90's or 90s?

[Makri]

Well, yeah, because of the natural language you use on top of the formalism.

Actually, I was going exactly in the oposite direction. As the term "natural language" is usually understood as encompassing syntax, semantics, and a lexicon, I was prepared to assume that the "English of maths" has a very restricted lexicon with no terms to refer to non-mathematical entities.

But a "formal language" is specified purely in syntactic terms. People speak of first order logic as a language. And because the specification of the formal language doesn't tell you what its terms refer to, you are free to introduce constants for anything you want. Mathematicians all the time introduce new constants, but they only refer to mathematical entities because that's what they're interested in; physical properties don't feature in the relevant inferential schemes.

[Iulus Cofield]

I'm really curious how you say "I desire something" and "I love someone" in math. I can see your point about being able to express physical actions with math, such as the velocity of a cat and a dog in relation to each other, but I'm very skeptical that you could express emotion of any kind, without an elaborate detailing of a person's vital signs and hormone levels.

[graatz]

If it's a language, then you should be able to convey the proposition, "I watched a cat chase a dog" in mathematics.

Can you?

Let C be the set of all cats and let D be the set of all dogs. Define the relationship a R b such that a R b if and only if a has chased b. Define the set S as the set of things I have observed. With those definitions, I propose:

P: There exists a c in C and d in D such that c R d exists in S

That's the language of math. If it's "cheating" that mathematical statements use English, then Japanese is also "cheating" that their word for cheeseburger is the English word cheeseburger.

[Makri]

That's what I had in mind.

Although I have to say that I find the idea of this S, in which c R d is supposed to be, a little problematic. But then, that's probably not the correct representation of the logical form of the English sentence anyway (that would involve events), so it doesn't matter that much.

[gmalivuk]

If it's "cheating" that mathematical statements use English, then Japanese is also "cheating" that their word for cheeseburger is the English word cheeseburger.

No, those are not analogous, because there are billions of people who do math without needing to know any English to do so. And if you've got a Language of Math (in English) and a Language of Math (in French) and a Language of Math (in Cantonese) and so on, and you need one of those real languages to make sense out of propositions in your Language(s) of Math, then I would argue that mathematics itself is therefore not a language.

[Makri]

And if you've got a Language of Math (in English) and a Language of Math (in French) and a Language of Math (in Cantonese) and so on, and you need one of those real languages to make sense out of propositions in your Language(s) of Math, then I would argue that mathematics itself is therefore not a language.

But of course you don't. Or you do only in the sense that you need these languages as meta-languages, just as a German learner of English needs German as a meta language for at least some time.

[Iulus Cofield]

Then please rewrite Graatz's post without using any English grammar at all, just as a fluent German speaker has no need to mentally translate from English to German.

And loaning words is not analogous to loaning grammars.

[gmalivuk]

Yeah the analogy still fails because there is no non-English metalanguage that's required to converse in English, even if there happens to be one temporarily when learning English as a foreign language.

[Makri]

Yeah the analogy still fails because there is no non-English metalanguage that's required to converse in English

Nor is any required to converse in predicate logic, once you know the values of the constants. You need English only to communicate those, and that's a metalinguistic task.

[phlip]

But it's a metalinguistic task you have to perform for every single conversation... because even once you've "learned" (to follow the analogy) that "R(c)" in Maths means "the cat is running" in English, that'll only hold for a single conversation, and if you were to then go on and say "R(c)" to another person, even if they're fluent in Maths, they probably won't know what you mean unless you do the metalinguistic step again.

I guess if you wanted to stretch the analogy to breaking point, you could say that every conversation in Maths ("conversation" here being used in the broadest possible sense to include things like papers and proofs and whatnot) is its own dialect of Maths, the separate dialects being mostly mutually incomprehensible... sharing much of the grammar, but using a large number of different words for things... the only words being common between dialects are those for common mathematical concepts (like numbers, or addition) and even those aren't universal. Not an especially useful language when every single conversation - even between the same people - spawns a new dialect that needs to be re-learned by all participants...

[Makri]

Right. That happens when something is a language only in the sense of a formal language (in the sense in which first order logic is a language) and not in the sense in which English is a language (with a lexicon!).

[gmalivuk]

Well yeah, but this discussion has (I thought) been about languages in the sense that English is a language, since I already said days ago that mathematics is indeed a formal language, but that that's not the kind of language we were really talking about here.

[Makri]

I see. Then I'm with you.

[graatz]

Mathematics might be described as (or more properly can be said to make use of) a formal language, and is involved in studying the logically resulting structures, but as such does not itself include semantics. And so if a communication system cannot actually say things about the external world, I don't see how you can consider it a language in the sense that we talk about languages in this forum.

And when someone uses expressions like "the language of mathematics", they are typically referring to a combination of this formal language and mathematical jargon that is part of the actual human language being used to discuss the math in question.

I'm confused about your definition of semantics. I'm also not sure what your definition of saying things about the external world is, or why it is necessary for a language to have semantics. I don't think that the "language of math" is the same as mathematical jargon.

Let's say that I wanted to prove to you that every number divisible by four is an even number. I can only really do it in the language of math. Number x is divisible by four means that there exists some n such that 4*n = x. Because 2*2=4, we can substitute that for each x divisible by four, there exists n such that (2*2)*n = x. Multiplication of natural numbers is associative, so equivalently 2*(2*n) = x. Natural numbers are closed under multiplication, so (2*n) is a natural number, lets call it m. By substitution, we have demonstrated that for all x divisible by four, there exists some m such that 2*m = x. But this implies that x is even by definition.

Similarly, I could say that a number divisible by four must be divisible by two, since four is divisible by two, and the product of two numbers is divisible by any number that either is divisible by. I could also say that two is a prime factor of four and thus of any number divisible by four. There's no difference between the long formal proof and any of these simpler appeals. In all of them, I'm using the language of math. I'm doing so in English, granted, but the underlying mathematical semantics would remain unchanged when translated to any other language.

[mausgang]

when talking about decades, its the '90s, since this is referring to a plural set of years, the apostrophe is cutting out the 19 into the 1990. Unless something belongs to somebody or something called 90, I think 90's is incorrect.

[azule]

My related question is on acronyms. Take "CPU" for examples. More than one is cpus? CPU's? With people not capitalizing words for fear of yelling, acronyms run the risk of appearing to have that "s" be part of the acronym...and sometimes they are.

[Bobber]

My related question is on acronyms. Take "CPU" for examples. More than one is cpus? CPU's? With people not capitalizing words for fear of yelling, acronyms run the risk of appearing to have that "s" be part of the acronym...and sometimes they are.

Yeah, like when people write "5 FLOPS" but "one FLOP". Confusing as hell until you realize that the S stands for Second.

[PM 2Ring]

My related question is on acronyms. Take "CPU" for examples. More than one is cpus? CPU's? With people not capitalizing words for fear of yelling, acronyms run the risk of appearing to have that "s" be part of the acronym...and sometimes they are.

I write the plural of CPU as CPUs. The s is not part of the initialism, so to avoid confusion it should not be in upper case.

When I went to school, the standard way to form the plural of numbers, letters and initialisms was to use apostrophe s. These days, I prefer to omit the apostrophe, and encourage others to do so as well, but as I have strong descriptivist leanings I don't consider the older method to be wrong.

My early grammar teachers were prescripitivists, but one of my middle high school English teachers introduced us to descriptivism, and I've never looked back. I guess I still harbour some prescripitivist inclinations, but I can exercise them in the context of programming languages. Descriptivism & computer languages don't mix well - the mess that is HTML is a prime example of what happens when standards are not adhered to.

[phlip]

Yeah, like when people write "5 FLOPS" but "one FLOP". Confusing as hell until you realize that the S stands for Second.

What kind of processor are you using where you only get 1 FLOPS, though? A guy in a cage with a pocket calculator?

[unus vox]

Acronyms require an apostrophe before the plural s, so as not to confuse it as part of the acronym. For further distinction, the s is lowercase (as noted by the poster above me). For this reason, many people tend to put apostrophes in a plural year, e.g. "the '90's," under the assumption that it functions like an acronym. However, that is unnecessary. Using an apostrophe for (grammatically ) truncated decades is mostly a matter of preference, as are many such issues with punctuation. Again, though: it's unnecessary.

Also, half of this thread seems to have devolved into a debate on the definition of what constitutes a language. That could be all well and good, but you guys aren't drawing a distinction between words and symbols. The function of a word is much more comprehensive and malleable than that of a symbol. And while I realize that, yes, a word is sort of a symbol (semiotics, etc.), not all symbols (read: numbers) function as words. It's seems silly to split hairs over the definition of "language" when it has multiple definitions for this very reason.

[Sheikh al-Majaneen]

While its correct to write '90s, I just write it out as the nineties. Typing numbers is always awkward for me (since I haven't stared at the keyboard while typing for the past five plus years, which is why it took me four tries to type the following parenthesis), so its faster just to type out the letters. However, when talking about the nineties, perhaps we would be better just saying 'fin de siecle,' or the gilded age. Less confusion.

[Pez Dispens3r]

However, when talking about the nineties, perhaps we would be better just saying 'fin de siecle,' or the gilded age. Less confusion.

Err, that's less confusing?

[azule]

When I went to school, the standard way to form the plural of numbers, letters and initialisms was to use apostrophe s.

School might have been where I learned that. (Probably where I learned most things...doi!)

Yeah, like when people write "5 FLOPS" but "one FLOP". Confusing as hell until you realize that the S stands for Second.

Thanks! I couldn't think of an example.

I read somewhere that the "s" shouldn't be included at all as it would already be part of the last initial. Such that "central processing unit" would be "central processing units" and still written CPU...but what about "FLoating point Operations Per Second", that would be "FLoating point Operations Per Seconds".... maybe. hmm.

[Bobber]

Yeah, like when people write "5 FLOPS" but "one FLOP". Confusing as hell until you realize that the S stands for Second.

What kind of processor are you using where you only get 1 FLOPS, though? A guy in a cage with a pocket calculator?

Well, the problem extends to "5 teraFLOPS" and "one teraFLOP" as well.

[keera]

I have a related question: what about plurals of chemical symbols?

I'm checking over the English of a paper my supervisor is writing, and he's used "Sn's" to refer to multiple tin atoms. I'm inclined to think this is correct (or at least acceptable) because it avoids ambiguity - writing about multiple gallium or iodine atoms as Gas and Is respectively would be very confusing.

But I wanted to check.

[Sizik]

I have a related question: what about plurals of chemical symbols?

I'm checking over the English of a paper my supervisor is writing, and he's used "Sn's" to refer to multiple tin atoms. I'm inclined to think this is correct (or at least acceptable) because it avoids ambiguity - writing about multiple gallium or iodine atoms as Gas and Is respectively would be very confusing.

But I wanted to check.

I think the correct way would be "Sn atoms".

[Alx_xlA]

I have a related question: what about plurals of chemical symbols?

I'm checking over the English of a paper my supervisor is writing, and he's used "Sn's" to refer to multiple tin atoms. I'm inclined to think this is correct (or at least acceptable) because it avoids ambiguity - writing about multiple gallium or iodine atoms as Gas and Is respectively would be very confusing.

But I wanted to check.

I think the correct way would be "Sn atoms".

Are we discussing multiple atoms, or multiple symbols?

[Teritus]

Yes, it's 90s. I hate when people use 90's. God, I hate it so much. I even corrected a teacher once when she used the apostrophe.
It looks like the right way becuase the apostrophe maybe makes it look "neater", but it's a plural so obviously no need for apostrophes. I see it so often as a mistake everywhere, but really 90s is the correct way.

[Pez Dispens3r]

Yes, it's 90s. I hate when people use 90's. God, I hate it so much. I even corrected a teacher once when she used the apostrophe.
It looks like the right way becuase the apostrophe maybe makes it look "neater", but it's a plural so obviously no need for apostrophes. I see it so often as a mistake everywhere, but really 90s is the correct way.

Hi there! You're new here, so you might not understand that it's considered polite to read through a thread, and consider and respond to the opinions of other people, rather than to just necro a threat so you can assert how other people are wrong.

90's is quite fine because, amongst other things, apostrophes mark where the separation of characters might enhance readability. This is exactly why the apostrophe is still used this way in AmE publications, such as the New York Times, and was used in BrE publications, such as The Economist, until recently. In fact, it's used and neglected in both AmE and BrE publications as a matter of stylistic choice. You are, therefore, a patronizing jerk to tell other people they're wrong to use a convention which is still very popular amongst professional, educated English writers.

Welcome to the forums, by the way: I hope you enjoy your stay.

[skullturf]

Let me also reiterate that many style guides find it quite acceptable to use apostrophes when pluralizing a single letter: for example, A's and B's rather than As and Bs.

[Teritus]

Yes, it's 90s. I hate when people use 90's. God, I hate it so much. I even corrected a teacher once when she used the apostrophe.
It looks like the right way becuase the apostrophe maybe makes it look "neater", but it's a plural so obviously no need for apostrophes. I see it so often as a mistake everywhere, but really 90s is the correct way.

Hi there! You're new here, so you might not understand that it's considered polite to read through a thread, and consider and respond to the opinions of other people, rather than to just necro a threat so you can assert how other people are wrong.

90's is quite fine because, amongst other things, apostrophes mark where the separation of characters might enhance readability. This is exactly why the apostrophe is still used this way in AmE publications, such as the New York Times, and was used in BrE publications, such as The Economist, until recently. In fact, it's used and neglected in both AmE and BrE publications as a matter of stylistic choice. You are, therefore, a patronizing jerk to tell other people they're wrong to use a convention which is still very popular amongst professional, educated English writers.

Welcome to the forums, by the way: I hope you enjoy your stay.

Wow, ok. Yes, I am new, and I'm sorry if I offended you or anyone else. I didn't mean to sound like a "patronising jerk"; I was just stating my opinion. I apologise for sounding rude, as I am only new here and don't know a great deal of things. What I meant to say is that I always thought that 90s was the correct way though I never knew it for sure, which is why I came to this thread. It came out badly and made me sound like a ..., well, never mind. The important thing is that it's my first post, and I'm sorry and it won't happen again.

So then, it's okay to write 90's and 90s, or must you use the apostrophe?

[PM 2Ring]

So then, it's okay to write 90's and 90s, or must you use the apostrophe?

The traditional way to make the plural of non-words like numbers and single letters is to use an apostrophe, the modern trend is to drop the apostrophe. I like the modern form, and I think that the older form may encourage some people to use apostrophes for simple plurals, i.e. the dreaded greengrocers' apostrophe.

[Teritus]

Yeah, I've seen these mistakes fairly often recently. "I had a few apple's today".

Regardless, I realise that I was wrong with the way to write 90s without the apostrophe; it appears that both can be acceptable. Once I again, I apologise for anything which I said earlier. I hadn't known a great deal about it, and I'm glad I do now. @Pez Dispens3r, I hope you know now that what I said wasn't right at all. I'm seldom such a "patronising jerk" as I may have appeared, I might've have just been in a bad mood that day. Anyhow, I won't do it again, and I'll make sure next time to read through all the replies first before putting in my own imput.

[AvatarIII]

personally i prefer '90s, you are dropping the "19", so it makes sense to put an apostrophe at the beginning.