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2 + 2 : What else it could be

Discuss any topics related to metaphysics (the philosophical study of the principles of reality) or epistemology (the philosophical study of knowledge) in this forum.
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WisdomNotStrife
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2 + 2 : What else it could be

Post by WisdomNotStrife » June 9th, 2017, 2:54 am

With respect to 2 + 2 = 4, I was once asked, "What else could it be?". It was probably more like, "What else could it be?!"--notice the exclamation mark. I don't remember the context. Probably a discussion about postmodernism; public education and critical thinking skills; or something like that.

Anyway, people are adamant that it is self-evident that 2 + 2 = 4, that 2 + 2 could be nothing else, and that to even entertain the idea that 2 + 2 could be something other than 4 is absurd.

But recently I imagined being in a different universe than the one where we have concluded that 2 + 2 = 4. A different universe does not necessarily have the same physical laws as the former. I imagined taking a quantity that in this universe we call 2, combining it with another quantity that in this universe we call 2, and such act of combining yielding the quantity that in this universe we call 8. Therefore, 2 + 2 = 8.

If you need help visualizing it, imagin adding 2 cups of water to a glass of 2 cups of water and the result being 8 cups of water. That would violate the physical laws that we have formulated by manipulating and observing the universe we are a part of. But who says that there are not other universes with different physical laws?

What else could it be? It could be 8.

I could be anything, really.

If you see everything in terms of your own self, I believe that is called being egocentric. If you see everything in terms of your own culture, you are being ethnocentric. If you see everything in terms of humans, you are being anthropocentric.

If you see everything in terms of the one universe that you are aware of...I don't know if there is a word for it. We need a word for it. Snobbish responses like "What else could it be?" limit inquiry and understanding as much as ethnocentrism, et al.--and they get very tiresome.

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Re: 2 + 2 : What else it could be

Post by LuckyR » June 9th, 2017, 11:55 am

WisdomNotStrife wrote:With respect to 2 + 2 = 4, I was once asked, "What else could it be?". It was probably more like, "What else could it be?!"--notice the exclamation mark. I don't remember the context. Probably a discussion about postmodernism; public education and critical thinking skills; or something like that.

Anyway, people are adamant that it is self-evident that 2 + 2 = 4, that 2 + 2 could be nothing else, and that to even entertain the idea that 2 + 2 could be something other than 4 is absurd.

But recently I imagined being in a different universe than the one where we have concluded that 2 + 2 = 4. A different universe does not necessarily have the same physical laws as the former. I imagined taking a quantity that in this universe we call 2, combining it with another quantity that in this universe we call 2, and such act of combining yielding the quantity that in this universe we call 8. Therefore, 2 + 2 = 8.

If you need help visualizing it, imagin adding 2 cups of water to a glass of 2 cups of water and the result being 8 cups of water. That would violate the physical laws that we have formulated by manipulating and observing the universe we are a part of. But who says that there are not other universes with different physical laws?

What else could it be? It could be 8.

I could be anything, really.

If you see everything in terms of your own self, I believe that is called being egocentric. If you see everything in terms of your own culture, you are being ethnocentric. If you see everything in terms of humans, you are being anthropocentric.

If you see everything in terms of the one universe that you are aware of...I don't know if there is a word for it. We need a word for it. Snobbish responses like "What else could it be?" limit inquiry and understanding as much as ethnocentrism, et al.--and they get very tiresome.
It is all a matter of perspective. In base three: 2+ 2 = 11
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Re: 2 + 2 : What else it could be

Post by NicoL » June 10th, 2017, 4:48 pm

In a universe with different physical laws, perhaps salt would not dissolve in water, but 2+2=4 would still be true. Mathematical relations hold of metaphysical, not natural necessity.

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Re: 2 + 2 : What else it could be

Post by Eduk » June 13th, 2017, 10:16 am

In a different universe with different laws then if you had 2 apples and I gave you 2 apples you might end up with 8 apples. Incomprehensible to humans born in this universe but perhaps possible. Of course it is also perhaps impossible. 2 apples just might not make sense in a universe where 2 + 2 = 8. On the whole though someone scoffing at the idea that 2 + 2 could equal 8 is probably only thinking about our universe. I don't think that is entirely unreasonable of them but it depends on what you are trying to say. Of course scoffing at people who are trying to have a serious conversation with you is rude, so I recommend you limit your time with such individuals if after pointing out their rudeness they fail to change.
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Re: 2 + 2 : What else it could be

Post by NicoL » June 13th, 2017, 11:54 am

Eduk, the truth value of mathematical statements could be different in other possible worlds only if they represented contingent states of affairs - that is events. Entertaining this possibility would require one to commit to mathematical events consisting of mathematical objects exemplifying mathematical properties, and standing in mathematical relations to each other. In addition, one mathematical event could be the cause of some effect, which would be another mathematical event. But even a Platonist who admits mathematical objects in his/her ontology, would be talking of them as eternal and unchanging. The introduction of "mathematical change" implied by the postulated contingency of mathematics is a curiosity I would genuinely be interested in reading more about, and this is not intended as a stab at all.

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Re: 2 + 2 : What else it could be

Post by WisdomNotStrife » June 13th, 2017, 3:29 pm

NicoL wrote:In a universe with different physical laws, perhaps salt would not dissolve in water, but 2+2=4 would still be true. Mathematical relations hold of metaphysical, not natural necessity.



I thought that math is a language in which signifiers signify physical reality. "5 x 5 x 5" is signifying a physical reality: the dimensions of a particular cube. "5 x 5 x 5 = 125" is signifying a physical reality: the volume of a particular cube.

If there was nothing physical to signify, would that language exist?

Reason seems to dictate that if the physical thing being signified changes then the signifiers are going to change. If the quantity that is signified by "8" is the result of combining the quantity signified by "2" with another quantity signified by "2", the statement signifying physical reality will then be "2 + 2 = 8".

-- Updated June 13th, 2017, 3:37 pm to add the following --

If a donut and a pretzel are not topologically equivalent because the pretzel cannot be transformed into the donut without tearing, and if math reflects metaphysical reality rather than physical reality, does that mean that in a universe where the pretzel can be transformed into the donut without tearing they would still not be topologically equivalent?

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Re: 2 + 2 : What else it could be

Post by wanabe » June 14th, 2017, 12:06 am

Arithmetic requires all ones to be equal. In the real world things are never exactly equal.

One cup of water will have a slightly different amount of water than a second cup. They can be close to two cups, but probably very rarely, if ever, exactly two cups.

People are generally fine with approximations. So generally 2+2=4.

In reality it's more accurately stated ≈2 + ≈2 = ≈4. Depending on the usage this will not achieve desirable results.
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Re: 2 + 2 : What else it could be

Post by NicoL » June 14th, 2017, 4:36 am

Hi WNS, and thanks for your reply. I will try to answer to some of your points below.
WisdomNotStrife wrote: I thought that math is a language in which signifiers signify physical reality. "5 x 5 x 5" is signifying a physical reality: the dimensions of a particular cube. "5 x 5 x 5 = 125" is signifying a physical reality: the volume of a particular cube.
There are numerous terms that do signify (=mean) something, but arguably do not refer to (=represent) anything in the physical world. For example, names of fictional objects like "Harry Potter", or purely formal terms like "entity", "exists", "identity" or "1". "5 x 5 x 5 = 125" does not refer to the volume of any particular cube, it just expresses a formal relation that always and necessarily obtains between any three sets with a cardinality of 5 and any set with a cardinality of 125. Again: the above statement is not about four particular sets of physical entities, but about any four sets of entities/b] whose cardinalities are as stated.
WisdomNotStrife wrote: If there was nothing physical to signify, would that language exist?


Why not? Terms can have meaning without having reference. I can make such a language by combining the English grammar rules and function words with this stock of content words here: {"Optimus Prime", "Megatron", "provokes", "fights", "kills"}.

The terms of mathematics, along with those of logic and metaphysics (and probably disciplines like systems science) are formal terms: they have function but no particular content, no reference.

WisdomNotStrife wrote: Reason seems to dictate that if the physical thing being signified changes then the signifiers are going to change. If the quantity that is signified by "8" is the result of combining the quantity signified by "2" with another quantity signified by "2", the statement signifying physical reality will then be "2 + 2 = 8".


Your unstated assumption is that physical things can change in absolutely any way possible, but also in any way impossible. This is a contradiction. A quick example is this: it is naturally impossible to remove the load-bearing elements from a building without the building ceasing to exist. It will simply fall. Another example that involves logical, instead of natural, possibility is this: it is logically impossible for a proposition not to materially imply itself. And my point about mathematics, involves possibility with metaphysical modal force: it is metaphysically impossible that a set with 5 members does not contain exactly 2 plus 3 members. To rephrase this in a way that answers to this thread's topic quite on point: 5 = 2 + 3 in all possible worlds.

Consider this: the universe is a system with an unchangeable structure and a changeable form/configuration. But it can only change within the degrees of freedom its structure provides, just like sliding windows can move in only one dimension. To say that it could change any more than that does not even make any sense: it would simply cease to exist as one and the same universe and there would be nothing to talk about. My understanding is that this fundamental structure of the universe is expressed by ontology (for entities / individual things) and mathematics (for pluralities, change and space-time), and thus ontological and mathematical statements could not be otherwise in any possible world.

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Re: 2 + 2 : What else it could be

Post by NicoL » June 14th, 2017, 4:42 am

wanabe wrote:Arithmetic requires all ones to be equal. In the real world things are never exactly equal.

One cup of water will have a slightly different amount of water than a second cup. They can be close to two cups, but probably very rarely, if ever, exactly two cups.

People are generally fine with approximations. So generally 2+2=4.

In reality it's more accurately stated ≈2 + ≈2 = ≈4. Depending on the usage this will not achieve desirable results.
First, you have to decide whether you are talking about the cup of water or about the portion of water that is inside it, as the two refer to different objects of different kinds. But, nevermind that - what about 1 molecule of water? Is it also approximately 1? What about the cardinality of the set of people that are in the same room as you right now? Is it a real number approximating an integer, or is it an integer?

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Re: 2 + 2 : What else it could be

Post by WisdomNotStrife » June 14th, 2017, 2:12 pm

NicoL wrote:"5 x 5 x 5 = 125" does not refer to the volume of any particular cube,..."




I meant a particular kind of cube.



NicoL wrote:it just expresses a formal relation that always and necessarily obtains between any three sets with a cardinality of 5 and any set with a cardinality of 125. Again: the above statement is not about four particular sets of physical entities, but about any four sets of entities/b] whose cardinalities are as stated...




But if something is found that it does not apply to then "always" and "necessarily" are not true.



NicoL wrote: (Nested quote removed.)


Why not? Terms can have meaning without having reference. I can make such a language by combining the English grammar rules and function words with this stock of content words here: {"Optimus Prime", "Megatron", "provokes", "fights", "kills"}...




A language is something that people create.

If there was no concern about or need to control physical things, I doubt that people would have created the language known as math.

But I guess maybe if you were a member of the privileged elite in Athens and you were bored and needed something to do while the common people toiled in the fields you might start speculating about metaphysical relationships and create a language to represent them.



NicoL wrote:The terms of mathematics, along with those of logic and metaphysics (and probably disciplines like systems science) are formal terms: they have function but no particular content, no reference...





But I thought that you said that they do refer to something: relationships.



NicoL wrote: (Nested quote removed.)


Your unstated assumption is that physical things can change in absolutely any way possible, but also in any way impossible. This is a contradiction. A quick example is this: it is naturally impossible to remove the load-bearing elements from a building without the building ceasing to exist. It will simply fall. Another example that involves logical, instead of natural, possibility is this: it is logically impossible for a proposition not to materially imply itself. And my point about mathematics, involves possibility with metaphysical modal force: it is metaphysically impossible that a set with 5 members does not contain exactly 2 plus 3 members. To rephrase this in a way that answers to this thread's topic quite on point: 5 = 2 + 3 in all possible worlds.

Consider this: the universe is a system with an unchangeable structure and a changeable form/configuration. But it can only change within the degrees of freedom its structure provides, just like sliding windows can move in only one dimension. To say that it could change any more than that does not even make any sense: it would simply cease to exist as one and the same universe and there would be nothing to talk about. My understanding is that this fundamental structure of the universe is expressed by ontology (for entities / individual things) and mathematics (for pluralities, change and space-time), and thus ontological and mathematical statements could not be otherwise in any possible world.




I did not say or assume that anything is the case. I said if something is the case then 2 + 2 could be something other than 4.

If anything is being assumed it is that only certain things are possible, and I am not one making that assumption.

-- Updated June 15th, 2017, 12:13 am to add the following --

NicoL wrote:"5 x 5 x 5 = 125" does not refer to the volume of any particular cube,..."





I meant a particular kind of cube.




NicoL wrote:it just expresses a formal relation that always and necessarily obtains between any three sets with a cardinality of 5 and any set with a cardinality of 125. Again: the above statement is not about four particular sets of physical entities, but about any four sets of entities/b] whose cardinalities are as stated...




But if something is found that it does not apply to then "always" and "necessarily" are not true.



NicoL wrote:Why not? Terms can have meaning without having reference. I can make such a language by combining the English grammar rules and function words with this stock of content words here: {"Optimus Prime", "Megatron", "provokes", "fights", "kills"}...




A language is something that people create.

If there was no concern about or need to control physical things, I doubt that people would have created the language known as math.

But I guess maybe if you were a member of the privileged elite in Athens and you were bored and needed something to do while the common people toiled in the fields you might start speculating about metaphysical relationships and create a language to represent them.



NicoL wrote:The terms of mathematics, along with those of logic and metaphysics (and probably disciplines like systems science) are formal terms: they have function but no particular content, no reference...





But I thought that you said that they do refer to something: relationships.



NicoL wrote:Your unstated assumption is that physical things can change in absolutely any way possible, but also in any way impossible. This is a contradiction. A quick example is this: it is naturally impossible to remove the load-bearing elements from a building without the building ceasing to exist. It will simply fall. Another example that involves logical, instead of natural, possibility is this: it is logically impossible for a proposition not to materially imply itself. And my point about mathematics, involves possibility with metaphysical modal force: it is metaphysically impossible that a set with 5 members does not contain exactly 2 plus 3 members. To rephrase this in a way that answers to this thread's topic quite on point: 5 = 2 + 3 in all possible worlds.

Consider this: the universe is a system with an unchangeable structure and a changeable form/configuration. But it can only change within the degrees of freedom its structure provides, just like sliding windows can move in only one dimension. To say that it could change any more than that does not even make any sense: it would simply cease to exist as one and the same universe and there would be nothing to talk about. My understanding is that this fundamental structure of the universe is expressed by ontology (for entities / individual things) and mathematics (for pluralities, change and space-time), and thus ontological and mathematical statements could not be otherwise in any possible world.




I did not say or assume that anything is the case. I said if something is the case then 2 + 2 could be something other than 4.

If anything is being assumed it is that only certain things are possible, and I am not one making that assumption.

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Re: 2 + 2 : What else it could be

Post by Fan of Science » June 27th, 2017, 9:37 pm

I agree with Nicol -- mathematics is an axiomatic system, not empirically based. A mathematical truth is only true based upon the axioms in the system. At the same time, any physical laws outside the system are irrelevant. Think about it this way --- all mathematical objects are abstractions and one cannot perform experiments on abstractions. Mathematicians manipulate the abstraction with logic.

On the other hand, I also see your point, and in such a universe, it's likely that different systems of mathematics would arise to deal with a violation of the conservation laws, which I think was what you were illustrating.

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Re: 2 + 2 : What else it could be

Post by Wayne92587 » July 15th, 2017, 1:49 pm

The word Imagine is the key to problem with your thought process. Your thoughts are the result of your Rationalizations', Illusions of Reality; in your case make that delusion.

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Re: 2 + 2 : What else it could be

Post by Eduk » July 15th, 2017, 2:29 pm

The word Imagine is the key to problem with your thought process. Your thoughts are the result of your Rationalizations', Illusions of Reality; in your case make that delusion.
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Re: 2 + 2 : What else it could be

Post by Wayne92587 » July 15th, 2017, 3:54 pm

No!

Sorry it was rude, however I felt it necessary,iIt was only meant to shock, hoping to cause someone to be more Logical.

Reason is the source of logical, however Man's Reason, Ration Mind has serous defects.

Reason in the extreme, ignoring the truth, Reality itself, itself results in Rationalizations that boarder on Insanity.

-- Updated July 15th, 2017, 1:10 pm to add the following --

That was poorly worded, in to much of a hurry.

"Reason is the source of logic, however Man's Reasoning ability, the Ration Mind, is seriously flawed, man in the beginning ran out of the house, without putting on his pants on, bare, before he was fully dressed.

Reason in the extreme, ignoring Reality itself, the truth, results in Rationalizations that boarder on Insanity."

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