29 ms·

Pedantic distinction that exists only in English.

by pwdisswordfish 9y ago

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).

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).