The only thing I denied on this thread and which you defended, thus being the difference between us, is that I denied that “an infintely large sentence can be constructed”.
reading the rest of your posts I can see that we are in complete agreement over the concepts - for some reason though we differ substantially on precisely what the sentence an “infintely large sentence can be constructed” means. Personally, I find it odd that you would say that:
This seems to me to suggest that you too believe that the construction of one sentence that is infinitely long is a)impossible and b)unnessary, and yet you still believe that “an infintely large sentence can be constructed” has been both proved and essential to the case in hand. I can only conclude that you see some difference in the statements:
- the construction of one sentence that is infinitely long is possible and;
- an infintely large sentence can be constructed.
And yet, for all my want of trying, I see no difference between the two. At any rate, I would deny both of the above, but my oringial intention was purely to show that there is no limit to how long a meaningful sentence can be: which we both agree on (or though for some reason you think I have denied, despite my repeated insistence that it is the case).
I think you’re right. Discussing was the wrong word, I should have said debating.
With all due respect, my point is being misunderstood in this forum. I read it over and found that my original post was inarticulate. It rambled before coming to the main thesis. So, let me restate it.
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I never denied from the very first post, that started this thing off, that we could (in the abstract) create an infinite sentence. Though, I will admit I didn’t explicitly state this originally.
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I addressed myself to the real world that is the physical environment we reside in and all that goes with it. For instance, it’s well known we have limits as living beings. We can’t enunciate more than a certain number of sounds (which accounts for the same phonemes cropping up in different languages). Physicists propose that as finite-state-machines, our cognitive processing abilities are limited. Our states of being are large but limited. Our physical feats of body are limited. I could go on listing our limitations but the point is obvious, so I won’t.
With the above in mind, I posited that the real world meaningful sentences we can make are limited. If all the human beings in the world consorted to write one sentence that would be infinite for the entirety of their lives, the output would still be limited. Even if succeeding generations carried it on, as all of us will eventually die out in this part of the universe (of course this isn’t an absolute certainty, but damn very likely). We could never create that sentence. If there is weak point in my argument its here. It could be argued that human existence (as a species in the universe) is potentially infinite, and thus we could generate an infinite sentence(s) given enough time. Even if that is true, the problem would then become whom understands this infinite sentence we’re in the process of making? This starts to get into the God argument thing and thus I abruptly drop this line of reasoning. That is, the potentially infinite sentence that we’re creating in the universe is only understandable by an infinite being that witnesses its infinte creation…ohhh that kind of junk sickens me…so lets not even go on with it.
But, yes I did go further and conclude that we could never make an interpretable sentence that is infinite in our real world. This is clear because its physical impossibility precludes its perceptual possibility. Again, I didn’t deny conceptually that an infinite sentence could be made. The question of this being done is a triviality. My point is not so much a dissension with Pinker, but a caveat. I agreed with his point, but remarked that realistically this sentence is not possible. In fact, as I remember it, I wasn’t even addressing one infinite sentence but a set of infinite sentences, but of course formally what applies to one sentence would apply to its multiples.
What applies to sentences, applies to their constituents: words. I don’t believe we can make an infinite real world word either. If we do it using repetitive constructions the meaningless of it is palpable. Take the word good. If we strung together something like good good good good good good good good good good good good good good good good, and called that a word, it would be nonsense. If somebody said that many goods to you you’d think they were mad. If this process were carried on infinitely, would that mean we’ve got the infinite good? Pun intended here.
Personally, I find it odd that you would say (on April 29), “The sentence I constructed can be expanded ad inifinitum without losing it’s meaning. There is no upper limit on how many times it can be expanded,” without realizing that expanding (lengthening) a sentence ad infinitum is exactly what one would have to do to construct an infinitely large sentence - which you now say is impossible!
Of course, one would need an infinite length of time to do so. But that can’t be your objection, since one would likewise need an infinte length of time to expand (lengthen) your list of possible sentences “ad infinitum”.
Naturally, either expansion process (the lengthening of the list or the lengthening of the sentence ad infinitum), by whatever algorithm or procedure one chose, would “go on forever” as I have said, but you would never come to a sentence of infinite length, just as you can never “reach” infinity. In that sense, both the infinitely long list of sentences and the infinitely long sentence are “impossible”, but neither is more “impossible” than the other. Constructing anything infinite is “impossible” - unless you are given an infinite amount of time to do it.
But the issue as originally posed is not whether it is possible to “construct” a list - or a sentence - of infinite length. It is rather an issue of whether in principle there is any limit on the number of possible different sentences, PLUS the unrelated issue of whether there is any limit on the length of a meaningful sentence. Pinker says no to both issues, and I agree with him.
Do you?
I understood your point 1 above, and I agree with it. That’s why I disagreed with brevel_monkey when he said it was “just silly” and that nobody argues for it. Obviously you, Pinker, and I do argue for it.
The “real world meaningful sentences we can make” are limited only by time and space, but not by the language itself, which is the point Pinker was making. The language itself imposes no a priori limit on the number of meaningful sentences that can be created. (Nor on the length of a meaningful sentence, but that’s another point).
As I have explained earlier in the thread, I already understand the meaning of the “infinite sentence” that brevel_monkey’s proof would produce, given an infinite number of iterations of the 13-word string, without even having to read it.
Call me God if you must, but I maintain that you and anyone else of average or better comprehension can understand the meaning of it as well. The meaning of those 13 words is clear, and it does not become less so through endless reiteration.
Harold Niddly, you were so close to getting my point and missed it at the end. Not to condescend, I don’t intend that. You did agree that real world meaning sentences are limited by time and space. But, then you seem to misunderstand again, that I’m referring to real world understanding not abstract understanding. I would like to try a variant of that story about muts to bring my point out.
Lets say we have a story that starts off: I went down the mountain and tripped over a log, then turned around find the stone, and came up the mountain and saw an eclipse, and climbed in a cave and saw a light and walked toward it, and then I was in a cloud and but it wasn’t a cloud, I realized I was in a plane, it starting going down fast, then I was in a boat with a vast ocean before me, but it wasn’t really an ocean but a lake…etc, etc.
lets assume this kind of phantasmagoria of scenes on and on never ending, never repeating its described scene that its protagonist is experiencing, okay?
Now, we’d have an infinite sentence in the abstract that would necessitate you actually reading it forever to understand its content. If you ever stopped reading it, it would be like watching a movie and then not seeing it to the ending and thus not understanding the content of the movie. It won’t suffice to know it oh well this story never ends, because you to have know what is happening in the story endlessly. In fact, the way I’ve started telling this story you don’t even know if it’ll go on endlessly. I say clearly you can’t! You’d have to live forever and the story would have to be told forever. What I say is that real world event can’t happen and thus this unfolding sentence can’t be infinite (ignore the conceptual abstract notion that it is infinite, on this we agree). And that’s the sense in which I’m saying human beings can’t make an infinite sentence in the real world!
Yes, I understand that point perfectly. And you have created an example of an infinite sentence that cannot be understood without reading it “all the way”, which is impossible because it never ends. I get that.
But in the special case of the example provided by brevel_monkey, where the infinite expansion of the sentence is perfectly predictable in advance, I DO know what the infinite sentence says, and it IS understandable in a “real world” sense. So it is a counter-example that disproves the proposition that no infinite sentence is understandable in a “real world” sense. Other counter-examples could be created just as easily.
In fact, probably an infinite number of them. 
no that’s exactly what I’m saying that thing about the dogs is not. It’s not real world. When I say real world I’m talking about experiencing, hearing, touching, feeling, seeing, etc. Not some conceptual idea that something goes on forever. That’s the problem with that example we can only understand it as a concept NOT as real world experience. To understand it real world, at least as I mean it, you have to see with your own eyes this infinite series of events take place, you can’t, I can’t, nobody can do that. And thus, as real world experience this dog-chain thing doesn’t exist and this sentence in that sense is meaningless. It never will happen in our tangible, physical world, it has no real world instantiation, it describes something is intangible to us in the real. Regardless of the fact, that it describes something that is readily understandable in the abstract. 2 different ways of understanding. In my way, it’s meaningless. As any infinite sentence will be for us in the world 5 of senses we live in. We can’t experience them because we’re finite and the sentence is infinite.
The idea of a dog eating food is perfectly amenable to the human senses, as is the idea of making food out of other dogs. That a dog could be made into food to feed another dog, and that dog could likewise be made into food to feed another dog, and that this process could go on forever, without stopping, without limit, is something even a child could understand. There’s nothing intangible about it.
I think you just have a problem with accepting the concept of infinity (or endlessness, or limitlessness, same thing). It’s really not beyond our comprehension at all.
I give up you’re not getting my point. I just said this is not conceptual. It has nothing to do with conception. I admitted copiously that the concept of endless dogs eating dogs is infinite and can be meaningful to human mind. I am not talking about that…oh for christ sakes. bye.
Well, I’m back again, I’ve been involved in an intensive project at work that kept me from this site for well 3 months. I know I upset a lotta people way back then, with an emphatic denial that there is no infinite sentence that can be created in this language or any other. I made my argument based on the perspective (kinda like David Hume) of our being finite beings with a limited ability to express in spoken or written language, the perceptual world that surrounds us. I was rebuffed on this point, and I believe misunderstood. At least one poster gave what I call a conceptual sentence that appeared to disprove my argument. I did a little research, mathematically on this topic. I looked into the theoretic and found the infinite theory of ordinal numbers actually supports my claim, even on the conceptual level. I’ve posted my article on my website and here is the snippet that is applicable.
Most of these constructions use a subject that refers to itself and names an object. For instance: The man that saw a man, and that man saw a man, and that man saw a man… Sentences of this type have the verisimilitude of infinite construction. Yet, they don’t. Sentences of this type run smack into some form of the Burali-Forti Paradox . This paradox occurs in the theory of transfinite ordinal numbers. It applies to numbers but just as easily can apply to words in a sentence structured in ordinal sequence.
Burali-Forti Paradox (BFP) can easily be applied to the simple infinite sentence I cited. First, lets get an idea of what the paradox means. BFP creates a paradox from 3 existence conditions:
- Every well-ordered set has a unique ordinal number.
Well-ordered means the set is arranged from least number to greatest. The unique order number is the number that defines the place of every number before it. Thus a 5th ordinal number applies to a set (1,2,3,4)
- Every segment of ordinals has an ordinal number, which is greater than any ordinal in that segment.
This means a subset of numbers arranged in least to greatest has an ordinal that is not a part of it and must be greater than its ordinal in the subset. The example above applies again. So, the subset (1,2,3,4) of natural numbers has an 5th ordinal, which is greater than any of the ordinals in the set. E.g. the number that names all the numbers in order before itself.
- There is a set B of all ordinals in natural order (least to greatest) that is well-ordered (has a smallest member).
Here is where a contradiction arises. If such a number say x in B exists, it is greater than itself, by condition 2. This contradiction arises precisely because set B is an infinite ordinal set. Being such a set, an ordinal for any subset of it will always have a successor ordinal that is larger than the ordinals in this subset, and not a part of this subset.
Lets apply this to the sentential string example. To see this, we will number the objects of these sentences as such: The man that saw a man (1), and that man saw a man (2), and that man saw a man (3), …and that man a saw a man (Nth).
Generation of this set infinitely, we would have set the following natural numbers, well-ordered: {1,2,3,4,5,6,7,8,10,11,12,13,14,15…∞}. But the Nth ordinal of this set would have to be not in the infinite natural set by the Burali-Forti Paradox. This would mean that there exists a man such that man DID NOT see the previous man on the order specified. Which, in turn would mean that even conceptually this infinite sentence would break down in its meaningfulness.
Even if one could say an infinite number of things, who would want to listen? 
There seems to be a very positivist assumption right at the beginning of the thread that language is statements, subjects and predicates. Any proofs for or against using such formalised descriptions will miss out on the much meaning anyway, as you are corralling “meaning” into “description”.
We can of course say “Water.” We can ask “Water?” Implore: “Water!” Tentatively assert “… water(?)”. Meaning correlates to experience and desire, prescription as well as description. It’s as finite as the human sum of experience, desire and logically-bounded imagination; probably not infinite, but what use is there in knowing what the dark recesses of infinity hide from us if we can’t communicate meaningfully about it anyway?
I’ll take that as a qualified yes to my rebuttal. You seem to think this whole question is a triviality. I would probably agree with you. Except for the notion that we can’t express, by deduction our knowledge of infinity thru our native tongues. This seems like a profound result. Since my background is in infinite sets and the logically implications of these sets it, concerns me deeply. It seems anything involving infinity is closed to us in the epistemo…man wait while I look up how to spell this big word…no screw that, in the theory of knowledge. Damn Latin term…Anyway, if I can’t say infinite things or write sentences in the infinite, how could we know infinite concepts?
That’s gets me bad! I don’t like this logical conclusion. Just as much, as I don’t Cantor’s existence proof of transfinite sets. It leads right into the hands of religionists, who are all too willing to jump and say: See, that means there is an infinite being beyond us, he’s personal and real and beyond our understanding. I wanna agree that there really is a linguistic infinity. I really do, but can’t get over the philosophic problems therein…Of course we don’t need to be able to express infinity linguistically to have knowledge and that saves the whole argument from become a ridiculous.
But, look don’t put this down to trivialism. In the early 20th century most scientists believed that there could not be any atomic interaction in a vacuum, until to smart MIT engineers found that ‘virtual’ particles still resided in vacuum tubes and sparked and area that lead to micro-chips and we know where that lead.
The discussion of an infinite language is fertile grounds. BTW, I do believe there are artificial infinite languages, like PERL, or Unix’s PYTHON. Though their contextual meaningfulness is limited to virtual environment under which they are applied, thus not human languages and have not real world sense of meaning.
Okay I’m out again.
I don’t think it’s a triviality, insofar as I don’t dismiss the use of infinite sets and the study of them at all. My point is more that the assumptions of the argument effectively transpose the discussion into mathematics, so any truths you arrive at will be mathematical truths, not linguistic ones.
As to the second point; very, very little knowledge is purely deductive, no? And native tongues were not designed to handle infinities, but the finities of existence that they grew up in - any such abstraction is bound to require specialised language.
That’d be ancient Greek 
But… if I can’t speak ancient Greek, how can I know anything of it?
The concepts themselves are not infinite, they can be handled as other concepts. I can have a concept of God without being God, however imperfect that concept must be - I do my best with my litre-and-a-half of monkeybrain.
If they want to survey mankind’s ignorance and call it “God”, I should leave them to it; this is the standard approach of creationists, after all, retreating from the advancement of scientific knowledge all the time, falling back to the first point of ignorance. If there is a God, I should think and hope she’ll be most unpleased with the compliment.
It’s worth examining just how far beyond our understanding they actually go in their claims before anthropomorphising this infinite being.
Well, as I said, in my view the problem is a (n interesting) mathematical one, not a philosophical or linguistic one. I’m afraid I’m mathematically unqualified to do much more than follow the arguments…But I have good news - you can express infinity linguistically. Look, just there, you did. You know what you meant, others know what you meant, that’s language. Of course there are almost certainly things of which we have no comprehension, that are unlike anything we have experienced, and we can have no words for such things - but as our comprehension grows, so will our language.
Human meaningfulness is limited to the environment under which it is applied, too.
Yes, you’re right it is Greek. Epistemology! I should have known that. Anyway, God’s a woman? Wow, you must be a woman. I thought that this non-existent being had no sex. Or you’re joking with me. But, hey that’s way way off point. And I’m sorry I guessed you’re sex. If you wanna berate me for it, please do. I deserve it.
Now, on to the topic. You make a point about language being something that is perceptual and in our perceptual world. You go on to make a point that reminds me of Russells paradox. I want to first point out that the Burali-Forti paradox is no proof. It’'s just a paradox about infinite ordinal numbers. These gents didn’t submit a proof that infinite sets of ordinals can lead to the contradiction I described…damn my cell …probably my daughter…hang on…
Anyway, Russell’s paradox is like this:
Name a number that is 13 billion digits long and can not be described in less than those digits or more than those digits.
Well, you can’t can you? But by describing as such, you NAMED the number. The description itself does it. But, the description also says you can’t do that. Thus, we have a paradox. Not an unprovable statement in math logic, but a conundrum. Most logicians approach this from the standpoint that the ‘name’ is being used in an ambiguous way. I agree. It’s like Goedel’s imcompleteness problem in formal systems, but with the twist that IS self-contained and need no larger system to be understood… hey I’m getting so far field, I feel as if I’m drifting from my original point.
I appreciate your strange supporting opinion on this issue, but feel …oh forget it, I gotta git some cigarettes now.
It’s not much cause for “wow”, around 50% of humans are women. 
And I’m not a woman, I was just being facetious to highlight the difference between my postulated god and theirs. Do women have female gods? It would seem reasonable for some faiths to allow women to speak of Her and men of Him, if we’re talking of a being that is reflected in all of us or in some way part of us. I digress.
Didn’t Russell more or less solve this with his Theory of Descriptions, though? At least, he said that you could name nonexistent entities but do very little with them; I could no more name the King of France or the Tsar of Australia. “There is an x such that x can be described: x is a number that is 13 billion digits long and can not be described in less than those digits or more than those digits” is false. What am I missing?
But “infinity” is not such a definite descriptor, is it? I’m not an expert on infinit(y/ies), but as I understand it, it’s not self-contradictory. You don’t need to be able to say something infinite in order to talk of infinity. I don’t need to talk Russian to speak of the Russian language; I don’t need to know that “Russian” in Russian is “Русски”; there’s no guarantee that a native Russian speaker will be able to say more about his (/her) language than I can, speaking of it in English.
To answer your questions, Russell’s theory of types didn’t solve the problem at all. It compounded it. Classification only creates a metasystem that relies on self-reference for its foundation.
Regarding your statements about infinity, I can say this. The answer depends on which philosophic camp you wanna agree with. If you’re in the Platonist camp there is a real existing infinity that doesn’t need our knowledge of it to be what it is. It exists as a conceptual object of our minds and need be nothing else. If you’re in the intuitionist camp, infinity is a potential existence that we discover thru our study of it. It’s directly inaccessible to us, being finite. We can only theorize about it, never experience it. That was my point regarding an infinite sentence. Its reality is in the conceptual not the perceptual. Perceptually it is meaningless-that’s an infinite sentence. Infinity like the universe is beyond or reach (at present at least, lest we become Gods at some point). And I agree that doesn’t stop us from knowing all manner of things about it; classifying it, using it to prove the structure of finite things, employing it in our pursuits of science like physics, etc. Knowledge of infinity doesn’t solve the paradoxical nature of the concept.
What is becoming more intriguing to me is finitude. We certainly know of limited things and states of beings but is this a necessity of there being infinity? For instance, we know that the atoms here on Earth are constantly being recycled going thru different states of being. Must that be the case? All matter remains constant and simply changes state. Here is a finitude that leads to an infinity, unless at some point matter becomes non-existent, not a such wild idea but a different topic. Even a limited substance (to use the old medieval word for matter) is not really finite. We can’t create or destroy it, so it is infinite in time. The real question becomes what is finitude? As strange as that sounds. Is there really a finite? Stranger as that sounds. It seems finitude can be infinite in time, it’s just in our state of being we don’t have enough time to experience it. God do I wish we were Gods! As contradictory as that sounds! Not to mention transfinity. Even in set theory take 1 and 2 a finite set. But, if we use an operation like division we have 1/2. We can take the square root of this quantity and keep going on and on and all of a sudden a simple set (1,2) is infinite. Isn’t anything that remains finite? I ask?
Damn, I’m rambling okay me shut up now…