3 ms·

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

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.

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.