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In the sciences and in mathematics there are a great number of words and terms in use that do not, in any literal sense, describe the concept they are meant to describe.

Let's explore the use of "reaction" as it used in chemistry or physics: Yes yes, we all know the commonly USED meanings of the word. We can and do infer rather than decode all the time. That "re" prefix seems to just be crazy to use if you're wanting to be accurate - which I assume is important to most scientists. So why is inferred meaning OK in this case? Wouldn't using a word that, when decoded, actually defined the thing be better for scientists to do, even if that word was relegated to science and was not in common use in the general public? But scientists do use it to mean "interact" as well as "re-act" (act again) and also "a series of interactions" and "the results of n interactions"...

Another one to explore is the term "irrational number" - which i know has its own questions in these stacks but not in the same context as my question. When you look at the etymology of it it sure seems to me that early USE of the term for maths (as the originators of the concept groped for greek words to describe it) led to our modern definition: 'not able to be represented as a ratio'. Past a certain point going back in time it was really just referencing rationality of thought. But, mathematicians have so long used it that it has actually morphed meaning. On it's own, morphing is no biggie, languages change, word use changes yadda yadda. But in a field where clarity and precision are so very important, it seems really weird that the term survives in this sense. Why has a term not been created to separate the two ideas, rationality of thought vs ratio-ABILITY of numbers?

There are only two examples - there are so many more.

And to be honest here, this strange use of English within mathematics is the primary reason I found maths so challenging when I was young... None of the words used to describe the numbers and what the numbers were doing made any logical connection to what was actually being done with them!

EDIT: To clarify part of what I'm getting at here - a base tenet of science and maths is the formulation, testing, and modification of hypotheses. Yet that approach is not taken with the English usage. It is never asked "we began using this term because we were struggling to describe X - but why are we still using it when we know it to be inadequate?" We would not continue to use a theory if evidence appeared to show it to be wrong, yet we can show many of these words to be 'wrong' (by word-part breakdown or by use morph) and everyone seems to just shrug and say "yeah it doesn't really describe what hat is, but F*** it- it is just too much trouble to find or create a word that actually means X."

So I ask the crowd:

Why do fields that highly value precision in so many ways continue to use very imprecise language having had ample opportunity to 'clean up' their specific field's language?

closed as too broad by Robusto, Hot Licks, Chenmunka, jimm101, Nigel J Feb 20 at 17:07

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    @111936 - It's just that there isn't likely to be an answer that isn't opinion-based, which would be off-topic here. The reason is that for the users of the argot in question, they likely are using unambiguous language. They understand each other well. It's only looking from the outside that it might seem imprecise. – Jim Mack Feb 20 at 0:31
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    @111936 The language is very precise to those that use it. It is not going to change, because the current usage is well-established. There is a body of work using the established language that would be obsoleted by such change. Revolutions in language are extremely rare. – michael.hor257k Feb 20 at 1:01
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    "React" does not mean "act again" the Oxford Dictionary Online has a number of very specific meanings including ones from both physics and chemistry but the basic one is Act in response to something; respond in a particular way. This is the souce of the chemical, and physical meanings and is only indirectly related to "do again". Rather it imples that the action is a respose to presented conditions. – BoldBen Feb 20 at 1:53
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    @111936, you are falling into the etymological fallacy. Words mean what they mean, not what you might think they meant from looking at their origin. – Colin Fine Feb 20 at 16:39
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    Jargon is always right to its users. – KannE Feb 20 at 20:24
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This is a very interesting question and gets to the heart of a lot of problems with understanding the meanings of words.

You say that words used in mathematics and science are vague and distort the real meaning of the original word. One half of this the case, the other the opposite.

Math and science use existing terms or invents new ones from existing parts in order to label new concepts. If an existing word is used, there is sometimes an attempt to have it be evocative or metaphorical but often sadly falls very short, distorting the original meaning. Irrational numbers aren't at all irrational (to our usual idea of that word). Imaginary ones likewise; its replacement 'complex' also metaphorical but closer to the true technical meaning is only part way there. Similarly in other sciences, 'power', 'force', 'capacitance', any technical term is its own thing only suggested by the informal generic term.

But math and science vague? No, that's exactly what they're not. The whole point of knowledge is to reduce vagueness. The vocabulary that is used for the new precise concepts is often Fixed. The term is then not vague at all. When used in the technical context, the label is as precise as possible. This is called

stipulative definition.

Whatever preconceptions one may have of a vocabulary item is only a nice story, but the label (in the technical context) has its meaning stipulated, said to be only attached to the precise concepts. 'Irrational' may mean informally something vague like crazy, but in math it means exactly not expressible as a fraction. That is very precise and not vague at all.

From the outside, when you don't know what these stipulated meanings are supposed to be, when you're just being exposed to them and haven't learned them properly, they seem just as vague as the informal terms, or really, even more vague because the concept hasn't been learned well. Technical meanings don't need to be cleaned up because they're cleaning up the informal definitions (or even making up totally new but very precise ones).


Think of the language of math and science as a foreign language with a lot of false friends. The words in your language may be very specific and the words in math in science may be very specific, but because the same sounding word means different things in the two languages, it feels like those foreigners aren't using it right and can't be pinned down to a coherent meaning.


TL;DR Math and science terms are the least vague of terms; they are intentionally made ('stipulated') to have particular meanings. It is the learning of these meanings that leaves them imprecise at the beginning.

So don't take things so literally. An everyday word used in a technical capacity has become much more specific. The vagueness is in the informal usage or being early in the learning of the technical meaning.

  • There's a lot to say here, stuff about the etymological fallacy (meanings drift, so the meaning of a word is not necessarily the same as it used to be or to what the combo of its parts is), and that mental concepts/ideas are not the same thing as words that we label them with. Those are alluded to but are merely supportive to the main point about stipulative definitions. – Mitch Feb 20 at 16:34
  • 1) I'll accept this an an answer, it seems to sum up the other commentary and gives context to those comments above. – 111936 Feb 20 at 18:08
  • 2) I fully accept and live in the real world where words have no consistency of meaning, I thought I'd made that clear enough before. But I still do wish there was any actual consistency or some clear decoding ability to the language so that this process of "re-learning words" to learn math was not needed.. Terrifying to see this view is tied to the third reich (vie wikipedia about etymological fallacy). – 111936 Feb 20 at 18:13
  • Which view is tied to the Third Reich? That people don't stick to the original meaning of a word or that people consider that a mistake/only one of many viable meanings? – Mitch Feb 20 at 18:58
  • The wikipedia page for etymological fallacy cites a reference that itself discusses this fallacy in relationship to the Nazi's supremacy/purity ideas. So now I fear my attitude about hating ambiguous words and desiring consistency in word-part/word-origin/usage/etc is somehow attached in some people's minds to being a psycho racist. Lovely. – 111936 Feb 20 at 21:12

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