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IIRC the moral of the original 2+2=5 guy's comment was "if someone reaches a different conclusion than you, ask them under which axioms they reached that conclu

IIRC the moral of the original 2+2=5 guy's comment was "if someone reaches a different conclusion than you, ask them under which axioms they reached that conclusion." I think that's valuable advice. Note that he didn't say you have to accept their axioms. Clearly working in arithmetic modulo 1 is meaningless in most circumstances, and you can criticize that. But if you're not reasoning under the same axioms, you cannot have a productive discussion.

Tainnor 6y ago
A bit late, but are you referring to this Twitter thread by any chance? https://mobile.twitter.com/kareem_carr/status/1289724475609501697 https://mobile.twitter.com/kareem_carr/status/12897244756095... If so, then the argument he makes is totally braindead. He doesn't even consider special algebraic structures or anything. He's just coming up with the most obvious observation ever: if your mathematical model doesn't match the reality or asks the wrong questions, then the results are worthless. This is probably obvious to any high school student but that's certainly no reason to run around and say that 2+2=5. In any case, there is zero mathematical insight there, he doesn't even make a mathematical argument for it, and the "I am a former mathematician" part only serves to distract from that fact. I could go onto an entire different rant about his infinity argument and how mathematics seemingly haven't figured out how to work with infinity "naturally" (I don't know what he means by naturally, but they certainly have figured out how to work with it precisely), but let's leave it at that.
Tainnor 6y ago
Sure, this is true. But it's also true that some people just like shifting the goal posts or redefining terms whenever it suits them (not in mathematics, outside of it, that is). So in terms of a productive discussion, saying 2+2=5 without context and then backtracking and saying "well but I'm talking about Z/Z (or R/Z, see uncle comment)" would be kind of annoying and it's not generally what mathematicians do. I think this is one of the fascinating and difficult aspects of maths: On the one hand, once you fix your axioms, there is no way in hell you can avoid the conclusions - they might be hard to find (sometimes even impossible to find), but if you find and verify them, they are unmistakably true. This can turn off some people that are more used to thinking about everything being just shades of gray and there always being multiple valid opinions. Maths is the subject where you can't just make up your mind, the evidence when you're wrong is deafening. On the other hand, real maths can also turn off some of the more OCD-ish kind of people that think maths is all about the one single truth and everyone agreeing about everything, whereas maths is infinitely malleable and you can say things like "what if the parallel axiom is wrong" or "what if negative numbers have square roots" and even if it sounds silly, you can create proper maths out of it. If you've ever seen people with only high school maths knowledge arguing passionately online about the correct order of operations or whether the square root of -1 is i or -i (or, in another context, Grammar nazis), you know the kind of people I mean.
- ookdatnog 6y ago
  I think mismatched-axioms misunderstandings happen all the time and it really is a useful mental model to ask people about their axioms. In fact, I think it's even helpful when people are arguing in bad faith. If they have to state their axioms you pin them down and there are then at least some things they can't redefine on the fly. I think even really high profile debates suffer from mismatched-axioms misunderstandings, such as the abortion debate. For instance, I think a lot of people have very different definitions of what constitutes a person. You're probably not going to have a meaningful discussion about abortion if you disagree about that, you probably have to argue about the definition of personhood first. I think your characterization of maths is spot-on and most people don't understand what "mathematical truth" means. But my impression is that the 2+2=5 guy understands all of this (I think he was a maths PhD student too) and his point was completely valid, including its application outside of mathematics. The reactionaries who caricaturized his argument, however, don't understand any of this and believe he was making a different point entirely, namely that all truth is relative and that every person's point of view is valid. Of course, this misunderstanding is on them.
  - Tainnor 6y ago
    I don't doubt that the guy with a maths PhD understood the mathematical content. And I would even go farther than to say that many disagreements are based on different axioms. Many disagreements are even due to different definitions (such as "free will"). I think that was one of the key points of late Wittgenstein. So yes, in many cases, laying out the assumptions carefully is a good idea, I agree. I just didn't think 2+2=5 was the best example.
    - ookdatnog 6y ago
      Yes, and perhaps more importantly, Twitter seems like the wrong forum to bring up such a subtle point. Especially in a political debate where you have hordes of people who will simultaneously not understand what you're saying and be very eager to turn your argument into a viral caricature.

Tainnor 6y ago

A bit late, but are you referring to this Twitter thread by any chance? https://mobile.twitter.com/kareem_carr/status/1289724475609501697 https://mobile.twitter.com/kareem_carr/status/12897244756095... If so, then the argument he makes is totally braindead. He doesn't even consider special algebraic structures or anything. He's just coming up with the most obvious observation ever: if your mathematical model doesn't match the reality or asks the wrong questions, then the results are worthless. This is probably obvious to any high school student but that's certainly no reason to run around and say that 2+2=5. In any case, there is zero mathematical insight there, he doesn't even make a mathematical argument for it, and the "I am a former mathematician" part only serves to distract from that fact. I could go onto an entire different rant about his infinity argument and how mathematics seemingly haven't figured out how to work with infinity "naturally" (I don't know what he means by naturally, but they certainly have figured out how to work with it precisely), but let's leave it at that.

Tainnor 6y ago

Sure, this is true. But it's also true that some people just like shifting the goal posts or redefining terms whenever it suits them (not in mathematics, outside of it, that is). So in terms of a productive discussion, saying 2+2=5 without context and then backtracking and saying "well but I'm talking about Z/Z (or R/Z, see uncle comment)" would be kind of annoying and it's not generally what mathematicians do. I think this is one of the fascinating and difficult aspects of maths: On the one hand, once you fix your axioms, there is no way in hell you can avoid the conclusions - they might be hard to find (sometimes even impossible to find), but if you find and verify them, they are unmistakably true. This can turn off some people that are more used to thinking about everything being just shades of gray and there always being multiple valid opinions. Maths is the subject where you can't just make up your mind, the evidence when you're wrong is deafening. On the other hand, real maths can also turn off some of the more OCD-ish kind of people that think maths is all about the one single truth and everyone agreeing about everything, whereas maths is infinitely malleable and you can say things like "what if the parallel axiom is wrong" or "what if negative numbers have square roots" and even if it sounds silly, you can create proper maths out of it. If you've ever seen people with only high school maths knowledge arguing passionately online about the correct order of operations or whether the square root of -1 is i or -i (or, in another context, Grammar nazis), you know the kind of people I mean.

ookdatnog 6y ago
I think mismatched-axioms misunderstandings happen all the time and it really is a useful mental model to ask people about their axioms. In fact, I think it's even helpful when people are arguing in bad faith. If they have to state their axioms you pin them down and there are then at least some things they can't redefine on the fly. I think even really high profile debates suffer from mismatched-axioms misunderstandings, such as the abortion debate. For instance, I think a lot of people have very different definitions of what constitutes a person. You're probably not going to have a meaningful discussion about abortion if you disagree about that, you probably have to argue about the definition of personhood first. I think your characterization of maths is spot-on and most people don't understand what "mathematical truth" means. But my impression is that the 2+2=5 guy understands all of this (I think he was a maths PhD student too) and his point was completely valid, including its application outside of mathematics. The reactionaries who caricaturized his argument, however, don't understand any of this and believe he was making a different point entirely, namely that all truth is relative and that every person's point of view is valid. Of course, this misunderstanding is on them.
- Tainnor 6y ago
  I don't doubt that the guy with a maths PhD understood the mathematical content. And I would even go farther than to say that many disagreements are based on different axioms. Many disagreements are even due to different definitions (such as "free will"). I think that was one of the key points of late Wittgenstein. So yes, in many cases, laying out the assumptions carefully is a good idea, I agree. I just didn't think 2+2=5 was the best example.
  - ookdatnog 6y ago
    Yes, and perhaps more importantly, Twitter seems like the wrong forum to bring up such a subtle point. Especially in a political debate where you have hordes of people who will simultaneously not understand what you're saying and be very eager to turn your argument into a viral caricature.