[xrange]

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?

[mrighele]

In Italy math is considered generally part of science. In fact here at the universities math is part of "Mathematical, Physical and Natural Sciences Faculty" (roughly translated).

I am a bit surprised of the distinction; the term science comes from latin "scientia" which roughly means knowledge, so at least historically it was correct to consider math a science. Maybe it is a more recent (or just English) thing ?

[ajuc]

In Polish the word for science is "nauka" (noun from verb nauczyć = to finish learning/teaching), and it also covers math. People still obviously understand the differences and there are more specialized (almost never used [1]) terms like nauka matematyczna and nauka empiryczna (doświadczalna), we just don't see the reason to specifically say "science other than math" very often, so unless you're talking about philosophy of science you'll just say nauka and be done with it.

It's like when you're talking about batteries in Tesla you don't specify they are reachargeable every time you use the word batteries.

I used this example, because the same difference in language works the other way for batteries. English has batteries (unsepcified) and rechargeable or non-rechargeable batteries. Polish has baterie (always non-rechargeable), and akumulatory (always rechargeable), and no general word for both, so you always specify which ones these are.

[1] Much more common distinction is "nauki ścisłe" (exact sciences - math, physics, etc) vs the rest.

As for induction and deduction I understand the terms and they exist in Polish (indukcja and dedukcja), but I don't see the point. Both are used in math and in sciences?

[dvt]

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]

> 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]

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]

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).

[dvt]

First off, Hume rejected Descartes' cogito argument. Second of all, in Sceptical Doubts concerning the Operations of the Understanding[1], Hume makes a very rudimentary distinction between "Matters of Fact" (what we'd now call logical truths) and "Relations of Ideas" (what we'd now call empirical truths). Again, these classifications were intuited long before Hume/Descartes, but they exemplify them pretty well.

[1] http://www.livingphilosophy.org.uk/philosophy/David_Hume/Sce...

[wsy]

You claim that "the now well-established distinction between a and b was intuited long ago", but in the discussion refer to various a'/b' distinctions that separate the whole into quite different parts than today's a/b distinction.

I concede that expecting predecessors to split the whole exactly along today's a/b border would be asking too much. On the other hand, there is no objective measure that would allow us to test if a'/b' is similar enough to a/b to support your claim. So if you think it is similar enough, and I think it isn't, it seems to be more a matter of opinion than a matter of knowledge.

And my argument on "cogito ergo sum" was not about if Hume would consider it as true or false, but if he would consider it as logical or empirical statement. So your remark about that is true but irrelevant here.

[moomin]

It's a funny one, because as has already been pointed out, science means more than one thing in English. There's "rigorous study" and there's "natural science". It's assumed that the latter is rigorous and our best philosophical model for this is Popper's falsifiability. And whereas pretty much everyone except string theorists now accepts this model, it's pretty recent. Many ancient Greeks, for instance, favoured thinking hard about a problem over experimental evidence, either before or after the fact.