7 ms·

And this what science is about. I'm wrong and I'll say so. I've been proved wrong, because I was wrong.

by DrBazza 9y ago

dekhn 9y ago
math, not science
- pwdisswordfish 9y ago
  Pedantic distinction that exists only in English.
  - quirkot 9y ago
    This is correct. In another language we'd refer to the distinction with a different word
    - wsy 9y ago
      In German, "Wissenschaft" includes all kinds of academic knowledge production, regardless if mathematics, natural sciences ("Naturwissenschaften"), humanities ("Geisteswissenschaften"), or engineering ("Ingenieurwissenschaften"). So, when translating the remark to German, it would be difficult to come up with a "different word" for the distinction. For the collectors of useless knowledge: for a while, there was an attempt to establish the term "Strukturwissenschaften" (science of structures), covering mathematics, computer science, and system theory. But that term did not really stick.
  - lmkg 9y ago
    The distinction is significant, despite their relationship they're from totally different universes. Science is empirical: truth is validated by observation of the real world. Math is logical: truth is validated purely by internal consistency.
    - chestervonwinch 9y ago
      Yea well, that's just like, if you're a mathematical formalist, man. edit: I was merely pointing out that the parent's comment was an opinion based the branch of mathematical philosophy that the commenter appears to subscribe. I thought I'd add some humor by wrapping it in a Big Lebowski reference. And now I've explained away any attempt at humor ...
    - pash 9y ago
      The idea that the domain of science is restricted to falsifiable theories, and is therefore fundamentally empirical, dates only to the early part of the twentieth century. Since the Enlightenment, and also in the much older Western classical tradition, the term science (and its closest translations in Greek, Latin, German, French, and many other languages) has referred much more broadly than that restriction permits, to all fields of knowledge established in a rigorous manner, whether deductive or inductive. It's in that sense that Gauss crowned mathematics the "Königin der Wissenschaften," the Queen of the Sciences. And indeed in German the term Wissenschaft in ordinary usage still includes mathematics, referring to all knowledge amenable to investigation (as opposed to received knoweldge) [0]. The terms for science in many other Western languages also retain this broader meaning to a greater extent that does contemporary English, and the same is true in many non-Western cultures as well. The problem here is mainly a terminological one: in English we've found it useful to have a word that refers specifically to the Popperian notion of what counts as science (mainly, I think, to gain the power easily to distinguish "scientific" ideas from "non-scientific" bunk), but we haven't come up with a new term for the older, broader meaning of science as rigorously establishable knoweldge. I should also point out that Popperian science involves plenty of deductive reasoning—we call it theory—so while it is true that Popper's notion of science requires empiricism, it is not correct to identify it with the distinction between empirical and deductive reasoning. At the same time, the practice of mathematics certainly does involve empirical reasoning, often resulting in a conjecture whose truth is subsequently subjected to rigorous deductive arguments. (There is a section in the English Wikipedia article on mathematics that discusses this a bit more [1].) 0. https://en.wikipedia.org/wiki/Wissenschaft https://en.wikipedia.org/wiki/Wissenschaft 1. https://en.wikipedia.org/wiki/Mathematics#Mathematics_as_science https://en.wikipedia.org/wiki/Mathematics#Mathematics_as_sci...
  - xrange 9y ago
    Interesting. I'd like to learn more about this. Any pointers to how other languages and cultures don't distinguish between math and science? Does it apply to other things like the difference between induction and deduction as well?
    - dvt 9y ago
      There are no pointers because just about every culture distinguishes between empirical and logical truths. I'm not sure if he's just being cute, but there's a very clear philosophical difference between math and science. This is not a pedantic distinction. (Someone from reddit that "loves science" might think so, though.)
      - wsy 9y ago
        > just about every culture distinguishes between empirical and logical truths Actually, having this distinction is quite young even in our own western culture: depending what exactly you mean, ~300 years (Kants distinction between "Synthetisches Urteil" vs. "Analytisches Urteil"), or 150 years(Gottlob Frege's 'invention' of formal logic). And modern philosophy of science is already doubting it again (e.g., W.V. Quine).
        dvt 9y ago
        Nope. Descartes, Leibniz and Spinoza were rationalists. Hume, Berkeley, Locke were empiricists. This distinction wasn't formalized until relatively recently, but the intuition is very old. In antiquity, Pythagoras and Plato fall in the former camp; Serapion of Alexandria and Philinus of Cos fall in the latter.
        wsy 9y ago
        I have no expertise in ancient philosophy, so can't comment on these philosophers. Is 'cogito ergo sum' a logical or an empirical truth? For Descartes it was a logical truth (undoubtably true). However, from the point of view of Hume, it must be viewed as empirical truth, because it is based on an empirical observation. So if even philosophers of that time couldn't agree on the distinction between logical and empirical truth, I think I can safely conclude that this distinction was not at all an established part of the Western culture at that point of time. Rationalists vs. Empiricists is what we call these groups of philosophers now, it is not that they grouped themselves in two schools of 'logical truth' vs. 'empirical truth'. In fact, Hume most probably believed that his own philosophical insights can be derived just by thinking, so they must be logically true. And still, this is quite different from what we today call logically true (i.e., formally provable).
- alexanderstears 9y ago
  They both share the view that explanations/hypotheses can either be retained or rejected (and better explanations can retained). Math is unique in that the standard of proof is more comprehensive and the domain is bounded but this is a good example of someone employing the scientific method and exhibiting good scientific community values.
  - xyzzyz 9y ago
    No, mathematics works completely different than science. In both math and science, you do some observations, and then formulate theory that explain some of these observations. However, in science, you then design experiments and predict the results based on your theory, taking care to ensure that the experiments distinguish between the reality in which your theory holds, and the one where it doesn't. In math you might also do that as a sanity check, but that's not the point. In math, the point is to actually _prove_ your theory to be correct, something which is absolutely impossible to do in science, where you can only prove theory to be _wrong_.
    - deleted 9y ago
      [deleted]
    - alexanderstears 9y ago
      >taking care to ensure that the experiments distinguish between the reality in which your theory holds, and the one where it doesn't. I get the impression that you're thinking of specific domains within science. Many theories are contextualized within something (e.g a theory of why there's lightning might be more domain specific than a theory of electromagnetism). I don't disagree that things are proved within mathematical systems and scientific claims / hypotheses are categorically different (and weaker, I suppose). But the author made a claim, discovered an error in their claim, and alerted the community to his mistake and signaled their intention to address it. That's not behavior that's exclusive to mathematics. Many scientists have made claims that they think the evidence supports, and then they realize that something wasn't correct, and they make the correction. Cartographers / mariners used to think that California was an island: https://en.wikipedia.org/wiki/Island_of_California https://en.wikipedia.org/wiki/Island_of_California They had solid evidence to think that's the case but then eventually they realized the mistake and they've corrected it.
- wsy 9y ago
  > math, not science While true, it is an artefact of the usage of the term science in English. For example, theoretical computer science is no science according to that distinction between math and science.
  - dekhn 9y ago
    yes, CS is misnamed.
    - gleenn 9y ago
      I'll probably get lambasted with all the pedants coming out, but I chuckled when someone pointed out that most majors in college with the word science in them aren't really science i.e. Political Science, Computer Science, Sports Science, contrasted with i.e. Physics, Chemistry, etc.
      - pmyteh 9y ago
        In Britain "political science" is strictly the process of applying (social) scientific approaches to the study of politics, with the rest of the discipline simply called "politics". Nobody trusts the political scientists, sadly. There are too many bloody variables and collecting good enough data to build cumulative models is hard. We persevere, though.
        KGIII 9y ago
        What do they do for reproducibility? I'm pretty sure those types of things, such as social sciences, can be tested and reproduced, but I'd imagine there are ethical concerns. How do you reproduce Hitler's affect on politics and not end up on the receiving end of a tribunal in Hague?
        Armisael16 9y ago
        The same way you reproduce things in astrophysics or epidemiology: natural experiments.
- Govannon 9y ago
  Formal Science?
- omg_ketchup 9y ago
  I was always told that math is the most exact science.
- gkya 9y ago
  No need to be pedantic as the comment you're responding to is not really referring to something particular to mathematics or natural sciences. And even if it did, whether or not maths is a science is a philosophical issue, not an invariable truth.
- danielam 9y ago
  Math is a science, just not an empirical science. It is a formal science.
  - eighthnate 9y ago
    Not in the general sense that people use. Everything is a "science" just like everything is a "philosophy". In general day to day usage, science = natural/empirical science.

And this what science is about. I'm wrong and I'll say so. I've been proved wrong, because I was wrong.

dekhn 9y ago

math, not science

pwdisswordfish 9y ago
Pedantic distinction that exists only in English.
- quirkot 9y ago
  This is correct. In another language we'd refer to the distinction with a different word
  - wsy 9y ago
    In German, "Wissenschaft" includes all kinds of academic knowledge production, regardless if mathematics, natural sciences ("Naturwissenschaften"), humanities ("Geisteswissenschaften"), or engineering ("Ingenieurwissenschaften"). So, when translating the remark to German, it would be difficult to come up with a "different word" for the distinction. For the collectors of useless knowledge: for a while, there was an attempt to establish the term "Strukturwissenschaften" (science of structures), covering mathematics, computer science, and system theory. But that term did not really stick.
- lmkg 9y ago
  The distinction is significant, despite their relationship they're from totally different universes. Science is empirical: truth is validated by observation of the real world. Math is logical: truth is validated purely by internal consistency.
  - chestervonwinch 9y ago
    Yea well, that's just like, if you're a mathematical formalist, man. edit: I was merely pointing out that the parent's comment was an opinion based the branch of mathematical philosophy that the commenter appears to subscribe. I thought I'd add some humor by wrapping it in a Big Lebowski reference. And now I've explained away any attempt at humor ...
  - pash 9y ago
    The idea that the domain of science is restricted to falsifiable theories, and is therefore fundamentally empirical, dates only to the early part of the twentieth century. Since the Enlightenment, and also in the much older Western classical tradition, the term science (and its closest translations in Greek, Latin, German, French, and many other languages) has referred much more broadly than that restriction permits, to all fields of knowledge established in a rigorous manner, whether deductive or inductive. It's in that sense that Gauss crowned mathematics the "Königin der Wissenschaften," the Queen of the Sciences. And indeed in German the term Wissenschaft in ordinary usage still includes mathematics, referring to all knowledge amenable to investigation (as opposed to received knoweldge) [0]. The terms for science in many other Western languages also retain this broader meaning to a greater extent that does contemporary English, and the same is true in many non-Western cultures as well. The problem here is mainly a terminological one: in English we've found it useful to have a word that refers specifically to the Popperian notion of what counts as science (mainly, I think, to gain the power easily to distinguish "scientific" ideas from "non-scientific" bunk), but we haven't come up with a new term for the older, broader meaning of science as rigorously establishable knoweldge. I should also point out that Popperian science involves plenty of deductive reasoning—we call it theory—so while it is true that Popper's notion of science requires empiricism, it is not correct to identify it with the distinction between empirical and deductive reasoning. At the same time, the practice of mathematics certainly does involve empirical reasoning, often resulting in a conjecture whose truth is subsequently subjected to rigorous deductive arguments. (There is a section in the English Wikipedia article on mathematics that discusses this a bit more [1].) 0. https://en.wikipedia.org/wiki/Wissenschaft https://en.wikipedia.org/wiki/Wissenschaft 1. https://en.wikipedia.org/wiki/Mathematics#Mathematics_as_science https://en.wikipedia.org/wiki/Mathematics#Mathematics_as_sci...
- xrange 9y ago
  Interesting. I'd like to learn more about this. Any pointers to how other languages and cultures don't distinguish between math and science? Does it apply to other things like the difference between induction and deduction as well?
  - dvt 9y ago
    There are no pointers because just about every culture distinguishes between empirical and logical truths. I'm not sure if he's just being cute, but there's a very clear philosophical difference between math and science. This is not a pedantic distinction. (Someone from reddit that "loves science" might think so, though.)
    - wsy 9y ago
      > just about every culture distinguishes between empirical and logical truths Actually, having this distinction is quite young even in our own western culture: depending what exactly you mean, ~300 years (Kants distinction between "Synthetisches Urteil" vs. "Analytisches Urteil"), or 150 years(Gottlob Frege's 'invention' of formal logic). And modern philosophy of science is already doubting it again (e.g., W.V. Quine).
      - dvt 9y ago
        Nope. Descartes, Leibniz and Spinoza were rationalists. Hume, Berkeley, Locke were empiricists. This distinction wasn't formalized until relatively recently, but the intuition is very old. In antiquity, Pythagoras and Plato fall in the former camp; Serapion of Alexandria and Philinus of Cos fall in the latter.
        wsy 9y ago
        I have no expertise in ancient philosophy, so can't comment on these philosophers. Is 'cogito ergo sum' a logical or an empirical truth? For Descartes it was a logical truth (undoubtably true). However, from the point of view of Hume, it must be viewed as empirical truth, because it is based on an empirical observation. So if even philosophers of that time couldn't agree on the distinction between logical and empirical truth, I think I can safely conclude that this distinction was not at all an established part of the Western culture at that point of time. Rationalists vs. Empiricists is what we call these groups of philosophers now, it is not that they grouped themselves in two schools of 'logical truth' vs. 'empirical truth'. In fact, Hume most probably believed that his own philosophical insights can be derived just by thinking, so they must be logically true. And still, this is quite different from what we today call logically true (i.e., formally provable).
alexanderstears 9y ago
They both share the view that explanations/hypotheses can either be retained or rejected (and better explanations can retained). Math is unique in that the standard of proof is more comprehensive and the domain is bounded but this is a good example of someone employing the scientific method and exhibiting good scientific community values.
- xyzzyz 9y ago
  No, mathematics works completely different than science. In both math and science, you do some observations, and then formulate theory that explain some of these observations. However, in science, you then design experiments and predict the results based on your theory, taking care to ensure that the experiments distinguish between the reality in which your theory holds, and the one where it doesn't. In math you might also do that as a sanity check, but that's not the point. In math, the point is to actually _prove_ your theory to be correct, something which is absolutely impossible to do in science, where you can only prove theory to be _wrong_.
  - deleted 9y ago
    [deleted]
  - alexanderstears 9y ago
    >taking care to ensure that the experiments distinguish between the reality in which your theory holds, and the one where it doesn't. I get the impression that you're thinking of specific domains within science. Many theories are contextualized within something (e.g a theory of why there's lightning might be more domain specific than a theory of electromagnetism). I don't disagree that things are proved within mathematical systems and scientific claims / hypotheses are categorically different (and weaker, I suppose). But the author made a claim, discovered an error in their claim, and alerted the community to his mistake and signaled their intention to address it. That's not behavior that's exclusive to mathematics. Many scientists have made claims that they think the evidence supports, and then they realize that something wasn't correct, and they make the correction. Cartographers / mariners used to think that California was an island: https://en.wikipedia.org/wiki/Island_of_California https://en.wikipedia.org/wiki/Island_of_California They had solid evidence to think that's the case but then eventually they realized the mistake and they've corrected it.
wsy 9y ago
> math, not science While true, it is an artefact of the usage of the term science in English. For example, theoretical computer science is no science according to that distinction between math and science.
- dekhn 9y ago
  yes, CS is misnamed.
  - gleenn 9y ago
    I'll probably get lambasted with all the pedants coming out, but I chuckled when someone pointed out that most majors in college with the word science in them aren't really science i.e. Political Science, Computer Science, Sports Science, contrasted with i.e. Physics, Chemistry, etc.
    - pmyteh 9y ago
      In Britain "political science" is strictly the process of applying (social) scientific approaches to the study of politics, with the rest of the discipline simply called "politics". Nobody trusts the political scientists, sadly. There are too many bloody variables and collecting good enough data to build cumulative models is hard. We persevere, though.
      - KGIII 9y ago
        What do they do for reproducibility? I'm pretty sure those types of things, such as social sciences, can be tested and reproduced, but I'd imagine there are ethical concerns. How do you reproduce Hitler's affect on politics and not end up on the receiving end of a tribunal in Hague?
        Armisael16 9y ago
        The same way you reproduce things in astrophysics or epidemiology: natural experiments.
Govannon 9y ago
Formal Science?
omg_ketchup 9y ago
I was always told that math is the most exact science.
gkya 9y ago
No need to be pedantic as the comment you're responding to is not really referring to something particular to mathematics or natural sciences. And even if it did, whether or not maths is a science is a philosophical issue, not an invariable truth.
danielam 9y ago
Math is a science, just not an empirical science. It is a formal science.
- eighthnate 9y ago
  Not in the general sense that people use. Everything is a "science" just like everything is a "philosophy". In general day to day usage, science = natural/empirical science.