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The fact that mathematics gives us power to predict events in the real world makes it independent of social consensus. If everyone in the world believes that 2

The fact that mathematics gives us power to predict events in the real world makes it independent of social consensus. If everyone in the world believes that 2+2=5, that doesn't make it less true that 2+2=4 - in the sense that I know for sure, if I take throw two rocks on a pile of two rocks, I'll get a pile of four rocks, not five rocks. I hate this sociologist view that everything depends on the social consensus. Going extreme with it is how you end up in a 1984-esque society: Anything could be true. The so-called laws of Nature were nonsense. The law of gravity was nonsense. ’If I wished,’ O’Brien had said, ’I could float off this floor like a soap bubble.’ Winston worked it out. ’If he thinks he floats off the floor, and if I simultaneously think I see him do it, then the thing happens.

jfengel 4y ago
That's actually an example of what OP was talking about. You have defined + as the operator that mimics what piles of rocks do, and defined numbers as counting rocks. That's only a tiny fraction of what math does. An interesting and useful one, and mathematicians have put a lot of work into studying basic arithmetic. They have expanded out into numerous other forms, some of which turn out to have correspondence to the real world like non-Euclidean geometry. Others turn out to be completely abstract and are merely curiosities. There are an infinite number of them, each containing truths, almost all of them of no interest. Interest is defined by mathematicians, not physics. Even so it turns out to sometimes be useful, such as the beautiful theorems of prime numbers that drive Internet security centuries after they were invented. That is what the OP means. You can make up any axioms you want and prove true theorems. But the hard part is convincing other mathematicians to care.
- deleted 4y ago
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- bheadmaster 4y ago
  > But the hard part is convincing other mathematicians to care. My point is that whether other mathematicians care or not is completely irrelevant and doesn't subtract from mathematics' power of predicting phenomena in the real world. Each and every mathematical theory has to be consistent with basic rules of reality - if nothing else, symbolic manipulation relies on basic arithmetic and set theory. Without symbolic manipulation, you can't even express all those "abstract" mathematics - to say that "abstract" mathematics can not have correspondence to the real world is completely false, because of this basic connection. Now that I think about it - claiming that "mathematics is a social consensus" is exactly what I'd expect from a mathematics professor - a person whose whole life is isolated from reality, limited to the rigid structure of academia, and whose whole existence depends on other people caring. I doubt there is a single (professional) engineer that would say something like that.
  - ethanwillis 4y ago
  - version_five 4y ago
    Reading the discussion, I think you're both right. There is a common sense notion of mathematics that exists independent of what people want to believe or agree upon. There are also ways to philosophize about the nature of things in order to frame math as a human construct. I think both views can be simultaneously correct
  - jxdxbx 4y ago
    You can construct a formal system with any axioms you choose. It is not arbitrary that some of these systems turn out to be useful in modeling the world. But there are other systems that are only dry exercises in symbol manipulation that may be of little use to physics or engineering. Or of course they might end up being super important 100 years later. But in the meantime mathematicians might be interested in them anyway.
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  - gilbert_vanova 4y ago
    > I doubt there is a single (professional) engineer that would say something like that. I suspect an engineering professor would be even more compelled to highlight how social consensus is the foundation of everything else that follows. You only have to read the surface layers of this or that performance debate to see how it is unfortunately the case. "Performance" is a fluid term that doesn't mean much of anything on its own -- and people arguing that they've juiced another drop of performance juice from this or that application's fruit are often just talking past each other in terms of priorities or perspective. The symbolic manipulation at the heart of mathematics is a byproduct of language -- another system beholden to social consensus. It's inescapable.
vegetablepotpie 4y ago
I know nothing of OP, or the professor he talked to, but I think they might be talking about the higher level concepts of math. For example, set theory. If set theory allowed self reference you could have set R, a set of sets that do not contain themselves. Would R contain R? It can’t, but it can’t not either. It’s self contradictory. The solution, reached through consensus, was to restrict the definition of the set to not allow sets to reference themselves [1]. [1] https://youtube.com/watch?v=HeQX2HjkcNo https://youtube.com/watch?v=HeQX2HjkcNo
- graycat 4y ago
  The way I learned how to resolve the Russell paradox: Over here on the left in a pile we have the elements we will work with. Now, for the sets, they are made of the elements and are in a separate pile, are over here on the right. Sooo, with this little preliminary step, there is no way to consider the set of all sets that are not elements of themselves. As I recall, there was a paper by Robert Tarjan where he observed that most paradoxes are from self referencing. Soooo, rule out self referencing and will rule out most paradoxes!
mola 4y ago
You got it backwards. 1984 is possible because it's fundemental that some truths are social constructs.
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- zaphar 4y ago
  I would argue that those aren't truths. They need some other term to describe them but truth doesn't really fit the bill. Conflating them with truth leads to weird outcomes in your reasoning. A more accurate term might be stories rather than truth.
- version_five 4y ago
  If Winston and O'Brian both believe O'Brian is levitating, that still doesn't make it actually true. "Sanity is not statistical" as Winston says in the book
SideburnsOfDoom 4y ago
> that 2+2=4 - in the sense that I know for sure, if I take throw two rocks on a pile of two rocks, I'll get a pile of four rocks, not five rocks. That depends on if one of the rocks breaks in half as you throw it onto the rock-pile or not. And also if the resulting piece knocked off is large enough to pass your fuzzy and contextual distinction between "rock" and "pebble". But IMHO, arithmetic such as counting numbers and 2 + 2 = 4 are not part of the natural world. If I have a rock and another rock, I can with minor effort tell them apart: they have different weight, size, shape, density, composition etc. They are each unique individual assemblages of huge numbers of atoms in distinct never-to-be-repeated arrangements. In what way are these 2 unique things "the same" ? If I have an apple and you give me a frog, I have an apple and a frog. They're not the same. If I have apple A and you give me apple B, do I have 2 apples? I have unique apple A and unique apple B. We can pretend that they're the same if you like, but that category is in our thinking, not in the world, and we also know that we can also notice differences between them. tl;dr the natural world is not fungible, but behaving as if it is, is a convenient abstraction for mathematics and commerce, not a property of the natural objects.
- bheadmaster 4y ago
  > tl;dr the natural world is not fungible, but behaving as if it is, is a convenient abstraction for mathematics and commerce, not a property of the natural objects. If it wasn't a property of natural objects (in some way), then how could our predictions work so well in the real world?
  - SideburnsOfDoom 4y ago
    What prediction is that? Are you arguing that two rocks or apples or people are actually "can't tell them part" identical? It works for electrons. But when was the last time that you interacted knowingly with a single electron?
    - bheadmaster 4y ago
      > What prediction is that? For example, all the predictions that make us capable of building skyscrapers that don't fall down for centuries. Does it matter that two bricks are not "the same piece of matter" if our predictions work the same for both of them? In terms of their behavior under particular circumstances, they are the same.
ethanwillis 4y ago
What's a rock?
- bheadmaster 4y ago
  What's a "what's"?
  - ethanwillis 4y ago
    Well for either of us to know, we'd need consensus on language, meaning, words, etc.
    - edgyquant 4y ago
      Nope. The idea of describing an object is built in to humans and likely all mammals.
  - edgyquant 4y ago
    An inquiry for a description of an object. Nothing in language is difficult it’s finding the smallest abstraction to generate all the rules for all language that is. You’re asking a simple grammar question under the impression it’s an unsolved science question.
    - bheadmaster 4y ago
      No, I'm merely pointing out the absurdity of asking "what's X" to a needless extent. Everyone knows what a rock is. Everyone knows what I mean by "throwing two rocks on a pile of two rocks and getting a pile of four rocks" - almost everyone has done it countless times as a child. The "What's a rock" comment is just pointless philosophizing, masquerading as profoundness.
postalrat 4y ago
2+2=4 stops being true when you use a different method of counting.
- rsj_hn 4y ago
  That's like saying "I am five foot tall" stops being true when you use a different definition of "tall" (switch it to weight, for example). This isn't insightful and it's also false. People have agreed on how the plus sign should be defined when it comes to adding two integers, and they've agreed on how to write integers, in which case 2+2 is always four. The only way to change that is to change the meaning of at least one of the four symbols "2", "4", "=", or "+" to some private meaning which no one else shares -- e.g. to distort the language in order to sow confusion, which the use of agreed upon meanings for symbols is designed to eliminate. Moreover this idea that a sentence changes its truth value the moment someone changes the meaning of one of the words in the sentence is not some deep statement or interesting observation, it's just pointing out that language is useful only if people agree on the meaning of the words.
ordu 4y ago
> If everyone in the world believes that 2+2=5, that doesn't make it less true that 2+2=4 - in the sense that I know for sure But not everyone believes that 2+2=5, isn't it? I mean, if you criterion to separate truth from lies is the reality, then now you are talking about a counterfactual reality without proving that this counterfactual reality is possible. So this your statement is unproven, I'd say it cannot be proved. I can argue, that if world believes that 2+2=5 then it makes 2+2=4 to be false. Just think about it. Try to imagine a plausible counterfactual reality where people believe that 2+2=5. They probably would believe that succession of numbers goes like this: 1, 2, 3, 5, 4, 6, 7, 8, 9, 10, ... And in such a counterfactual reality it would be very strange to believe, that 2+2=4. You could if you liked, and you could build a mathematics around it, but you would have a lot of problems of communication with others.
- fspeech 4y ago
  In il nome della rosa William of Baskerville tells us that concepts are signs and words are "signs of signs". In math logic we can define systems of symbols and logical connectives and deductive rules. We can argue for the correctness of a logical system but we can not do it in the same system; we have to go "meta". Similarly a formal system could be a model of something "real", but the correspondence would be beyond mere logic.
uoaei 4y ago
Math doesn't do that, models (including language: a model of communication around which we have already reached consensus) do.

jfengel 4y ago

That's actually an example of what OP was talking about. You have defined + as the operator that mimics what piles of rocks do, and defined numbers as counting rocks. That's only a tiny fraction of what math does. An interesting and useful one, and mathematicians have put a lot of work into studying basic arithmetic. They have expanded out into numerous other forms, some of which turn out to have correspondence to the real world like non-Euclidean geometry. Others turn out to be completely abstract and are merely curiosities. There are an infinite number of them, each containing truths, almost all of them of no interest. Interest is defined by mathematicians, not physics. Even so it turns out to sometimes be useful, such as the beautiful theorems of prime numbers that drive Internet security centuries after they were invented. That is what the OP means. You can make up any axioms you want and prove true theorems. But the hard part is convincing other mathematicians to care.

deleted 4y ago
[deleted]
bheadmaster 4y ago
> But the hard part is convincing other mathematicians to care. My point is that whether other mathematicians care or not is completely irrelevant and doesn't subtract from mathematics' power of predicting phenomena in the real world. Each and every mathematical theory has to be consistent with basic rules of reality - if nothing else, symbolic manipulation relies on basic arithmetic and set theory. Without symbolic manipulation, you can't even express all those "abstract" mathematics - to say that "abstract" mathematics can not have correspondence to the real world is completely false, because of this basic connection. Now that I think about it - claiming that "mathematics is a social consensus" is exactly what I'd expect from a mathematics professor - a person whose whole life is isolated from reality, limited to the rigid structure of academia, and whose whole existence depends on other people caring. I doubt there is a single (professional) engineer that would say something like that.
- ethanwillis 4y ago
- version_five 4y ago
  Reading the discussion, I think you're both right. There is a common sense notion of mathematics that exists independent of what people want to believe or agree upon. There are also ways to philosophize about the nature of things in order to frame math as a human construct. I think both views can be simultaneously correct
- jxdxbx 4y ago
  You can construct a formal system with any axioms you choose. It is not arbitrary that some of these systems turn out to be useful in modeling the world. But there are other systems that are only dry exercises in symbol manipulation that may be of little use to physics or engineering. Or of course they might end up being super important 100 years later. But in the meantime mathematicians might be interested in them anyway.
  - deleted 4y ago
    [deleted]
- deleted 4y ago
  [deleted]
- gilbert_vanova 4y ago
  > I doubt there is a single (professional) engineer that would say something like that. I suspect an engineering professor would be even more compelled to highlight how social consensus is the foundation of everything else that follows. You only have to read the surface layers of this or that performance debate to see how it is unfortunately the case. "Performance" is a fluid term that doesn't mean much of anything on its own -- and people arguing that they've juiced another drop of performance juice from this or that application's fruit are often just talking past each other in terms of priorities or perspective. The symbolic manipulation at the heart of mathematics is a byproduct of language -- another system beholden to social consensus. It's inescapable.

vegetablepotpie 4y ago

I know nothing of OP, or the professor he talked to, but I think they might be talking about the higher level concepts of math. For example, set theory. If set theory allowed self reference you could have set R, a set of sets that do not contain themselves. Would R contain R? It can’t, but it can’t not either. It’s self contradictory. The solution, reached through consensus, was to restrict the definition of the set to not allow sets to reference themselves [1]. [1] https://youtube.com/watch?v=HeQX2HjkcNo https://youtube.com/watch?v=HeQX2HjkcNo

graycat 4y ago
The way I learned how to resolve the Russell paradox: Over here on the left in a pile we have the elements we will work with. Now, for the sets, they are made of the elements and are in a separate pile, are over here on the right. Sooo, with this little preliminary step, there is no way to consider the set of all sets that are not elements of themselves. As I recall, there was a paper by Robert Tarjan where he observed that most paradoxes are from self referencing. Soooo, rule out self referencing and will rule out most paradoxes!

mola 4y ago

You got it backwards. 1984 is possible because it's fundemental that some truths are social constructs.

deleted 4y ago
[deleted]
zaphar 4y ago
I would argue that those aren't truths. They need some other term to describe them but truth doesn't really fit the bill. Conflating them with truth leads to weird outcomes in your reasoning. A more accurate term might be stories rather than truth.
version_five 4y ago
If Winston and O'Brian both believe O'Brian is levitating, that still doesn't make it actually true. "Sanity is not statistical" as Winston says in the book

SideburnsOfDoom 4y ago

> that 2+2=4 - in the sense that I know for sure, if I take throw two rocks on a pile of two rocks, I'll get a pile of four rocks, not five rocks. That depends on if one of the rocks breaks in half as you throw it onto the rock-pile or not. And also if the resulting piece knocked off is large enough to pass your fuzzy and contextual distinction between "rock" and "pebble". But IMHO, arithmetic such as counting numbers and 2 + 2 = 4 are not part of the natural world. If I have a rock and another rock, I can with minor effort tell them apart: they have different weight, size, shape, density, composition etc. They are each unique individual assemblages of huge numbers of atoms in distinct never-to-be-repeated arrangements. In what way are these 2 unique things "the same" ? If I have an apple and you give me a frog, I have an apple and a frog. They're not the same. If I have apple A and you give me apple B, do I have 2 apples? I have unique apple A and unique apple B. We can pretend that they're the same if you like, but that category is in our thinking, not in the world, and we also know that we can also notice differences between them. tl;dr the natural world is not fungible, but behaving as if it is, is a convenient abstraction for mathematics and commerce, not a property of the natural objects.

bheadmaster 4y ago
> tl;dr the natural world is not fungible, but behaving as if it is, is a convenient abstraction for mathematics and commerce, not a property of the natural objects. If it wasn't a property of natural objects (in some way), then how could our predictions work so well in the real world?
- SideburnsOfDoom 4y ago
  What prediction is that? Are you arguing that two rocks or apples or people are actually "can't tell them part" identical? It works for electrons. But when was the last time that you interacted knowingly with a single electron?
  - bheadmaster 4y ago
    > What prediction is that? For example, all the predictions that make us capable of building skyscrapers that don't fall down for centuries. Does it matter that two bricks are not "the same piece of matter" if our predictions work the same for both of them? In terms of their behavior under particular circumstances, they are the same.

ethanwillis 4y ago

What's a rock?

bheadmaster 4y ago
What's a "what's"?
- ethanwillis 4y ago
  Well for either of us to know, we'd need consensus on language, meaning, words, etc.
  - edgyquant 4y ago
    Nope. The idea of describing an object is built in to humans and likely all mammals.
- edgyquant 4y ago
  An inquiry for a description of an object. Nothing in language is difficult it’s finding the smallest abstraction to generate all the rules for all language that is. You’re asking a simple grammar question under the impression it’s an unsolved science question.
  - bheadmaster 4y ago
    No, I'm merely pointing out the absurdity of asking "what's X" to a needless extent. Everyone knows what a rock is. Everyone knows what I mean by "throwing two rocks on a pile of two rocks and getting a pile of four rocks" - almost everyone has done it countless times as a child. The "What's a rock" comment is just pointless philosophizing, masquerading as profoundness.

postalrat 4y ago

2+2=4 stops being true when you use a different method of counting.

rsj_hn 4y ago
That's like saying "I am five foot tall" stops being true when you use a different definition of "tall" (switch it to weight, for example). This isn't insightful and it's also false. People have agreed on how the plus sign should be defined when it comes to adding two integers, and they've agreed on how to write integers, in which case 2+2 is always four. The only way to change that is to change the meaning of at least one of the four symbols "2", "4", "=", or "+" to some private meaning which no one else shares -- e.g. to distort the language in order to sow confusion, which the use of agreed upon meanings for symbols is designed to eliminate. Moreover this idea that a sentence changes its truth value the moment someone changes the meaning of one of the words in the sentence is not some deep statement or interesting observation, it's just pointing out that language is useful only if people agree on the meaning of the words.

ordu 4y ago

> If everyone in the world believes that 2+2=5, that doesn't make it less true that 2+2=4 - in the sense that I know for sure But not everyone believes that 2+2=5, isn't it? I mean, if you criterion to separate truth from lies is the reality, then now you are talking about a counterfactual reality without proving that this counterfactual reality is possible. So this your statement is unproven, I'd say it cannot be proved. I can argue, that if world believes that 2+2=5 then it makes 2+2=4 to be false. Just think about it. Try to imagine a plausible counterfactual reality where people believe that 2+2=5. They probably would believe that succession of numbers goes like this: 1, 2, 3, 5, 4, 6, 7, 8, 9, 10, ... And in such a counterfactual reality it would be very strange to believe, that 2+2=4. You could if you liked, and you could build a mathematics around it, but you would have a lot of problems of communication with others.

fspeech 4y ago
In il nome della rosa William of Baskerville tells us that concepts are signs and words are "signs of signs". In math logic we can define systems of symbols and logical connectives and deductive rules. We can argue for the correctness of a logical system but we can not do it in the same system; we have to go "meta". Similarly a formal system could be a model of something "real", but the correspondence would be beyond mere logic.

uoaei 4y ago

Math doesn't do that, models (including language: a model of communication around which we have already reached consensus) do.