The fact that you couldn’t ever possibly write a sentence of infinite length, (or even a sentence of finite length containing, say, a googolplex of words) is irrelevant.
You might as well say that mathematical infinity can’t be understood because you can’t write down all the numbers from 1 to infinity.
I have never read the fifth sentence in brevel_monkey’s proof above, nor do I ever intend to. And yet, I know and understand precisely what it means*; moreover, I could, if I wished, write it or verbalize it with complete accuracy. Are you saying it’s not a sentence until somebody reads it or writes it? Is it like the tree that falls in the forest with nobody around to hear it - it doesn’t make a sound?
*Edited to add: I also know that it is different in both form and meaning from every other sentence in that infinite sequence of sentences; and I can tell you exactly how it differs from any other given sentence in the sequence. I actually know as much about that sentence as I would if I had read it. And I can make the same claim about any other sentence in the series.
Or rather, I could understand mathematical infinity via a finite set of sentences explaining it. But it is a numerical concept, not a literal one. Sentences (including, even, run-on ones) conform to grammatical rules, one of which is that there’s a period. The meaning is “contained” in the writing. Now, on the other hand, if we’re talking poetry, there might be an issue.
Not only don’t you intend to, you never could, because no such sentence can exist… even in an infinty of reincarnations.
Well, I argue that you may know something poetic or mathematical about such a concept, but the reason it is unique as a grammatical entity is because it doesn’t exist… except for its ellipsical representation.
oops… just caught my mis-read re: the “unread fifth sentence”. The responses applied to an “infinite sentence”. Regarding the unread sentence, you could project its meaning because you could project a period, and envision the possiblilty of writing it. You would understand it pertained to the fifth dead dog. The infiniteth dead dog, however, runs away… …thus, see spot run…
… we should maybe hypostatize what sorts of issues hang on this one… what difference does either position make more generally? If there’s a significant positive out of understanding that a sentence can be infinite, I’m read to jump over… just not clear on what’s at stake, so I’m sticking with grammar by default.
The numbered list of sentences in brevel_monkey’s proof contains finite sentences and only finite sentences. Every one of them has a period at the end and a finite number at the beginning.
We are not talking about a sentence that has no period at the end. Ellipsis doesn’t enter into the picture.
Forget infinity for a moment. Think instead of “no limit”.
There is no limit to the number of sentences in the list; no matter how long the list goes on it will always be possible to add another sentence different from all the previous ones.
There is no limit to the length of the sentences that can be generated; no matter how long the list goes on, it will always be possible to add another sentence longer than all the previous ones - a sentence ending with a period.
That’s all Steven Pinker means when he says it’s possible to make an “infinite” number of sentences. And that’s all I mean when I say the possible length of a sentence is “infinite”.
The paradox of infinity is that every term in an infinite series is finite. Every sentence in the list is finite, and is preceded by a finite numeral, but there is no limit to the length or number of the of the sentences in the list.
Yes, I have no problem with the infinite finite sentences version. Perhaps there’s an infinite number of sentences approaching the “infinite sentence”… but I’d still want to be saying that the infinite sentence itself does not/cannot exist, at least not as a sentence. So: an infinite “number” of sentences – yes; an infinite “sentence” – no (albeit on a technicality)
I agree that the “infinite sentence” does not/cannot exist, for the same reason that the “infinite number” cannot exist. You can count finite integers indefinitely and never run out of them, just as you can lengthen the sentence indefinitely, 13 words at a time, and never reach a point where you cannot make it longer.
You never reach the “infinite number” and you never reach the “infinite sentence”, even in principle. But to say that does not in any way negate their quality as “infinite” - it rather defines the essence of their infinite quality.
Perhaps one way one could imagine the “infinite sentence” is as follows:
The dog ate food which had been made from the remains of another dog that ate food […add additions here…] which had been made from the remains of another dog.
Well, OK, if that makes it easier for you to accept the concept of unlimited length.
I would just point out that all you have done is move the ellipsis back ten words, rather than putting it immediately before the final period. What you have is a representation of a sentence that has an ending, but is infinitely long in the middle.
Yes, it is a dimensional shift, and in terms of actually attempting to imagine the sentence, I’d ixnay the lipsiseaslay… but I’d still have my cherished period, so I’d be psychologically secure.
Oh what the hell why don’t I go and stir up some more dissent…
The problem of meaning in language and infinite sentences or words is really a philosophic one. I claim that an infinite sentence would lose its meaning as a perceptual object in our real world experience. This notion can easily be confused with my believing that only things we can perceive can be understood and thus made meaningful. This is not true, and this response is one-dimensional. I know that many a thing we don’t experience physically can be understood and meaning attributed to it. Imagined objects for example. Freud created a whole field of psychology based on non-real world experiences called dreams and their interpretations, which was for a long time considered as interpreting the meaning(s) behind our nocturnal experience. I propose that meaning is interpretation of our perceptual reality. That is, we experience reality through our senses and apply an interpretation of what we’ve experienced. In another article, I considered an example of smell. Smell is a sense we all have. We perceive smell through our olfactory system and then interpret what we smell. That is we apply a meaning to it. We interpret what stinks, or what is aromatic or what is arid, steamy, damp, dry, mild, etc. The real world source of these interpretations has no such meanings attached to them. Fundamentally, what we do as human beings is this very process. We experience (perceive) and interpret our experiences. To invoke a cliché, meaning and interpretation are two different sides of the same coin. Perhaps a better synonymous construction would be to equate meaning with understanding.
The same idea is true for language and its constituents: words and sentences. Before going on, I will reiterate what I indicated above. I am not referring to our conceptual knowledge of language and its constituents. I know we can understand any sentence or word no matter how long it may be as a concept. As an example of what I intend by meaningless, the hilarious nonsense constructions in Joseph Heller’s best-selling novel Catch-22, provide excellent material. At one point in the novel the pilots are at a briefing before a bombing mission. They are asked if anyone has questions about the mission ahead. They come up with the following:
When is Spain?
When is Hitler?
Now of course these sentences are meaningless. These are finite sentences note. They are meaningless because they violate the rules of grammar that Steven Pinker goes to pains to explain, I might add. We know that a proper noun like Spain can’t be the object of an interrogative demonstrative pronoun like When which specifies some temporal period! But the sentence When is Spain? as an object of conception is readily understood as being an ungrammatical sentence. We know it’s meaningless perceptually because it can’t be interpreted as an experience. The same can be said for the second sentence. And the same can be said of a sentence, which uses a clever tool of recursively carrying on its original atomic statement infinitely. They can’t be interpreted as real world experiences and thus are nonsensical. This amounts to their being meaningless. Why I think this profound is that I’m not saying we should simply exclude sentences of this type, I’m saying we can’t understand sentences of this type. They are not a part of human language. By saying this, I’m implying that we have a limited set of expressions we can make. I know this kind of comment invites those that dissent, to rein hell down upon me.
One thing I will make clear is I’m not proposing that fallacious argument of John Locke in his An Enquiry Concerning Human Understanding. He makes the mistake of identifying things we perceive through our senses with ideas and then claiming that only the ideas are what we manipulate in our minds. That is, we only understand ideas not the real world percepts. He believed that only the concept is understood not the percept. He would have agreed that an infinite sentence is very meaningful.
I think you have lost Pinker’s point entriely now:
All Pinker is saying is that the amount of possible sentences is arbitrarily large. That there are indefinitiely many possible sentences. That if I was to go on making new sentences up for the rest of time, ceteris paribus, I would never have to stop. I have showed that this is the case. This is the entire claim of Pinker - it is all that is necessary to justify his remark.
Almost everyone on this thread blindly believes this involves some sort of comitment to an infinitely large sentence, but it just doesn’t. Sorry.
You are arguing that an inifinite sentence would be meaningless. You have taken it one step too far: simply the phrase “an infinite sentence” bears no meaning: there is no point discussing it.
but the infinite number of monkeys typing on an infinite number of word processors to make a copy of the bible just isn’t as fun without infinite sentences…
An excellent example of what I just described above is in Oughtist’s reply. He illustrates how interpretative meaning is what we do as human beings. Even when someone spews nonsense speech or writing, we still try to make sense out it. So, he reinterpreted the meaningless sentence When is Spain?, to mean When did Spain exist? Then answered it with the dates the Spanish republic could be said to have formed. We do this all the time. A person with a speaking disability tries to communicate with you, you say: What did you say? What’s my name, Oh, what? Yes I’m fine, how are you? But, in fact the person could’ve have said: The declination of the Orion nebula seen from the southern hemisphere is 1 minute 39 seconds. Please don’t call me out on those coordinates; I made them up for illustrative purposes only.
That meaning can be attributed to a nonsense statement adds or subtracts nothing from what I said. Take it he’s pulling my leg, so to speak.
I got Pinker’s point about the possibility of creating infinite sentences. I acknowledged that in the original post and many after that. I added a caveat to what Pinker said: that this infinity of possible sentences would not all be meaningful in the real world sense I’ve described in detail. In fact, I would even augment the conceptual infinity idea and bring in Georg Cantor’s transinfinity construction, and agree that a quantity of sentences beyond infinity could be made. My only point has been sentences as understood thru our real world are limited as are our experiences, including dreams, fantasies, etc (but not an infinite etc, mind you, just very many of them). These sentences are the meaningful class of sentences. I think another poster whose name escapes me now, expressed the same idea. Wow, I’ll leave it alone now. Too many neg responses makes me shut the store down.
I don’t know what you think philosophy consists of: if you expect a load of people to politely agree with everything you say, you’ve got the wrong idea. The entire point of a philosophy board is to criticise each others ideas (agreement is dull, anyway). I appreciate people like me (who take a largely critical roll but rarely contribute actual theories) can be annoying - but thats just how philosophy works.
This post makes clear a new problem in your argument: that of circularity.
Your original argument was that:
Language is limited
Therefore, thought is limited.
But now it looks as if your argument for the first premise is that language is limited because thought is limited.
The circle is viscous - the argument is no argument at all.
I don’t know whom you are referring to, but I know I am not among those people.
I believe that your proof of Pinker’s proposition also proves that there is no limit to the length of a meaningful sentence. I realize this is a completely unintended side effect of your proof, and a proposition which you yourself deny, but it is there nevertheless.
