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>Nobody would ever dream of arguing against eurocentrism in number theory. There are strong cultural biases that show up in the history of mathematics. For ins

>Nobody would ever dream of arguing against eurocentrism in number theory. There are strong cultural biases that show up in the history of mathematics. For instance the English mathematics community preferred Newton's notation over Leibniz due to a Anglocenteric bias in English mathematics community despite Newton's notation being clearly inferior. As wikipedia says: >"The priority dispute had an effect of separating English-speaking mathematicians from those in the continental Europe for many years. Only in the 1820s, due to the efforts of the Analytical Society, did Leibnizian analytical calculus become accepted in England." https://en.wikipedia.org/wiki/History_of_calculus#Leibniz https://en.wikipedia.org/wiki/History_of_calculus#Leibniz This change was brought about by the Analytical Society created by Babbage and others to defeat Anglocenteric notation in favor of the better Leibnizian Newton. >If you think an idea is worth teaching just because it came from a certain culture, you must not care if it's right. Consider two axiomatic systems with different starting axioms. They are both internally consistent but may differ widely. How do we choose which ones to teach? Is diversity and scope important to building an objective perspective?

yummyfajitas 10y ago
First of all, it wasn't "clearly inferior" historically. Liebniz' arguments why it was valid were heavily based on infinitesimals and monadology, which were not known at the time to be valid. (In fact, many of Liebniz' arguments weren't valid, although the conclusions turned out to be.) Secondly, if biases exist, one need not argue for diversity in order to achieve it. Liebniz notation didn't win because someone argued that anglos were biased and diversity was needed, it won because mathematical arguments demonstrated it was better. Unfortunately the authors of this piece don't actually make that latter argument.
- EthanHeilman 10y ago
  Lets assume your claim that Newtonian notation was not "clearly inferior"* to an unbiased person of the time, it follows then that teaching both ideas in English Universities might have helped to more quickly determine which notation is more useful. Consider the result for the English Mathematical community if the Analytical Society was never formed. If biases exist then a spectrum of ideas from cultures which hold a different of set bias can be a critical aid in the search for truth. *I disagree with this assumption but it is a hard case to make in either direction and I recognize the value of your perspective.
  - Chris2048 10y ago
    Wouldn't it make more sense to either standardise the notation, or translate papers into both notations? I feel this is a poor analogy to cultural cross pollination: notation is not the same kind of 'idea' as those found in philosophical paper.
    - yummyfajitas 10y ago
      The fundamental dispute was not over the notation, but over whether the notation was misleading. I.e., is df/dx = (df/dz)(dz/dx) a real description of what is happening, and a valid calculus, or just a coincidence that sometimes won't work? Newton had a variety of arguments in favor of why his calculus worked, only some based on infinitesimals. Liebniz just asserted without proof that infinitesimals were fine, used them, and got good results. Additionally, there were a variety of religious arguments mixed into this, most of which are lost in the sands of uninteresting history. I.e., disputes over whether god (the perfect watchmaker) periodically wound his watch or whether he build a perfect watch that never needed winding. For instance, Liebniz believed in noninteracting dualism, but got set up the world so perfectly that the mind and body agreed. (I'm a mathematician and only minimally familiar with these - they have been discarded by history.) These religious arguments did play a role in the debate over infinitesimals, and acceptance of divine coincidences like Liebniz notation - unjustified though it may be - working perfectly all the time.
      - shanacarp 10y ago
        Variations of those arguments exist to this day unresolved in the form of Platonic Realism vs Nominalism. Resolving that argument in some ways is really important to our understanding of physics and certain parts of biology, especially evolution.
      - Chris2048 10y ago
        Then, both factions were fighting over pet bogosities? I believe https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of... and similar methods are used to show equivalence today. The subject seems more insulated from this kind of philosophy.
- altendo 10y ago
  > Liebniz notation didn't win because someone argued that anglos were biased and diversity was needed, it won because mathematical arguments demonstrated it was better. > Unfortunately the authors of this piece don't actually make that latter argument. Is this to imply there is a more-correct philosophy? I have no formal training in philosophy but I feel that to claim one philosophy is objectively better than another is a bit much.
  - yummyfajitas 10y ago
    Yes, there is. Modern philosophy is judged by it's intellectual consistency, the simplicity and intuitiveness of it's underlying principles, and how those underlying principles lead to conclusions that make sense. Many philosophical traditions simply don't measure up. That's not a crack at non-western traditions, most western traditions have also been discarded due to being nonsense. Quite a few more probably should be but are kept alive for non-intellectual reasons.
    - shanacarp 10y ago
      >Yes, there is. Modern philosophy is judged by it's intellectual consistency, the simplicity and intuitiveness of it's underlying principles, and how those underlying principles lead to conclusions that make sense. It is also judged by outcome matters, which is why the west still teaches Foucault and Dedirra, even though they are by far way less consistent than analytical philosophers (who are also taught) One of the reasons that happened if that some correctly constructed Analytical Philosophical thought gets very non-intuitive results that seem to create exceptions, such as ethics of genocide, whereas classic continental philosophy, because of its room to breath, doesn't. Hence why philosophy still has problems to solve to this day
  - shanacarp 10y ago
    >Is this to imply there is a more-correct philosophy? I have no formal training in philosophy but I feel that to claim one philosophy is objectively better than another is a bit much. Quality of thought as better. Internal consistency is but one measure of quality, given that you also want non-intuitive results (EG: Can't justify genocide accidentally with the way ethics is set up, even if all of the pieces of the argument are internally consistent.) This topic overall reminds me I should write to an old friend with a phd in Philosophy and the son of a phd in Philosophy, a great mathematician (pity he didn't go for the phd in that) and a really excellent talmudist when he feels like it... he probably has thoughts on what they are saying.
ricksplat 10y ago
At the risk of sounding facetious - isn't the whole Leibniz versus Newton thing akin to VHS vs Betamax? Considering Leibniz was perhaps superior and certainly published first, I believe Newton's principia was a more complete body of work, more widely read and as a result more widely disseminated. I read somewhere also that Leibniz came with a good bit of (potentially heretical) baggage that might have made it more difficult for his work to find mainstream acceptance. He tried to meet up with John Locke on a couple of occasions to discus his monadic theory of mind but Locke was always "unavailable". Also, worthy of consideration in the wider context of OP article is that both versions of calculus emerged from pretty much the same European cultural milieux - there was much exchange between English and German academia and both came up with it similarly because it was "what was happening at the time".
clavalle 10y ago
>How do we choose which ones to teach? Which one leads to a richer vein of further research? Which one makes better predictions? Which one finds more applications? Diversity and scope can be important only so far as they improve the systems in terms of scientific validity. Your arguments are exactly the ones used by creationists for the purpose of making that internally consistent system seem as valid as the theory of evolution.
- EthanHeilman 10y ago
  >Your arguments are exactly the ones used by creationists for the purpose of making that internally consistent system seem as valid as the theory of evolution. Science is different than Mathematics in that science must be both internally and externally consistent.
  - clavalle 10y ago
    Fair enough, but mathematics is robustly internally consistent. If a mathematical idea leads to the same results as another mathematical idea with no contradiction it is considered true and is celebrated. These ideas also need to avoid running afoul of fundamental axioms. I don't know much about philosophy but it seems like ideas lead directly to irreconcilable contradictions should be either thrown out or isolated into their own system (if the resulting system is rich enough) and those that fit into a system and lead to new paths of insight should be included in that system. Contradictions between systems should be explored but it seems that expanding an already rich system should be preferred to forcing contradictions into a coherent system or weakening working ideas to make room for ideas that don't lead anywhere new. Maybe that is what the author is advocating -- separate internally consistent systems and a relinquishing of the umbrella term Philosophy to make room for separate systems. But the title -- 'If Philosophy Won’t Diversify, Let’s Call It What It Really Is' seems to suggest a preference for Philosophy to diversify, to throw everything under the same big tent, contradictions and all, which I really don't think is helpful.
Chris2048 10y ago
The value added here was one culture dropped its inferior notational difference. There was no clear "cross-pollination", as each culture preferred its own notation, until reform came along. What is the equivalent in philosophical cross-pollination? Are some philosophies going to be dropped in favour of better ones? This doesn't even happen withing a lot of western cliques. The nearest equivalent to notational reform I can think of is terminology/lexical reform, maybe, though there are a lot of ambiguities that confound this (in contrast to mathematics). In fact, it might even imply that anglo-centrism is a good thing, due to the standard common language.
- gshubert17 10y ago
  I was exposed to both notations in college when I was studying math and physics. The mathematicians preferred Leibnitz's notation and so did the physicists for some things. But we used Newton's dot or prime notation for derivatives in mechanics and for some differential equations. It seems to me that Newton's notation and terminology lost market share but wasn't completely dropped.
shanacarp 10y ago
>Consider two axiomatic systems with different starting axioms. They are both internally consistent but may differ widely. How do we choose which ones to teach? Is diversity and scope important to building an objective perspective? If we want to evaluate the axioms, you better teach both. Internal consistency is just that - internal to that system. Metaphilosophy would want to judge both, but if you never teach both, how would you judge?

yummyfajitas 10y ago

First of all, it wasn't "clearly inferior" historically. Liebniz' arguments why it was valid were heavily based on infinitesimals and monadology, which were not known at the time to be valid. (In fact, many of Liebniz' arguments weren't valid, although the conclusions turned out to be.) Secondly, if biases exist, one need not argue for diversity in order to achieve it. Liebniz notation didn't win because someone argued that anglos were biased and diversity was needed, it won because mathematical arguments demonstrated it was better. Unfortunately the authors of this piece don't actually make that latter argument.

EthanHeilman 10y ago
Lets assume your claim that Newtonian notation was not "clearly inferior"* to an unbiased person of the time, it follows then that teaching both ideas in English Universities might have helped to more quickly determine which notation is more useful. Consider the result for the English Mathematical community if the Analytical Society was never formed. If biases exist then a spectrum of ideas from cultures which hold a different of set bias can be a critical aid in the search for truth. *I disagree with this assumption but it is a hard case to make in either direction and I recognize the value of your perspective.
- Chris2048 10y ago
  Wouldn't it make more sense to either standardise the notation, or translate papers into both notations? I feel this is a poor analogy to cultural cross pollination: notation is not the same kind of 'idea' as those found in philosophical paper.
  - yummyfajitas 10y ago
    The fundamental dispute was not over the notation, but over whether the notation was misleading. I.e., is df/dx = (df/dz)(dz/dx) a real description of what is happening, and a valid calculus, or just a coincidence that sometimes won't work? Newton had a variety of arguments in favor of why his calculus worked, only some based on infinitesimals. Liebniz just asserted without proof that infinitesimals were fine, used them, and got good results. Additionally, there were a variety of religious arguments mixed into this, most of which are lost in the sands of uninteresting history. I.e., disputes over whether god (the perfect watchmaker) periodically wound his watch or whether he build a perfect watch that never needed winding. For instance, Liebniz believed in noninteracting dualism, but got set up the world so perfectly that the mind and body agreed. (I'm a mathematician and only minimally familiar with these - they have been discarded by history.) These religious arguments did play a role in the debate over infinitesimals, and acceptance of divine coincidences like Liebniz notation - unjustified though it may be - working perfectly all the time.
    - shanacarp 10y ago
      Variations of those arguments exist to this day unresolved in the form of Platonic Realism vs Nominalism. Resolving that argument in some ways is really important to our understanding of physics and certain parts of biology, especially evolution.
    - Chris2048 10y ago
      Then, both factions were fighting over pet bogosities? I believe https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of... and similar methods are used to show equivalence today. The subject seems more insulated from this kind of philosophy.
altendo 10y ago
> Liebniz notation didn't win because someone argued that anglos were biased and diversity was needed, it won because mathematical arguments demonstrated it was better. > Unfortunately the authors of this piece don't actually make that latter argument. Is this to imply there is a more-correct philosophy? I have no formal training in philosophy but I feel that to claim one philosophy is objectively better than another is a bit much.
- yummyfajitas 10y ago
  Yes, there is. Modern philosophy is judged by it's intellectual consistency, the simplicity and intuitiveness of it's underlying principles, and how those underlying principles lead to conclusions that make sense. Many philosophical traditions simply don't measure up. That's not a crack at non-western traditions, most western traditions have also been discarded due to being nonsense. Quite a few more probably should be but are kept alive for non-intellectual reasons.
  - shanacarp 10y ago
    >Yes, there is. Modern philosophy is judged by it's intellectual consistency, the simplicity and intuitiveness of it's underlying principles, and how those underlying principles lead to conclusions that make sense. It is also judged by outcome matters, which is why the west still teaches Foucault and Dedirra, even though they are by far way less consistent than analytical philosophers (who are also taught) One of the reasons that happened if that some correctly constructed Analytical Philosophical thought gets very non-intuitive results that seem to create exceptions, such as ethics of genocide, whereas classic continental philosophy, because of its room to breath, doesn't. Hence why philosophy still has problems to solve to this day
- shanacarp 10y ago
  >Is this to imply there is a more-correct philosophy? I have no formal training in philosophy but I feel that to claim one philosophy is objectively better than another is a bit much. Quality of thought as better. Internal consistency is but one measure of quality, given that you also want non-intuitive results (EG: Can't justify genocide accidentally with the way ethics is set up, even if all of the pieces of the argument are internally consistent.) This topic overall reminds me I should write to an old friend with a phd in Philosophy and the son of a phd in Philosophy, a great mathematician (pity he didn't go for the phd in that) and a really excellent talmudist when he feels like it... he probably has thoughts on what they are saying.

ricksplat 10y ago

At the risk of sounding facetious - isn't the whole Leibniz versus Newton thing akin to VHS vs Betamax? Considering Leibniz was perhaps superior and certainly published first, I believe Newton's principia was a more complete body of work, more widely read and as a result more widely disseminated. I read somewhere also that Leibniz came with a good bit of (potentially heretical) baggage that might have made it more difficult for his work to find mainstream acceptance. He tried to meet up with John Locke on a couple of occasions to discus his monadic theory of mind but Locke was always "unavailable". Also, worthy of consideration in the wider context of OP article is that both versions of calculus emerged from pretty much the same European cultural milieux - there was much exchange between English and German academia and both came up with it similarly because it was "what was happening at the time".

clavalle 10y ago

>How do we choose which ones to teach? Which one leads to a richer vein of further research? Which one makes better predictions? Which one finds more applications? Diversity and scope can be important only so far as they improve the systems in terms of scientific validity. Your arguments are exactly the ones used by creationists for the purpose of making that internally consistent system seem as valid as the theory of evolution.

EthanHeilman 10y ago
>Your arguments are exactly the ones used by creationists for the purpose of making that internally consistent system seem as valid as the theory of evolution. Science is different than Mathematics in that science must be both internally and externally consistent.
- clavalle 10y ago
  Fair enough, but mathematics is robustly internally consistent. If a mathematical idea leads to the same results as another mathematical idea with no contradiction it is considered true and is celebrated. These ideas also need to avoid running afoul of fundamental axioms. I don't know much about philosophy but it seems like ideas lead directly to irreconcilable contradictions should be either thrown out or isolated into their own system (if the resulting system is rich enough) and those that fit into a system and lead to new paths of insight should be included in that system. Contradictions between systems should be explored but it seems that expanding an already rich system should be preferred to forcing contradictions into a coherent system or weakening working ideas to make room for ideas that don't lead anywhere new. Maybe that is what the author is advocating -- separate internally consistent systems and a relinquishing of the umbrella term Philosophy to make room for separate systems. But the title -- 'If Philosophy Won’t Diversify, Let’s Call It What It Really Is' seems to suggest a preference for Philosophy to diversify, to throw everything under the same big tent, contradictions and all, which I really don't think is helpful.

Chris2048 10y ago

The value added here was one culture dropped its inferior notational difference. There was no clear "cross-pollination", as each culture preferred its own notation, until reform came along. What is the equivalent in philosophical cross-pollination? Are some philosophies going to be dropped in favour of better ones? This doesn't even happen withing a lot of western cliques. The nearest equivalent to notational reform I can think of is terminology/lexical reform, maybe, though there are a lot of ambiguities that confound this (in contrast to mathematics). In fact, it might even imply that anglo-centrism is a good thing, due to the standard common language.

gshubert17 10y ago
I was exposed to both notations in college when I was studying math and physics. The mathematicians preferred Leibnitz's notation and so did the physicists for some things. But we used Newton's dot or prime notation for derivatives in mechanics and for some differential equations. It seems to me that Newton's notation and terminology lost market share but wasn't completely dropped.

shanacarp 10y ago

>Consider two axiomatic systems with different starting axioms. They are both internally consistent but may differ widely. How do we choose which ones to teach? Is diversity and scope important to building an objective perspective? If we want to evaluate the axioms, you better teach both. Internal consistency is just that - internal to that system. Metaphilosophy would want to judge both, but if you never teach both, how would you judge?