How many possible sentences in the English language

[Magical Realist]

"The claim, often repeated by linguists, that we can potentially produce an infinite number of sentences in a language, is not strictly true. For such a claim to be true there must either be the possibility of sentences of infinite length or there must be an infinite number of words in the language. Of course, neither of these requirements are possible for any human language (or for any imaginable communication system made up of discrete word-like units of meaning). We will examine the "infinite sentences" claim for English. If we assume:-

that English has about 500,000 words (there are about 450,000 in the 20 volume Oxford English Dictionary, but this excludes many colloquial forms - although it does include many obsolete forms),
that English sentences can be up to 100 words in length (a fairly reasonable working assumption)
that any individual word can occur 0 to 100 times in a single sentence (an unrealistic assumption)
that words can be combined in any order (a false assumption)

then we can determine that there could be as many as about 10 to the 570 possible sentences (very much greater than estimates of the number of atoms in the observable universe). Grammatical rules would greatly reduce this number of sentences, as would the requirement that all sentences be meaningful, but the resulting number of possibilities would still be extremely large (more than could ever be spoken in the entire history of human languages let alone during the much shorter life span of an individual language). So for all practical, non-mathematical, purposes we can say that the English language, or any other living language (1), is an open system. It's actually quite easy to come up with a unique, never before produced, sentence. To do so, for example, combine an unlikely (or impossible, or meaningless) event with a particular named person on a particular date. For example: "On 31st October 1999, whilst writing a lecture on animal communication, Robert had a colourless green idea." (2) Once this sentence has been written or spoken, subsequent productions of this same sentence are not unique, but unique sentences may potentially be generated from it by making slight changes to it (eg. change "green" to "red").

If we consider spoken language, then we would come to a similar conclusion if we examine only the word content of spoken sentences. We might additionally consider the manipulation of vocal resonance (frequencies of spectral peaks), vocal pitch (fundamental frequency), vocal loudness (intensity), rate of utterance and the placement and timing of pauses that occur as a consequence of the combined effects of prosody, vocal emotion, and size, age and gender differences. There are potentially an infinite number of infinitesimally different productions of any sentence (infinitesimal differences of frequency, intensity and timing). It is well known, however, that the human brain is only able to discriminate discrete (step-wise) changes in each of these dimensions. Across the possible human vocal range of these acoustic dimensions there is only a finite number of discriminable (just noticeable) steps. Additionally, it is also well established that meaningful changes in each of these dimensions tend to involve significantly larger changes than those changes that are just noticeable perceptually. This means that all of the meaningful vocal nuances of all of the possible sentences in English would be a large, but finite, number."--http://clas.mq.edu.au/infinite_sentences/

Remember too you can always create another sentence by saying "he said" or "she said" and then another sentence. Since this can be done indefinitely with any sentence, amounting in an infinite string of "he saids" culminating in any given sentence, I propose the number of possible sentences to be infinite. Also since any given sentence can contain any one or more of an infinite amount of numbers, like 10 to 5749, then there surely must be an infinite number of those sentences as well.

 

[dumbest man on earth]

Magical Realist, possible sentences.Would not a possible infinite amount possibly, be a given.You could replace the word "sentences" in your statement : " I propose the number of possible sentences to be infinite." with, possibly, any number of words, phrases or just about anything and it would, possibly, be a given.It would or could also, possibly, be inane or asinine.

May I state a proposal, and get your thoughts/feelings/musings/views on that proposal?

I propose the number of possibly inane or asinine Threads that Posters could start on SciForums to be infinite.
Remember too you can always create another possibly inane or asinine Thread by saying "he said" or "she said" and then another possibly inane or asinine Thread.

Just my $00.00000000000000001

 

[Fraggle Rocker]

* * * * NOTE FROM THE MODERATOR * * * *

My opinion of this thread:

• It doesn't have very much to do with linguistics.
• The question was answered in the O.P.: Since there are only a finite number of English words AND a sentence can only have a finite number of words, there is only a finite number of possible English sentences.
• A potential exception to that is the "he said, she said, they said, I said, you said" chain. But I think we all agree that a sentence with those clauses repeated infinitely would not be accepted in any form of edited writing. Certainly not on my watch. You get up to about four and I tell you to rewrite it so it can be understood!
• So the discussion is pretty much over, and the whole thread is getting pretty silly.
• I don't expect to see this continue without some new ideas or other major improvement.
• Also: The alleged insult in the second post was directed at the SciForums membership in general, not at anyone who has posted on this thread.

 

[Magical Realist]

* * * * NOTE FROM THE MODERATOR * * * *

My opinion of this thread:

• It doesn't have very much to do with linguistics.
• The question was answered in the O.P.: Since there are only a finite number of English words AND a sentence can only have a finite number of words, there is only a finite number of possible English sentences.
• A potential exception to that is the "he said, she said, they said, I said, you said" chain. But I think we all agree that a sentence with those clauses repeated infinitely would not be accepted in any form of edited writing. Certainly not on my watch. You get up to about four and I tell you to rewrite it so it can be understood!
• So the discussion is pretty much over, and the whole thread is getting pretty silly.
• I don't expect to see this continue without some new ideas or other major improvement.
• Also: The alleged insult in the second post was directed at the SciForums membership in general, not at anyone who has posted on this thread.

Sentences have nothing to do with linguistics? That's a new one on me. I will refrain from posting in your subforum in the future.

 

[mathman]

As a mathematician I will say that, if you place an upper limit on the number of words per sentence, the number of sentences is finite. Without an upper limit, you could create an infinite number of sentences, most of which would be nonsense.

 

[Magical Realist]

As a mathematician I will say that, if you place an upper limit on the number of words per sentence, the number of sentences is finite. Without an upper limit, you could create an infinite number of sentences, most of which would be nonsense.

Literature often pushes the limit of sentence length. Here's some examples:

1,288 words - The Guinness Book of World Records has an entry for what it claims is the longest sentence in English, from William Faulkner's novel Absalom, Absalom!.

4,391 words - The last section of James Joyce's Ulysses, Molly Bloom's soliloquy.[4]

13,955 words - Jonathan Coe's 2001 novel The Rotters' Club contains a 13,955-word sentence.[4][5]

469,375 words - Nigel Tomm's one-sentence novel, which does not have a proper subject-verb interaction, "The Blah Story".-- http://en.wikipedia.org/wiki/Longest_English_sentence

I can't imagine the function of writing such long sentences. A sentence that goes on too long would seem to wander off from its original point and lose its communicative power, lapsing into little more than stream of consciousness gibberish.

 

[Fraggle Rocker]

Sentences have nothing to do with linguistics? That's a new one on me. I will refrain from posting in your subforum in the future.

I didn't say that sentences have nothing to do with linguistics. What I said was that this particular discussion of sentences doesn't have very much to do with linguistics. It's more about math and logic.

As a mathematician I will say that, if you place an upper limit on the number of words per sentence, the number of sentences is finite. Without an upper limit, you could create an infinite number of sentences, most of which would be nonsense.

Uh... if you have an infinite number of words, then you could still have an infinite number of sentences.

Then we get into a whole new question: Is it possible to have an infinite number of words? If so, it's likely to be in one of the highly synthetic languages, like German or Finnish, where it seems (at least to us outsiders) that you can keep shoving morphemes together until nobody remembers what you were originally talking about.

Literature often pushes the limit of sentence length. Here's some examples: 1,288 words - The Guinness Book of World Records has an entry for what it claims is the longest sentence in English, from William Faulkner's novel Absalom, Absalom!. 4,391 words - The last section of James Joyce's Ulysses, Molly Bloom's soliloquy.

Faulkner and Joyce are famous for breaking the rules. English professors love to assign them for reading, but they DO NOT teach their students that this is a proper way to write.

13,955 words - Jonathan Coe's 2001 novel The Rotters' Club contains a 13,955-word sentence.

I'm not familiar with Coe. Somehow I'm pretty sure that I'm just as happy without him.

469,375 words - Nigel Tomm's one-sentence novel, which does not have a proper subject-verb interaction, "The Blah Story".

Again, this would never be permitted in any kind of writing except "great literature."

I can't imagine the function of writing such long sentences. A sentence that goes on too long would seem to wander off from its original point and lose its communicative power, lapsing into little more than stream of consciousness gibberish.

Ya think? More kindly, I suppose you could just take a normal page of writing and join all the sentences together with conjunctions like "and then."

But we actually try to teach people to write shorter sentences. That helps them clarify what they want to say.

 

[Captain Kremmen]

If you made a list of everyone in the world, that could make one proper sentence.

 

[dumbest man on earth]

If you made a list of everyone in the world, that could make one proper sentence.

Would not that list also always be incomplete or inaccurate?

 

[Fraggle Rocker]

If you made a list of everyone in the world, that could make one proper sentence.

If I were judging this, I would insist that a "sentence" be an actual grammatically correct sentence in the chosen language: a sentence that would be accepted in edited writing.

Every English sentence must have a subject and a verb. The only exceptions are interjections like "Hello!" You're never going to get to infinity that way.

A list of all human beings is not a grammatically correct sentence. I suppose you could make it one by adding just a few key words:

Aaron Aarhus, Abigail Aarhus . . . . Zygfield Zzyzzx and Zygote Zzyzx all live together happily on this planet.​

Nonetheless, the population of this planet is finite.

So how about this one:

The first year of the universe's existence was followed by the second year of the universe's existence, which was followed by the third year of the universe's existence, which was followed by the fourth year of the universe's existence . . . .​

 

[dumbest man on earth]

If I were judging this, I would insist that a "sentence" be an actual grammatically correct sentence in the chosen language: a sentence that would be accepted in edited writing.

Every English sentence must have a subject and a verb. The only exceptions are interjections like "Hello!" You're never going to get to infinity that way.

A list of all human beings is not a grammatically correct sentence. I suppose you could make it one by adding just a few key words:

Aaron Aarhus, Abigail Aarhus . . . . Zygfield Zzyzzx and Zygote Zzyzx all live together happily on this planet.​

Nonetheless, the population of this planet is finite.

So how about this one:

The first year of the universe's existence was followed by the second year of the universe's existence, which was followed by the third year of the universe's existence, which was followed by the fourth year of the universe's existence . . . .​

To me, that would seem to qualify.

 

[rpenner]

It seems to me that there is no known finite upper limit on the number of English sentences capable of being formed. Even if you found such a finite upper limit for sentences of less than, say, 100 words, the introduction of a new noun, verb, adjective or adverb would significantly increase the so-called upper limit. And new words and new uses for old words happen all the time. Likewise, since one may always add adjectives and adverbs to a sentence of any appreciable length, there is no possible finite upper limit on the grammatical allowable maximum sentence length.

What is more of a linguistics question is what is the longest expression in English that has a 50% chance of being communicated letter-perfect upon first hearing or reading by an adult listener/hearer and how does this compare to other common languages.

 

[ElectricFetus]

Well lets see... how many words are in the English language?

http://oxforddictionaries.com/us/words/how-many-words-are-there-in-the-english-language

171,476? Ok now how long can a English sentence get?

http://en.wikipedia.org/wiki/Longest_English_sentence

oh... OOOH that fucking long! OK so the idea is the upper limit to this question is simply the number of possible words multiplied by the length of the longest sentence, this gives an upper limit for which we know that the maximum number of coherent sentences would be much less. So say 1,288 by 171,476 gives you only 220 million possible sentences, which is not really that big when you think about it.

 

[rpenner]

Ah -- but you calculated the number of sentences where the length is chosen from a number up to 1,288 and the first word is chosen from a list of 171,476, and then you say nothing about the other words in the sentence.
the correct upper bound from your data is $$\sum_{k=1}^{1288} \; 171476^k \quad \approx \quad 171476^{1288} \quad \approx \quad 4.5 \times 10^{6741}$$.

This is larger than the number of all possible 920-person teams assembled from humanity (this will be true as long as humanity stays under 7,234,735,288 persons).

$$\begin{pmatrix} 7234735288 \\ 920 \end{pmatrix} \quad \approx \quad 4.5 \times 10^{6741}$$.

If you took 44 differently marked decks of playing cards, this number is greater than a billion, billion, billion, billion, billion times all the different ways you could shuffle the combined decks.

$$10^{45} \; (44 \times 52)! \quad \approx \quad 7.1 \times 10^{6739}$$

Not all of these can be grammatically or logically coherent sentences. But neither are these true upper bounds because your statistics and dictionaries are descriptive, not prescriptive.

 

[Fraggle Rocker]

What is more of a linguistics question is what is the longest expression in English that has a 50% chance of being communicated letter-perfect upon first hearing or reading by an adult listener/hearer and how does this compare to other common languages.

Based solely upon my own observations, I would say that most of the other Western Indo-European languages (the Celtic, Germanic, Italic and Greek sub-branches) have syntactical structures roughly the same as ours. Their verbs are inflected and they have a good set of prepositions and conjunctions, allowing a sentence to cover a span of time starting in the past and ending in the future, also including hypothetical activities. Therefore their sentences probably have more-or-less the same potential and the same constraints as ours.

I don't know enough about the Eastern Indo-European languages (the Balto-Slavic and Indo-Iranian sub-branches) to make a guess. I know even less about the singletons (Albanian and Armenian) and the extinct branches (Tocharian and Anatolian).

I do know something about Chinese. Based upon its syntactical structure, I would not expect it to be able to support long sentences. Its verbs have no tenses and it has less than a handful of conjunctions. On the other hand, although it has no prepositions, the function is served by verbs, so it's quite good at describing relationships--but only spatial relationships, not temporal. The way you specify that Action 2 occurs after Action 1 is to describe Action 1 first: "I eat breakfast ride bus attend school," not "I went to school on the bus after breakfast." This can get pretty cumbersome, and indeed I have never heard Chinese people use long sentences in conversation.

That only covers two language families: Indo-European and Sino-Tibetan. There are at least a dozen more.

 

[dumbest man on earth]

I have a fairly short expression that I commonly use, that would seem have a very small "% chance of being communicated letter-perfect upon first hearing or reading by an adult listener/hearer", because of the way it "sounds" when expressed vocally.

A lot of people either fail to make sense of it or misunderstand it, even when I present it to them in written form.

The expression I am referring to is : Real eyes realize real lies.

Does it qualify as a complete sentence?

 

[rpenner]

Real eyes realize real lies.

Not all of these can be grammatically or logically coherent sentences.

It appears to obey the laws of syntax and grammar, but the expression "Real eyes [always or frequently or as a matter of habit] realize real lies." does not meaningfully constrain what is meant by "realize" (did you mean discern or cause to happen?) or what is the import of the first and second uses of "real" and it comes across as gibberish or perhaps a cryptic motto where an aphorism is wanted.

 

[dumbest man on earth]

It appears to obey the laws of syntax and grammar, but the expression "Real eyes [always or frequently or as a matter of habit] realize real lies." does not meaningfully constrain what is meant by "realize" (did you mean discern or cause to happen?) or what is the import of the first and second uses of "real" and it comes across as gibberish or perhaps a cryptic motto where an aphorism is wanted.

Okay, I am not a linguistics brain scientist or a linguistics rocket surgeon, so I only grok'd the "appears to obey the laws" and "gibberish" part of what you wrote.
Was the rest of it kind of like the linguistic reasons behind what led to me stating : "A lot of people either fail to make sense of it or misunderstand it, even when I present it to them in written form."?

 

[Fraggle Rocker]

A lot of people either fail to make sense of it or misunderstand it, even when I present it to them in written form. The expression I am referring to is : Real eyes realize real lies. Does it qualify as a complete sentence?

Of course it does. It has a subject, verb and object, and the grammar and syntax are correct.

As for being understood, it seems clear enough to me in writing. The use of the verb "realize" is a little non-standard; "recognize" would be clearer, but the meaning is obvious. "Real eyes" is also a foolish turn of phrase, since it's not clear what other kind of eyes you're comparing them to. But still, the basic meaning is that sensible people know a lie when they hear or see it.

But obviously, if spoken, this will be very difficult to understand. It sounds like the same word repeated three times.

You must know that, or you wouldn't have bothered with it. It's just a word game. You're playing with us.

 

[dumbest man on earth]

Of course it does. It has a subject, verb and object, and the grammar and syntax are correct.

As for being understood, it seems clear enough to me in writing. The use of the verb "realize" is a little non-standard; "recognize" would be clearer, but the meaning is obvious. "Real eyes" is also a foolish turn of phrase, since it's not clear what other kind of eyes you're comparing them too. But still, the basic meaning is that sensible people know a lie when they hear or see it.

But obviously, if spoken, this will be very difficult to understand. It sounds like the same word repeated three times.

You must know that, or you wouldn't have bothered with it. It's just a word game. You're playing with us.

I stated how it is less understandable by how it sounds when spoken, or, as you put it :"It sounds like the same word repeated three times."
The use of the word "recognize" instead of "realize", as you point out, "would be clearer, but the meaning is obvious".

I asked does it qualify as a complete sentence? Because, even when written, numerous people have told me that it might be considered a statement or an opinion but not an actual sentence. I had always had the impression that a statement or an opinion could also be a proper sentence. I was, however, unsure.
When this thread started mentioning "syntactical structure" and Posters who were obviously learned in those areas, I merely thought this to be my opportunity to find out for sure or not whether it qualified as a complete sentence.

If I had known - I would not have bothered to ask.

Just as that 5-word, what I now know to be a complete sentence (thank you - by the way), phrase can be severely misunderstood when heard - I apparently misunderstood what I was doing by asking.

As, i stated before, I am not a linguistics brain scientist or a linguistics rocket surgeon.

Truly, sincerely, sorry that my inability to correctly state why I was asking and of course the phrasing of my question, was playing.