary, but logicians are now pretty much agreed that LOGIC is also discretionary: https://math.vanderbilt.edu/schectex/logics/ If logic is contingent, then a creator, a PantoKrator, can in principle specify the logic that a world follows. And also could have different parts of a world follow different logics. Which we pretty much knew, given how quantum mechanics follows different logic than macro scale matter.

Dcleve
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    The problem is that when you refer to alternative systems of math you are changing the definitions of the terms (different axioms to define them)--for example if someone says it's logically impossible two parallel straight lines could ever meet, thinking about the intuitive meaning of the terms in Euclidean geometry, does it really prove them wrong if you show this isn't true when you redefine a "straight line" to mean an arbitrary geodesic on a curved surface, like a great circle on a sphere, and define "parallel' in terms of parallel transport? – Hypnosifl Mar 17 '20 at 04:41
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    @Hypnosifl -- I think I agree with you, I believe that a logic or math claim has to come with a specified frame set, as in "1+1=2 in linear arithmetic summing", and the selected frame set is contingent. – Dcleve Mar 17 '20 at 04:53
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    Kant didn't say that Euclidean geometry was "logically" necessary. – Kristian Berry Apr 22 '20 at 21:37
  • @KristianBerry -- this author disagrees with you: https://www.researchgate.net/publication/271880703_Kant_and_Newton_on_the_a_priori_necessity_of_geometry. and while this one agrees, he concedes that the view that "Kant does say that Euclidean Geometry is an a prior necessity" is a near-consensus: https://repository.hkbu.edu.hk/cgi/viewcontent.cgi?article=1016&context=rel_ja – Dcleve Apr 22 '20 at 22:05
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    Kant thought Euclidean geometry was necessary synthetically a priori, not analytically so. The latter would be "logical" necessity. – Kristian Berry Apr 22 '20 at 22:08
  • @KristianBerry This author disagrees, and uses both geometry and arithmetic as examples of analytic a priori in Kant: http://homepages.wmich.edu/~baldner/sap.pdf. And this one's definition of synthetic a-priori would not include them either. https://medium.com/@rgrydns/kant-how-is-a-synthetic-a-priori-judgment-possible-45af58688600 – Dcleve Apr 22 '20 at 22:36
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    Well in the first Critique itself Kant says that Euclidean geometry is known synthetically a priori so I don't know what to tell you. – Kristian Berry Apr 22 '20 at 22:53
  • The two authors I linked point out that Kant was using the nature of "extent" and arithmetic summing to infer that arithmetic and geometry were logical prior assumptions embedded in our even considering matter and math. At the time, no non-euclidean geometry was imagined to be possible, hence Kant was arguing for a form of necessity for both arithmetic and euclidean geometry. His reasoning also presupposes the prior necessity of classical logic, and is a logical reasoning process. By inference, then, in Kant's language something "known synthetically a priori" IS "logically necessary". – Dcleve Apr 24 '20 at 15:48
  • @KristianBerry -- forgot to "at" you! Note, all three of the assumptions that Kant is cited as relying upon are now questioned by mathematicians and logicians. His paradigmatic cases of synthetic a priori, such that synthetic a priori produces a "necessity", are now rejected at NOT necessary. And, with the challenge to logic form and method being a discretionary choice, the possibility of ANYTHING being logically necessary is highly suspect. – Dcleve Apr 24 '20 at 16:39
  • Kant would have allowed that concepts of alternative geometries are logically possible. I suppose if you're using the word "logically" in some other sense, your remark goes through to that extent. – Kristian Berry Apr 24 '20 at 21:29
  • @KristianBerry -- the first two links I provided you show your interpretation of Kant is a small minority view among scholars. – Dcleve Apr 24 '20 at 22:04
  • Kant says that Euclidean geometry is necessarily true, but not analytically. He defines "logically" as "analytically" so that's that. – Kristian Berry Apr 24 '20 at 23:33
  • @KristianBerry -- Kant's claim of necessity is clearly false, the SAP link notes that Kant was using a different definition of "logic" than is used today. That his paradigmatic example of an unquestionably "necessary synthetic a priori" is not necessary or a priori makes him an excellent and noteworthy example of the false belief that our every-day experiences and presuppositions are "how things have to be". – Dcleve Apr 25 '20 at 16:11
  • @polcott -- this appears to be an irrelevant post with respect to my answer. – Dcleve Jul 23 '20 at 21:36
  • @polcott -- you have identified no equivocation, nor demonstrated any logical necessity. Nor tied anything to my answer. Your posts appear to be incoherent non sequiturs. – Dcleve Jul 23 '20 at 21:47
  • Would you mind linking some sort of reference to this exponential math where one plus one equals three? I've done a lot of math, and I have no idea what you're referring to. – JonathanZ Jan 04 '24 at 19:41
  • @JonathanZ If a feature of our universe does not sum linearly, but instead using the equation in linear math of X + Y = LN(X + 3.48169) + LN(Y + 3.48169), then if X and Y are 1, then the sum of them would be 3. There are multiple aspects of our universe that do not use linear math, although most do. This need not have been the case, particularly if we are postulating an omnipotent being who can select the math that applies to the universe. – Dcleve Jan 04 '24 at 20:49
  • But what does the "+" in "X+3.48169" represent? To evaluate that sum surely you should calculate LN(X+3.48169)+LN(3.48169) first, and then each of those "+"s just be unwrapped. And if we're postulating an omnipotent being then 1+1 can equal 2 on Wednesdays and 3 on Thursdays, except during the counting of the Omer, when it switches. This is definitely mathematical nonsense, and possibly circularly nonsensical mathematics. – JonathanZ Jan 04 '24 at 21:48
  • @JonathanZ -- it is linear summing of course. If you do not understand non-linear math operations or coordinate transforms, then I doubt your claim to be highly familiar with math. Nobody who fits non-linear relationships to data considers them to be "nonsensical mathematics". – Dcleve Jan 04 '24 at 21:59
  • The existence of non-linear relationships does not redefine addition. That's nonsense. – JonathanZ Jan 04 '24 at 22:11
  • If you have a process that is 50% successful then add a second process that is also 50% successful, what do you get? 25% or 75% success, depending on how the logic of the methodologies works. Add two wave functions together, and their phases have a dramatic effect on what they sum to. Not all summing is linear. Didn't you say you are familiar with math? – Dcleve Jan 04 '24 at 22:15
  • Also, the "sum" of two i.i.d. Bernoulli processes with p =1/2 is not another Bernoulli processes with p = either 1/4 or 3/4. – JonathanZ Jan 05 '24 at 00:29
  • @JonathanZ -- if the success rates sum, then the success rate increases to 75% by adding the second process. If the failure rates sum, then the success rates drop to 25%. In both cases, 50% plus 50% does not sum to 100%, the summation is not based on linear arithmetic. Note I have now provided you three different examples of non-linear summing, and you still are insisting this cannot happen! – Dcleve Jan 05 '24 at 21:42
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    "Summing"? Okay. It's Friday, so use that word for whatever process of combination you want. Why not? – JonathanZ Jan 05 '24 at 22:03
  • Oh, BTW, I got curious about that addition-with-logs thing you defined. It's not associative. I know we've agreed you can call anything you want addition, but not being associative is pretty embarrassing for an operation that's using "+". – JonathanZ Jan 05 '24 at 22:24
  • @JonathanZ -- You are now engaged in circular reasoning. Add two waves, and they sum, but the max height will vary, with linear summing being the outer envelope. Add two reliability processes, and they sum statistically. But you only want to count the arithmetic linear summing, then declare that all summing is arithmetically linear? Circular reasoning fallacy. Some aspects of our world happen to not arithmetically linear. And in the hands of an omnipotent creator, that some could possibly be all. – Dcleve Jan 05 '24 at 22:25
  • Truth + Falsehood = "Lies, damned lies, and Statistics." – Scott Rowe Jan 06 '24 at 16:13
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  • Just an attempt.

(1) If a proposition is contradictory, it logically implies any proposition.

(2) 1+1 = 3 is contradictory.

(3) God decides that 1+1 = 3.

(4) Therefore God decided that any proposition is true.

(5) Therefore, God decides that " 1+1 is not equal to 3 " is true.

(6) Therefore God decides that one and the same proposition has 2 truth values.

So , the question amounts to : " can an omnipotent being reject the principle of bivalence?".

  • Other attempt :

(1) An omnipotent being is a being that can do anything that is possible.

(2) It is not possible that 1+1 = 3.

(3) Hence, it is not the case that an omnipotent being can make 1+1 = 3.

  • Another attempt ( along Descartes' line of thought in Meditations):

(1) A bad or evil will is a sign of impotency.

(2) A world in which 1+1 = 3 is true is a bad world, for in that world if a proposition is true, it is also false, in such a way that truth and falsehood do not mean anything.

(3) God is omnipotent, infinitely powerful, hence infinitely good.

(4) God would never want to create a world in which 1+1 = 3, for this world would be a bad one.

(5) It is morally impossible God to make 1+1 = 3, because he is omnipotent.

  • thoughts: Your first (2), 2a, is not true for many forms of summing. Most entertainingly, it is not even true of people, as population math leads to 1+1 = 3, then 4, then many more. 2b presumes that logic preceeds a PantoKrator -- so, where did logic come from, and why can't it be modified? The multiple logics we have found, show that there is no single absolute "One True Logic". The argument in 6a unravels when one realizes that reasoning and logic cannot be justified by reason or logic -- the Munchausen Trilemma shows that reasoning cannot validly close on itself. – Dcleve May 02 '20 at 20:54
  • "(1) If a proposition is contradictory, it logically implies any proposition." Relevance logic understands that the principle of explosion is gibberish nonsense. That other logics do not understand this is their error. – polcott Jan 04 '24 at 17:21
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We first have to answer the question of what does omnipotence mean. If a being is omnipotent, is this being bound by the rules of logic, or can the being alter logical inference itself?

If God cannot alter the rules of logical inference, then if he created a universe where 1+1=3, this universe would automatically be degenerate. The rules of logical inference prove that 1+1=2 (e.g. use the Peano axioms). If 1+1=3 and 1+1=2 and logical inference is valid, then the principle of explosion implies that in this universe, every possible statement is both true and false.

However, if God can alter the rules of logical inference, then all bets are off. It is not possible for me or anyone else to rationally answer this question under that assumption, as doing so requires assuming rules of logical inference. I suppose one could argue that in such a universe, there would be nothing that we would recognize as numbers and so there wouldn't be such statements as 1+1=3, but since we have no way of conceptualizing such a universe, I don't feel comfortable to make any claim about it at all.

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Let's simplify: 1+1 = 3 -> 0 = 1.

Can an omnipotent being create a world where 0 = 1?

In an informal rephrasing:

Can an omnipotent being create something from nothing?

It depends on the definition of omnipotent but I believe most religions will answer yes.

Idiosyncratic Soul
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Firstly, I assume that you are not referring to the trivial case in which the number 2 is simply redefined as the symbol 3.

What you seem to be asking is whether it is possible to have a world in which a single shoe, for example, and another single shoe, when considered together in some way, are three shoes, so that somehow the third shoe has materialised from nothing.

There are one or two- or should that be one or three- problems with what you suggest. Let's take the nature of the shoes into account. Suppose the first shoe you encounter is a tasty left boot, UK size 9, with a Cuban heal and faux boa-skin upper. The second shoe is a dainty glass slipper of exactly the sort that would slide effortlessly onto Cinderella's left foot. What then, determines the size, style, handedness, degree of wear, and other properties of the third shoe that materialises from nothing?

And what actually constitutes the act of addition? Do the single shoes need to be brought together in some way for the third to appear, or is it sufficient simply to contemplate the single shoes and the third automatically springs to mind. Can you, indeed, contemplate a single shoe and then another single shoe in this strange world, as surely that would amount to the contemplation of two shoes, which is not allowed?

Now suppose we have a one litre bottle of some liquid, another one litre bottle of some liquid and three much larger containers. We empty all three of the bottles into one of the large containers, so that we have three empty bottles and three litres of liquid in one large container. Presumably we can pour all the liquid from one of the large containers into another of the large containers without breaking the rules of your special arithmetic. And presumably we can also pour a third of the liquid from the large container into another large container. The question then is whether, in your new mathematics, 3-1=1, because if so, when we take away a litre from the three litres we need to be left with just one litre. So how does that actually come about? How, in this new world, do you distinguish between the circumstances in which you are about to pour all three litres from one container into another, or put just one causing half of the remainder to disappear? It is all extremely puzzling. One thing is for sure, magicians and sleight-of-hand artists would find it hard to earn a crust in the world you envisage. And just imagine all the other confusions magicians would face. Tossing a coin with three faces would be a challenge. And I don't suppose my poor old binary computer would cope with all those extra bits that would pop up.

Marco Ocram
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  • What you seem to be asking is whether it is possible to have a world in which a single shoe, for example, and another single shoe, when considered together in some way, are three shoes, so that somehow the third shoe has materialised from nothing. -- yes.... and no. I mean, your phrasing is still sounding like it's coming from the point of view of someone for whom 1+1 is obviously 2, so in order to make it 3, something has to materialize from nothing. I think OP is meaning it in a more fundamental way, in a way where 1+1=3 naturally. And I think the answer is no, personally. – TKoL Jan 03 '24 at 12:00
  • "The number of the counting shall be Three." Some early computers used Ternary representation: positive voltage, negative voltage and zero. It works well for data transmission, as long as you don't have too many zeros in a row. – Scott Rowe Jan 06 '24 at 15:57
  • @TKoL there isn't a way in which one shoe plus one shoe is three shoes without a shoe appearing, and that's the point. – Marco Ocram Jan 06 '24 at 17:14
  • @MarcoOcram I agree with you. – TKoL Jan 06 '24 at 18:51
  • @TKoL thanks- that makes three of us! – Marco Ocram Jan 06 '24 at 20:12
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Disclaimer: this is just my own thoughts, and is NOT meant to be me presenting what is objective unquestionable fact.

In my view, mathematical facts are, somehow, more primal than just about anything else. Any physical law, you can imagine a universe where that law is different. Perhaps you can imagine a universe where gravity is weaker, or is nonexistent, or even repellant rather than attractive. You can imagine a universe where various physical forces are stronger or weaker than they are now.

But in all of those universes, certain mathematical truths remain true.

I believe that mathematical truths are the deepest primal truth, and if there were a God, the mathematical truths would be even more primal and unbreakable than him.

TKoL
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I like the thinking of Spinoza for this.

One of his criticisms of the interpretation of an "omnipotent god" is that it's contradictory to think that god can go against it's own nature.

If omnipotent god can act against itself then it is not omnipotent because the limits of its power would be itself.

So the answer would be: no, god cannot go against nature.

GONZALO ROCHA DE LA CRUZ
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A world in which counting is meaningless is necessarily a world in which measurements are meaningless. So if in that world 1+1 = 3, then the distance to the sun is both 93 million miles and zero. Such a world would be uninhabitable to humans.

niels nielsen
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  • Maybe if 1+1=3 were true, then all living things would look different, as well. Such a world might be inhabitable to some other human-like animal. – Mark Andrews Mar 17 '20 at 00:52
  • Your premise is quite simply false. Logarithmic, exponential, and statistical summing are not arithmetic, and some aspects of the world use all of them. We currently inhabit a world where 1+1 does not always equal two. We DO tend to require reasonable stability in our world, but either absolute stability, or arithmetic summing -- no. – Dcleve Mar 17 '20 at 03:38
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    The OP's question did not specify what form of summing to consider. I took the simplest example. If we accept 1+1 = 3, subtracting 2 from each side yields 0 = 1, an important result which establishes among other things that Winston Churchill is a carrot. Proof is left as an exercise to the reader. . – niels nielsen Mar 17 '20 at 04:53
  • Subtracting 2 from each side of 1+1=3 in exponential math does not yield 0 = 1. Your "proof" has presuppositions that are false. Have you ever done statistical summing or subtractions. Logarithmic, or frequency summing or subtractions? – Dcleve Mar 17 '20 at 04:57
  • I stated my presuppositions, they are not false, yes I have, but I will waste no further time on this. Since this is "philosophy", you are free to believe whatever you want. – niels nielsen Mar 17 '20 at 07:00
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You can do 1+1 apples only if both apples are absolutely identical. Can you find two apples having such characteristic? No way. What you will always do is selecting a scale to accept identity. That is "I will consider two apples if they weigh the same up to the limit of my balance, which shows hundredths of kgs". But in such case, you are just being subjective about what to consider an identity. You will be saying 1+1=2 to something similar to 1.0000+1.0001=2.0 (which is obviously wrong). 1+1=3 is exactly the same case:

Take a digital bathroom scale that's able only to display integers. Put 1.4 kg on it. It'll tell "1". Repeat with a similar weight. Now, put both on the balance, you'll read "3". That is, 1+1=3.

This is not a joke. A classical philosophical problem is the selection of a limit for the definition of objects. That means that what is 1 for you, could be 0 for another person. If you have a ton of apples in a truck and two persons count them, the results will ALWAYS be different, and not because of errors. Some apples will be partially smashed and one could count them as valid and the other might not.

In simple words, an object (represented mathematically by the unit, 1) is a subjective definition. The definitions of objects are never objective. Therefore, 1+1 is not factually possible, although we assume subjectively that it is, and accept that 1+1=3 in some cases. Therefore, 1+1=3 is a common fact, although we prefer to ignore it and focus the ideal provided by reason and the limitations of perception.

RodolfoAP
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  • Excellent point -- the logic of math NOT a constraint on our world, which does not have absolutes or categories intrinsic to it. – Dcleve Apr 22 '20 at 22:15
  • I switched to wife's bathroom scale to read in 'Stone' (14 pounds, still used in Ireland) one time. "Whaaat? 9.5?!?" – Scott Rowe Jan 06 '24 at 16:10
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The most dramatic example I could think of is 1+1=3. Ex: One shoe, another shoe, bam - 3 shoes. This concept of a world where 1+1=3 is really hard to conceptualize for me because it changes everything that I understand the world *

I am not quite sure what you mean by "One shoe, another shoe, bam - 3 shoes". Are you saying a world where law of conservation doesn't hold as it does in our World? In our World, you can make 3 shoes out of 1+1 (make smaller shoe -2/3rd of original); you can now count them up to 3, and probably even say, falsely though, 1+1=3.

If the other World is different, you may end up having 1+1=3 because that is how that World would be like. 1+1=3 will be the norm, and your question, under its current interpretation, will have no value.

Ajax
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  • Excellent point. Our world does not have "conservation of entity quantity", hence 1+1 can equal 3 in all sorts of situations. – Dcleve Jul 23 '20 at 21:08
  • @Dcleve Yes, and it suggests that Type Theory can be a (reasonable) foundation of mathematics. – Ajax Jul 24 '20 at 17:48
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If we're going to be inferring abilities from omnipotence, we'll be using some notion of inference, so we'll at least be holding the rules of that inference true even for our all-capable being. If 1+1=3 according to those rules, then...

Kristian Berry
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When we say that p is necessary we mean that it is not possible that not p . So when we say 1 + 1 = 2 is necessary we mean that it is not possible that 1 + 1 is not 2 . To say that God is able to make 1 + 1 = 3 is to say that God is able to do something that is impossible .

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How do you mean that? In the cause of maths it can be done, by simply omitting the alignment of the symbols, but math would still work the same. If you mean, it as in lying, there the ground rule of a world is to grift about The Truth and telling it is considered wrong and undesired, it could also be. I just don't know, why you would want that. The Romans had something similar, then it was considered normal to offer briber in court and have mobs intervene, being the fundamental part in it, also slander as a form of argument to further the plot. Obviously, in the course of history, it is no longer a common practice.

Walgekaaren
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This thought started off as 'If we are in a simulation, or if there exist a God/omnipotent being that can change the laws of physics (and everything) as we know it - is it possible for a change to defy reality as we know it?" The most dramatic example I could think of is 1+1=3. Ex: One shoe, another shoe, bam - 3 shoes.

Theoretically, if we were in a simulation, the laws of logic could not be changed. A simulation must run using the rules of the universe it is contained within, and thus the “real” universe would have the same rules of logic as ours.

If we’re discussing what an omnipotent being could do, it depends on what you mean by “omnipotent”. If this Being is the Judeo-Islamic God, then yes. God created the idea of existing concepts and non-existing concepts, as well as whatever’s in between. This includes logic itself, despite how fundamental it is.

If we’re talking about some sort of magical wizard who can manipulate the universe however he wants, then no, he can't manipulate logic. [See below for the reason.]

Is it possible for us to be completely sure that 1+1=2 and there's no other way around it? Or, am I having a trouble conceptualizing this simply because I've lived my whole life in a world where 1+1=2 and laws of the universe are possibly more fluid than I had originally imagined?

Logic isn’t some arbitrary set of rules, like physics. Logic dictates that if there is a loaf of bread, and also another loaf of bread, then the only things in that group are those loaves of bread. This is what 1+1=2 means on the simplest, most fundamental level. For 1+1 to equal three, there has to INHERENTLY have ALREADY been a third piece of bread, despite me adding ONLY one piece of bread to another.

This would apply even in thought: If I would mentally picture my house and your house, I'd be picturing three houses, not two. These three houses would consist of your house, my house, and... that's it. However, this number would be three houses. In the theoretical universe, this would be normal and totally understandable.

This would even be true if nobody’s picturing anything: If there is a tree in Alabama, and also a tree in America, then in the 1+1=3 universe, there are three trees in all. Nobody has to be thinking about those trees, and they don’t have to be close to each other; just by existing, that conceptual group has to consist of three trees, not by magic, but because it's the only reasonable conclusion.

One more example: A sandwich has to have two slices of bread to be considered a sandwich, but in the 1+1=3 universe, the first slice and the second slice together would equal three pieces of bread. In that world, this would be completely logical, conceivable, and non-contradictory, just like the number of bread slices in OUR world's sandwiches.

So no, you're not just "used to" 1+1 being 2. There is no more fluidity in logic than the amount of cabbages in the color blue.

(Note: Although I am indeed curious if 1+1=3 is possible in a theoretical world, please note that this is just an example for a bigger question)

The most powerful theoretical wizard couldn’t make any of that happen, nor could any extra-universe alien who’s simulating our world, or any being to whom any logic applies in any measure. Only the Judeo-Islamic God could change logic itself.

QwertyCTRL.
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  • Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. – Community Jan 03 '24 at 08:40
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An omnipotent being can create a world where everyone is 100% convinced that 1+1=3. Including all the mathematicians. That would be a world where you would ask “can an omnipotent being create a world where 1+1=2” and most people would think it’s impossible.

gnasher729
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  • When I was a child I thought I had to add 2 to go from 9 to 10: one to change the 9 to a 0 and one more to put the 1 in front. I kept getting consistently wrong answers using addition until someone got me to explain this thinking. He said, "it makes sense, but that's not how it works." (I also came up with the idea of multiplication around then) – Scott Rowe Jan 06 '24 at 15:51
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All words and numbers are based on definitions on how we understand them. 1 Woman and 1 Man interacting with each other will possibly get you to a family of 3

So we are essentially already living in the world you described.

To give a little bit more context.

All Areas of Mathematics are based on Axioms. Those are non-proveable statements which are just assumed to be true and show themselve to be "at least somewhat correct" by providing Theories which are derived by them which in turn provide us with possibilities to check if everything works out by real life experiments.

For now everything in the Axiomatik world of Mathematics looks good. But no one can be 100% certain that it will stay that way.

So the direct answer to your question is "we can not know", but the most likely one is "yes, because 1+1=3 is already the case for some underlying Definitions"

  • Excellent point, population dynamics is exponential, not arithmetic, so sometimes 1+1 does equal 3. – Dcleve Apr 22 '20 at 22:16
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It depends on the definition. For instance, if you have one infinity and add another infinity, is it now 2 infinities? or is it just a greater infinity? This theory could also be reversed. Making 1 infinity + 1 infinity = 3 infinities.

Foolish Lemon
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  • https://mathworld.wolfram.com/PeanosAxioms.html Can an omnipotent being make Successor(Successor(0)) = Successor(Successor(Successor(0))) ? No. – polcott Apr 19 '20 at 15:32
  • Good point, arithmetic summing does not work with infinities. However, fleshing the answer out with more content, so that it stands alone as an answer, rather than just a comment, would be a good idea. – Dcleve Apr 22 '20 at 22:12