Lambda the Ultimate

... I think this is false ...

Yeah sorry, it was hyperbole. My apologies.

many utterances are intelligible only with reference to the (non-linguistic) context of the situation they are in

I would say that those are semantic problems, but the "simple foundation" in my question is proposed to be previous to any interpretation. Is that unreasonable or naïve or - something?

I was suggesting a foundation that is a theory, so some semantics are needed, but a very sucinct theory, just interpreted in the (or in some, supposed) basic pre-semantic structure of the natural language, and so, previous to any intended semantics of the natural language. Is this unreasonable?

Think of Frege's Begriffsschrift, as if Russell's paradox didn't apply.

If you wish to provide a formal model of a subset of natural language then of course it is possible.

Could you, for example, choose the subset of the natural language that is needed to write a book on quantum mechanics? Is that doable (or sensible to ask)? In the sense of being able to feed the book to a machine that will detect any formal inconsistencies, independently of their meaning, v.g., A and -A, or A and A -> B and -B, or any other inconsistent combination using one of the rest of the (imaginary?) set of rules that govern formal transformations in the natural language.

There is also...

Those are also semantic questions, addressed above.

consistency is a semantic question. So I don't understand what you mean when say that you want to check it without semantics.

What I currently believe you are saying is that you'd like to recognize syntactic consistency. So that if the text says "wurbles" "are" "warm" and "wurbles" "are" "not" "warm" you can recognize that these two statements differ by "not" and therefore they are inconsistent with each other. However if the text uses "warm" and "cold" those two words are inconsistent with each other because of their semantic relationship.
Michael Wand proved that in general no statement can be transformed into any other statement (theory of fexprs is trivial) if arbitrary statements are allowed to reference other statements.
John Shutt showed it is easy to recognize which statements can be transformed, you just have to pay attention to what they /mean/ in the semantic space (environment).
For example "Professor Wicket says that all wurbles are warm, but in fact in patagonia there exist wurbles that are cold.
There is an apparent inconsistency between "warm" and "cold" but the quoting context makes it not inconsistent.

you'd like to recognize syntactic consistency.

Yes, exactly, absence of contradiction.

if the text uses "warm" and "cold" those two words are inconsistent with each other because of their semantic relationship

Agreed. But only in so far as the text does not include a sentence like "if something is cold, it is not warm, and viceversa".

Then you provide semantic arguments. But my query is about the possibility of a merely syntactic basic foundation.

Ah, no it is not possible.

When transforming expression you need to know not to transform expressions that are in a quoted context. In natural language it is undecidable whether something is a quoting context or not without (lots of) semantic knowledge.

I have been enjoying responses from Anders a lot, especially the priceless Pragmatean Bed reference (which seems to be written by Trey Jones, the speculative grammarian). It is difficult to over-estimate the effect of context on possible meanings of utterances, which Anders notes, especially in the form of quoting. The problem from a listener's perspective is basically: when is some of this intended to resemble something else in the form of a reference, rather being a literal proposition? This gets even harder when traces of humor are present.

There is an element of guessing what someone has in mind, to establish context, though little bombs may be present as intentionial jokes that force you to unwind and rebind to alternative meanings you didn't consider earlier. Some people sprinkle their remarks with traces of parody, which can be hard to recognize unless you allow degree of seriousness to vary from clause to clause. I imagine this would give automation a lot of trouble.

I sense a small undertone of logical positivism to the avenue of research you suggest: the idea of chopping things up into small, primitive, indivisible components you can use to build things back up in a consistent way that recovers an area with less internal contradiction. I tried to look at natural language that way once, exploring word etymologies with that frame of mind as a goal. I found when you strip away context, there is not a whole lot left. Some words just seem to be shorthand references to a scenario that emphasizes a certain set of roles.

On occasion I run into people who make remarks relative to some game they are playing in their minds, without ever saying what they think is literally true. Instead they make plays against the game state as they see it. This is hard to understand without recognizing which social or intellectual game might be involved. This might not make sense without a parody. What would a NL engine make of the following exchange?

     "I think you can extract truth from someone's remarks," Dex said.
     "You haven't hung around Ash much then," Wil observed. "What do you think, Ash?"
     "I'm just farming you guys for experience points," Ash demurred. "I don't take things seriously until level 50."
     "What?" Dex blurted.
     "If you defeat Wil in single combat after level 50, he has a chance of dropping a Legendary Chaotic Good Dev class mod," Ash explained. "I had a bad roll on my last one, and Wil's drop rates have increased."

Not to toot my own horn, but I have an article that was published in SpecGram.

I found when you strip away context, there is not a whole lot left.

"Not a whole lot" is something :)

For example, I would argue that negation, and conjunction, should be part of that something, because I can't think of a single "syntactic" form in NL (a single kind of meaningful expression in NL) that cannot be negated (or anded). So, if you strip away context, you will still be able to negate or to and.

Also, an expression and its negation, in principle, always carry a contradiction, which becomes very meta-meaningful, invalidating its linguistic context.

This is not to say that semantics cannot override contradiction, and negation. For example, if you have a contradiction, and call it a joke, perhaps based on some phonetic play between the diction and the contradiction, it ceases to be a contradiction, to be a joke based on a contradiction; if you see it as a contradiction, the joke's on you.

The question is whether that "something", which I argue in this comment that should include negation and conjunction, has a formal structure, or is fundamentally informal.

In natural languages, propositional connectives don't have a clear meaning. There are philosophical treatments on what they could mean.

In natural languages, propositional connectives don't have a clear meaning.

I *really* agree with that. My question would rather be whether they have a clear syntax.

And also, of course, they don't.

Take 2 sentences that you hold true. Let's call them A and B. I don't know their meaning, only you. Now I make a syntactic move: I produce the sentence "A and B". And now I can guarantee that this new sentence will be true for you.

Of course you can now say, "but no! to me, 'A and B', independently if what 'A' and 'B' mean, means what 'flowers smell nice' mean to you!"

So those are 2 ways of acquiring meaning. Are they the same? The second one I am calling "semantic", because it derives from expressions being in the meaning of other expressions. Is the first way of producing new truth also semantic? Or is it actually syntactic?

"You have the choice between an apple and an orange" versus "You have the choice between an apple or an orange."

There are worse examples than this.

If you take "an apple and an orange" and "an apple or an orange", the difference is clear. It's the default.

However, I must admit that the effect of "you have the choice between", taken as a fexpr that affects those, is quite mind-bending.

"I want the perfume or the ring." Now you have to take into account who says that and under which circumstances because in the polite case 'or' likely means 'and', and you better do something about it.

They're called exponentials.

For example, I would argue that negation, and conjunction, should be part of that something, because I can't think of a single "syntactic" form in NL (a single kind of meaningful expression in NL) that cannot be negated (or anded).

That sounds reasonable. :-) Sometimes verbal use of "and" results in notions not directly related to logical AND. Say a dev is debugging and finds two potential causes of a failure, and says, "I discovered X might be true and Y might be true." In this context, the dev is saying, "The problem might be caused by X, or by Y." If X and Y are antithetical to each other, and thus disjoint, we conclude, "The problem might be caused by X exclusive-OR Y." Sometimes "and" includes just piling up more clauses.

When I compared things similar to each other, after tearing them down, the nuance evaporated. Things taken apart resemble other things taken apart. What made them differ was more associations than details in primitives. I was particularly interested in spatial metaphors; when taken apart, most of the spatial metaphors looked like different takes on the same basic primitive, but with context removed that added nuance.

The basic primitive was related to arrows. You need at least two locations, here and there, and something between them or otherwise they would be the same place. Since they differ, latent in the situation is being able to move from here to there, or vice versa. Whatever separates them can wax or wane in difficulty to traverse. You can emphasize being here, or there, or moving. When considering movement, you can take the perspective of sending or receiving, or being in motion yourself, or being stopped by a barrier, which may come or go intermittently. All in all, you can spin many bits of nuance out of A->B, depending on what part of the scenario is highlighted. I found it acutely frustrating that most of the meaning variations were flavor on perspective. When simplified, it seems too dry to be interesting.

Sometimes "and" includes just piling up more clauses.

I must insist that I am taking into acount that any part of NL can be semantically modified. Including of course any fundamental syntactic core it may have. And I believe that you are referring to a contextual modification of the meaning of "and". One that is implicit, understood, and that can be made explicit if, for example (and following your example), a new recruit was tasked with investigating the problem, and, after finding a clear problem in X and fixing it, goes straight to look at Y. You might tell him: "no, hey, test the app, you must understand that here, sometimes 'and' means 'xor'!"

[...] The basic primitive was related to arrows [...]

I believe this is a too condensed rendition of what you had in mind. To me, it sounds more like an ontological quest than a linguistic quest. However, it has misterious echoes of a linguistic interpretation...

I believe this is a too condensed rendition of what you had in mind. To me, it sounds more like an ontological quest than a linguistic quest.

Yes, it's too condensed, and it was ontological. A longer rendition would have the problem of too little value for so much verbiage. It was just too thin. A simple idea doesn't need a long time-wasting explanation. My question might have been interesting, but the answer wasn't. I was looking for a way to refactor ontology in a constructed language to favor spatial metaphors, based on what I could find in English word etymologies. (I went through a two volume etymological dictionary with a highlighter.) Not all details are fresh in my mind after 25 years though; in summary, it was a bust.

I did not want to bring up ontology, but since you did, I can ask the next question in context. :-) What if part of language processing depends on recognizing ontology in what a speaker is saying? As in, "I see generally where you are going with this ...", which helps you assimilate the next parts expressed. This is sort of the opposite of the Sapir/Whorf hypothesis; instead of words guiding what you think, maybe what you think guides what words you will understand.

Ontology recapitulates philology
      — James Grier Miller (attributed by W.V. Quine)

And, from Quine (different essay): "I am not suggesting a dependence of being upon language. What is under consideration is not the ontological state of affairs, but the ontological commitments of a discourse. What there is does not in general depend on one's use of language, but what one says there is does."

I will answer you quoting myself, sorry. I just wanted to expand on my previous answer.

Also, an expression and its negation, in principle, always carry a contradiction

In fact, an expresion and its negation, can carry a contradiction, or can carry a joke (and probably more things). The question is, are those 2 "carry" the same thing? Granted that a contradiction is the default. But is the "contradictority" of an expresion and its negation, the product of experience and authority and semantic determinants (as is the "jokerity"), or is it a syntactic phenomenon?

I'm not altogether convinced natural language has a non-semantic part. Wrestling with automatic spell-checkers, it seems one can't even tell whether a word is spelled correctly without thinking about the meaning of the text, possibly all the way up into the "pragmatics", which afaics is just a fancy way of saying one has to take into account one's whole awareness of... well, everything.

I'm pretty sure that the things you're mentioning are co-nuclear (in the sense that they are not a valid area for exploration) in his theory of language. Those parts will be understood as non-rational and therefore unmanageable. He probably needs a mechanism for distinguishing valid from invalid before he feels comfortable enough to explore it.

There is an interesting technical challenge in using some sort of formal structure to describe a natural language. A description like that, though, is always going to be an approximation. If one is asking about things like Gödel, though, one isn't treating the formal structure as an approximation; one is imposing formal structure and then finding oneself subject to the limits inherent in formal structure. For the former, the difference between formal and informal is irrelevant; for the latter, this difference is central.

A description like that, though, is always going to be an approximation. If one is asking about things like Gödel, though, one isn't treating the formal structure as an approximation

Let me paint an imaginary scenario, related to this, to see if you think it is a possible scenario.

Let's imagine we have attained a formal word theory. With this I mean a formal theory interpreted in the universe of words of the natural language, and with axioms that govern the way in which those words can combine. In principle, a simple theory that only uses the most basic words, that might perhaps be "to be", some sort of restricted comprehension, etc.; a theory that we can extend with definitions and rules to interpret these extensions in specific texts.

The domain of interpretation of this theory would obviously be finite, since there are just a limited set of natural language words; so the questions of syntactic consistency and completeness would be trivial. However, we (well, Gödel) can produce a NL text that irrefutably shows incompleteness (in another domain).

Is this somehow absurd? [edited to add: I meant my reasoning, of course, not the fact that we can juggle semantics]

I'm not altogether convinced natural language has a non-semantic part.

Ok that's exactly my question. I guess that if you say "I'm not altogether convinced...", the answer is that there is no hard argument denying a basic syntactic foundation.

If NL has no non-semantic part, I think that one possible scenario that would apply, would be one where each of us has a complex "linguistic" neural network in the brain, that we can use to "reason", i.e., to extract new combinations of words out of old ones. No single part of this network, no single path is essential (since, then, that part might be thought of as the formal basis for NL). All networks would agree on deducing that the sun will rise tomorrow from the east, certainly, and so, all netwoks will have common parts; But if the earth were to spin backwards, there would be no problem in all networks agreeing on the sun rising from the west. Agreement then would only depend on similarity of the networks, and so brothers would more readily agree than neighbours that would more readily agree than antipodeans...

I see a problem with this kind of scenario, though, because the formal correction of let's say "scientific texts" seems like an absolute question, either correct or not, and not a matter of what neural network we use to check; even if it speaks about warbles that wirble. All brains would clearly agree that the sun will rise tomorrow from the east; but why would they agree on warbles that wirble, an agreement that should have to be absolute, independent on the semantic context where the network has been trained? If they do, that agreement seems to point to a syntactic, pre-semantic structure.

The alternative scenario is more difficult to describe, since it requires something we do not have, v.g., the basic syntactic foundation. I will try to approach it through 2 failed attempts at discovering it.

The first is by Frege. I seem to remember reading the story that Frege actually thought that he had "formalized the natural language" with his Begriffsschrift, even though he is mainly mentioned in the context of logicism, that was about math rather than NL. I cannot find confirmation for this in the internet or my smallish library, so I'm not sure of the historical accuracy of this. However, looking at the terminology he uses ("concepts" for classes, etc.) it certainly seems so. The idea was that unrestricted comprehension nailed the structure of the copular verbs, of "to be", and that we might add new verbs and concepts on top of this basic structure, given by UC, to add semantic content. So, in Frege's (supposed) scheme, UC would have been the basic structure upon which to mathematize any natural language reasoning.

The other attempt are description logics, where we take different sets of syntactic rules that allow us to produce different sequences of words. So in this scheme, the basic syntactic structure would be given by these assorted sets of operators: Atomic negation, Limited existential quantification, etc.

I consider both failed attempts, obviously. The issue I have is that it seems somewhat defeatist - Frege failed, DLs fail, so let's settle for AlphaGo. I mean, UC, and DLs, seem to point to something real...

I'm not altogether convinced natural language has a non-semantic part.

Ok that's exactly my question. I guess that if you say "I'm not altogether convinced...", the answer is that there is no hard argument denying a basic syntactic foundation.

I'm left honestly uncertain whether we're understanding "has a non-semantic part" to mean the same thing.

What I was thinking when I wrote that was that conventional natural-language processing is divided into phases — lexics, syntax, semantics, pragmatics — and I was expressing doubt that this phase-separation can really be anything more than convenient approximation.

I'm left honestly uncertain whether we're understanding "has a non-semantic part" to mean the same thing.

From what you say, it's clear to me that we don't. I am trying to limit my use of the word "syntax" to formal systems, and "semantics", either to the formal interpretations of formal systems, or to the very inaccurate and volatile meanings of expressions in NL that are the basis of NL's usefulness. I am trying to keep the natural language as a black box, that might have some basic structure, or not; but is basically determined by its role as an ecological advantage.

I guess it is clear that I think that there is some "simple foundation of NL", and that I have ideas about it; but here I am not trying to push any agenda. I am not starting this conversation to later try to steer it away from the originally intended goal and towards an originally undeclared goal. I am genuinely trying to round up the question I posed in the original post, to see whether it really is a question, or whether I was misusing terminologies to see a problem where there is none.

You question was "Is there some kind of proof or argument showing that the natural languages cannot be provided with a simple mathematical foundation.".

The answer was Yes.

I believe that what you are intending to talk about (instead of natural language), is a formal language where the symbols sound the same as english words. Otherwise I do not understand why you would ignore all the constructs that cannot be handled formally.

The answer was Yes.

You mean in the sense that quoting is essential to the NLs? So that you could hardly produce any NL texts if you cannot quote? I'm not sure, can you?.

Quoting /exists/ in NL so if you want to prove something about a NL text then you have to prove that it is never quoted. Your do not trust heuristic checks so the only way left to you is formally proving that quoting is absent.
You cannot formally prove that quoting is absent from a natural language text because there are un-enumerablebly many different ways to indicate that a statement is quoted.
Since you cannot formally prove the absence of quotation, you cannot formally prove anything about a natural language text.

If you choose to construct a text out of a language that has been designed to contain no quoting then that is not natural language but is a formal language. And you cannot embed it within a natural language text because the natural language context may quote and redefine parts of it, again destroying the formal proof.

I see what you mean. But I think that your argument only negates the possibility of an algorithm capable of parsing the Don Quijote and finding all contradictions.

I would think that it does not negate the possibility of a basic syntactic foundation for NL. We may imagine a perfectly consistent and computable core, to which we then add more structure, some of which is inconsistent or uncomputable. For example, in the foundational core we might only speak about something like syntagms, or symbols, or symbolic expressions, or whatever; and only later add the possibility of having different kinds of them, one of which might be quoted symbols.

But yes, it's clear that this formal core, if it exists at all, would not serve as base for "machine understanding" any book. It would still have its uses though.

I really appreciate that you take formalism seriously, and try to put it on a fully formal foundation. Too many people treat it as just a decorative flourish.
I've said all I needed to about the problems it will run into. So now that you are aware of them from now on I will be encouraging you to develop you basic syntactic foundation as far as possible.

I'd like to hear more about your proposed syntactic core. Can you show me some examples of it in action? What kinds of things would you use it for?

I've said all I needed to

I really appreciate that! Many thanks!

Can you show me some examples of it in action

There is something I did related to that here.

But I said I would not hijack the thread is this direction.

I sent that link to LtU some time ago :)

I'm left honestly uncertain whether we're understanding "has a non-semantic part" to mean the same thing.

From what you say, it's clear to me that we don't. [...] I guess it is clear that I think that there is some "simple foundation of NL", and that I have ideas about it; but here I am not trying to push any agenda.

Fair enough. :-)

I too use the term "syntax" for something formal. Somewhere above that level, I think, one gets into something that is rooted not in the sort of mechanical paradigm that we're describing as "formal", but in sapient thought which, I maintain, we don't remotely understand — to the point where I don't think any of our mainstream "AI" technology even addresses the distinction. For the current discussion it should suffice, as a representation of my position, that the "informal" stuff is not practically treatable as a formal system, so that for formal purposes we are obliged to set it apart as "other stuff" (or possibly "here be monsters"). I've been a bit loose, in my terminology, on the distinction between formal semantics and informal semantics; but certainly somewhere up there is some stuff that crosses the line from formal to informal. I don't really envision such a thing as "informal syntax"; to me, syntax is formal.

In relation to Anders Horn's remarks on quotation, I note that in the Lisp world, while quotation is typically resolved at a syntactic level — using one or more special-form operators — fexprs fully engage the formal semantics of the language, which is why they discomfit old-school computer scientists who want to optimize at the syntactic level (i.e., they want source-to-source optimization). The essential notion of fexprs (in Lisp) is that while you parse the syntax as an S-expression without having to know which subexpressions are or aren't evaluated (eval = semantic assessment), you then assess first the semantics of only the operator of a combination, and whether-and-how to assess the semantics of the operands depends on first knowing the semantics of the operator. Even in Lisp, this causes some theoreticians to freak out, because you can't determine whether an operand is to be evaluated until after you finish evaluating the operator — and evaluating the operator is in general a formally undecidable computation. This freakout-worthy situation can only get worse for natural language, where  (1) we don't have a nice, clean S-expression syntax that can be fully processed before we ask about evaluating subexpressions, and  (2) fully assessing the semantics of a subexpression... if we can figure out which one to assess first... may require us to dangle our feet into those deep waters labeled "informal"/"here be monsters".

If I understand correctly, and from an empiricist point of view, sapience would be a source of behaviour. One that has the very special property of being able to produce new behaviour, both in response to known or to unknown situations. Producing new sequences of words would be one of these behaviours. The processes that are involved in sapience are quite diverse, from visual to usage of NL to any weird thing that people experiment in their minds.

From this point of view, we might for example decide to research driving sapience, by observing the reactions of different drivers to different driving situations.

As regards NL, I would think that it would be involved in sapience in 2 different ways. One is that it is involved in the inner workings of sapience. As you say,

somewhere up there is some stuff that crosses the line from formal to informal. I don't really envision such a thing as "informal syntax"

In that "somewhere up there", that (partially?) determines sapience, NL is participating. But I would say that there is another way in which NL relates to sapience: as the product of linguistic sapience, which would be what determines new sequences of words. There is a problem with this, though, because those new sequences of words are produced in thought, and so are outside the reach of the experimentalist. So she would have to look at just spoken or written language, taking the subjects as a black box and studying their production of NL.

So my point would be: granted that NL may be intricatelly involved in the misterious inner workings of sapience. But, if studied as a product of linguistic sapience, why would we need to take into account how it participates in sapience? May there not be some formal core, which is what sapience takes advantage of, to use it and misuse it and twist it till it is unrecognizable? And which should be present in books and in speech - as a basis for all the semantic madness?

the "informal" stuff is not practically treatable as a formal system, so that for formal purposes we are obliged to set it apart as "other stuff"

What I mean is that I understand this "informal" stuff as something involved in the production of new sequences of words (and of behaviours of other kinds), but not necessarily involved in the fundamental structures that constraint these sequences - up to semantics.

I think I got a bit tangled with these silly inventions of mine, "driving sapience" and "linguistic sapience". It seems clear that the sapience that produces the different behaviours is the same, so those concepts seem a bit devoid of content. But I think that the general argument stands, if, instead of saying "driving sapience", I had said "the driving aspect of the effects of sapience" (or "the linguistic aspect...")

The nature of sapience is deep stuff — it's the subject of a draft blog post I'm trying to complete and get out the door atm — but I'm hoping we don't need to confront it here. My hope has been to treat it, for this discussion, as an unknown, x, and simply work around the lack of specification of the value of x. So I'm trying to keep my focus on the language rather than the thinker.

We are getting close, here, to the question of so-called Chomskyism, or universal grammar, the hypothesis that there are rules of language structure that are hardwired into the human brain. It is scarcely possible to name a more controversial hypothesis in modern linguistics. But that controversy, too, is something we can hope to avoid, or at least minimize our commerce with.

My point in mentioning fexprs is that their presence in Lisp causes the full complexity of Lisp semantics to intrude on the grammar of the language, in a pervasive way (whereas one might be more tempted to dismiss quotation as a special case). The semantics of Lisp are, of course, undecidable but not actually "informal"; and Lisp comes with an artificially imposed syntactic structure that places a hard bound on how far fexprs can carry semantics down into the syntactic realm. But, as I noted in my blog post last year on interpreted languages, fexprs endow Lisp with a property that makes it somehow qualitatively more similar to natural languages, and I suspect this intrusion of semantics toward the syntactic end of things is part of that. If natural language lacks the artificial barriers that prevent fexprs from intruding too far on Lisp syntax, then any attempt to process natural language without actually understanding what it means — which I take to require sapience, whatever exactly that is — will suffer chronic problems due to the sapience gap. From my experiences with the failures of automatic translators, both hilarious and appalling, I tend to think that ultimately natural language cannot be processed reliably, even at a syntactic level, without knowing what it means.

My point in mentioning fexprs is that their presence in Lisp causes the full complexity of Lisp semantics to intrude on the grammar of the language, in a pervasive way (whereas one might be more tempted to dismiss quotation as a special case).

I understand what you mean. I think that an interesting question in this sense is whether it is possible to have fexprs without sexps (or without something equivalent). Can we structure something like a discourse out of just fexpr-ing - or quoting? If we agree that we can't, then we need some kind of basic structure to quote, or to pass "semanticless". This structure might be what we are looking for, or it might be something encapsulating it, or it might again be something fundamentally informal. So in my opinion the consideration of fexprs doesn't solve the question.

then any attempt to process natural language without actually understanding what it means — which I take to require sapience, whatever exactly that is — will suffer chronic problems due to the sapience gap

I think that this is what I have agreed with Anders Horn. But I would add that there is a chicken and egg problem here, because processing NL, and understanding it, are the same, right? This would seem to indicate to me that there is need for a syntactic core, that can be understood without having to be understood beforehand.

In my opinion, this formal core should take account for contradiction, as it is manifested in NL. The reason is that contradiction seems like a condition for NL semantics, given that NL is all about truth. In the case of Lisp, I guess that a condition for semantics would be print, etc.

You can no doubt have contradiction that is semantically determined; but it needs a syntactic base, involving conjunction, negation, implication, cuantification, etc. For example, with an interpretation in a closed world, where all semantics are explicit, all contradiction should be "syntactically computable".

I would also agree that it is possible to imagine a proto NL in which negation and contradiction were not present, and which would certainly have had semantics. So I acknowedge that this supposed core might have its origin in a totally informal behaviour. However, that doesn't mean that what came out of that proto language is informal. (What it would seem to imply though, is that "semantics" changed in the prehistory, from "free", to contradiction based... So we probably would experience both... Which would muddle the semantic picture even more.)

So, if you would agree with this farfetched idea (that contradiction is a condition for NL semantics), then the question could be reduced to whether it is possible to have a non-formal-system where contradiction can be detected. Whether contradiction can be informal.

If you don't, perhaps it would be possible to find some other syntactic property that is a necessity for the kind of semantics of NL?

This would seem to indicate to me that there is need for a syntactic core, that can be understood without having to be understood beforehand.

I believe you are asking how people can understand eachother when understanding requires already understanding.
Understanding comes before language, language is built on the scaffolding of non-linguistic interactions that are already understood.

NL is all about truth

Natural language don't really care about truth, natural language's primary purpose is coordinating collective actions and shared attention.

For example, with an interpretation in a closed world, where all semantics are explicit, all contradiction should be "syntactically computable".

You have made all the semantics represented in the syntax, so what you have could just as easily be called "semantic computation".

whether it is possible to have a non-formal-system where contradiction can be detected.

It is extremely easy to detect contradiction in a non-formal system. Just build an example and if there is a problem in the example then there is a contradiction.

processing NL, and understanding it, are the same, right?

Processing natural language without fully understanding it something that people do all the time. Consider answering questions on a test when you just remember some slogans from the class. You have to regurgitate them onto the paper without giving away that you don't have a clue what they mean. But this isn't a particularly linguistic process. People imitate other people's actions all the time without fully understanding the purpose of what they are imitating. There is a famous experiment where young children watched an adult do an activity one handed. Half the children watched an adult who was using their other hand to hold a blanket around them. The other half watched an adult who's other hand was free. The ones who saw the blanketed adult did the activity with both hands. The ones who watched the adult with a free hand did the activity one handed. They were able to quickly extract the form of the activity even without fully understanding the purpose. Is there a syntactic core to action? (there might be, and I would love to see it)

I believe you are asking how people can understand eachother when understanding requires already understanding.
Understanding comes before language, language is built on the scaffolding of non-linguistic interactions that are already understood.

Right. Otherwise toddlers would have it impossible to learn to speak, I guess. But I was referring more to the actual language; not to how people understand each other, but to how language holds meaning. For non-linguistic interactions to be understood, you need something to hold the meaning: a gesture of the hands, a shriek, a way of looking. What carries meaning in language, so that then you can use that meaning to modify the meaning of other pieces of language? Is it only words, or are there other more complex basic structures that are needed in order to start conveying semantics with NL?

Obviously, single words can hold meaning. But they do so in linguistic contexts (informal theories?), that are interpreted in whole domains. So perhaps, in this context, the main question in this thread might be phrased as: Could you construct NL with single words, provide them with semantics, and use those semantics to provide more complexity to the -up till now just made up of bare words- basic structures of the language? Or do you need more syntactic structure before you can start to establish NL semantics?

I want to remark that the question in the previous paragraph is not meant in an evolutionary sense. I don't see any problem with a language that only consists of words, a little like the language we share with our pets. This language might then evolve to have 2 semantically different kinds of words: say, for static forms -nouns- and for dynamic forms -verbs. Then, it might evolve again to allow the adjunction of 2 words, a noun and a verb, to produce primitive sentences. We can further imagine that the syntactic form of nouns and verbs has diverged, and it is possible to distinguish them without knowing their meaning. Then, some syntactic form would have appeared -sentences- originated in semantics, but already purely syntactic. Further, the semantics allowed by these new syntax will be more complex, and there will be interpretations made possible with sentences that were impossible with single words. In this new language, then, you will need sentences to start having semantics. You will naturally be interpreting the language in a domain that needs a language with the syntactic complexity of sentences to be model of. So in the previous paragraph I referred to the logical construction of NL, not to its evolutionary development.

natural language's primary purpose is coordinating collective actions and shared attention.

It might be argued that it achieves that purpose through agreements and disagreements about truths. But I guess that we might be arguing this with no end, there is no criterion that I can think of to finish this disagreement. I wuld argue that socially, its purpose is to organize; and semantically, its purpose is to say truths (in the sense that, semantically, the purpose of Lisp would be to print things, and socially, its purpose would be to organize information? I'm sure that this comparison is, like they always are, terrible; that's why I question it.)

You have made all the semantics represented in the syntax, so what you have could just as easily be called "semantic computation".

Well yes, but it is still syntactic; the question is that it can be detected by purely syntactic means. If you take the same theory, and provide it with another interpretation, this time open world, you will be able to detect exactly the same contradictions through syntactic means, even though contextual semantics would perhaps introduce new contradictions that are not detectable syntactically.

Just build an example and if there is a problem in the example then there is a contradiction.

I don't think this is correct. You might have problems building the example in some space but not in another. Also, contradiction "propagates": once there is a contradiction, you can derive anything, so every possible sentence ends up being contradictory with some other. Building an example of a contradictory system would be like finding problems in every possible aspect of the example, and at the same time not finding them. Contradiction disables the possibility of semantics. Observe that this is very different from saying that contradiction is necessary for semantics. It is very possible to have a system without negation, and with semantics. My wild theory was about contradiction being needed for NL semantics, and I am not trying to defend that here.

Processing natural language without fully understanding it something that people do all the time. [...]

Yes, I totally agree with that. But I think John Shutt was referring to processing in the sense of extracting meaning, of understanding.

I was referring [...] not to how people understand each other, but to how language holds meaning.

Does language hold meaning? That claim seems a bit problematic in itself.

Could you construct NL with single words, provide them with semantics, and use those semantics to provide more complexity to the -up till now just made up of bare words- basic structures of the language? Or do you need more syntactic structure before you can start to establish NL semantics?

I've seen it suggested that language doesn't require grammar, just words — iirc this figures prominently in the evolutionary theories of Derek Bickerton, whose starting point is research on creoles. An interesting thought to compare with that suggestion is that an idiom is, essentially, a phrase whose meaning cannot be deduced from the meanings of the individual words in it.

Does language hold meaning? That claim seems a bit problematic in itself.

I am using "to hold meaning" just to emphasize that if there is meaning, there must be *something* that means something else - or itself.

I've seen it suggested that language doesn't require grammar, just words — iirc this figures prominently in the evolutionary theories of Derek Bickerton, whose starting point is research on creoles

I hope that you read my remark in the paragraph following the one you answer ;-) In any case, I would add the observation that, when creole languages start as mere collections of shared words and idioms, their users also use other tongues, that fully function as NL for them; and that only when creole tongues have evolved into some structure, do they begin to be mother tongue to some - to serve as NL.

I hope that you read my remark in the paragraph following the one you answer ;-)

It's a fexpr on the one you quote!!

Lol. Rather fexpr-ish at that. :-)

Perhaps one could think of NL as postfix, where the listener revises their entire understanding of the text each time they hear another word suffixed to it?

I was mindful of the paragraph following that one; it just wasn't where I found the convenient target to quote. Admittedly Bickerton applied his ideas on grammarless language to evolution; that doesn't mean his ideas were limited to it (I'm undecided on whether I believe that part of his evolutionary theories anyay). I wanted particularly to mention idiom, as it wasn't clear to me that the things you mentioned in the later paragraph fully captured the aggressive non-cumulativity of idiom.

It occurs to me that an idiom may be thought of as a fexpr that completely changes the meaning of its operand, and has null syntactic representation; it is purely a matter of reasoning by the audience to decide whether or not to apply the operator. (When we say that Bob has lost his marbles, it is possible for this to indicate that Bob has misplaced the equipment for a game.)

I think I may be missing something with idioms. To me, they don't seem fundamentally different from single words. In principle, they have an atomic meaning, just like words. They have components that, isolated, have their own meaning; but there are words like that, say television or tug-of-war. As you say, they can be taken literally, or as idioms, i.e., they have more than one meaning; but there are also words that are ambiguous. Finally, both properties, taken together, don't seem to add up to more than their sum, at least as regards the relationship between their form and their meaning. Which there isn't.

The point I want to make is that the form of an idiom has no relationship to its meaning, and so, even if in origin that form was syntax, it cannot be called syntax any more, since it doesn't affect semantics. It would be like looking for meaning in the letters of a word, like the Kabbalah, right? So in my view, the idiom would have syntax (provided there is syntax in NL) when taken literally, and would lack it when taken as an idiom.

Were you thinking of some other property of idioms that is relevant?

Perhaps the fexpr metaphor has served its purpose.

It seems to me there are two different conceptual frameworks from which to think about NL, with contrast between the two underlying much of the discussions here, but the frameworks themselves tend to stay out of sight. In essence, one view supposes that meaning is derived from language, while the other view supposes that meaning is assigned by the observer.

In the former view, language contains meaning, which is built up as one adds more text. It seems to me you are assuming this; I see glimpses of it in your comments, from time to time, and it seems that various of your views would follow naturally from such an assumption.

In the latter view, meaning comes from the observer, through the observer's interpretation of what they observe, and in the case we're considering, what they observe is language — text. If one starts with this assumption, and asks whether the language-contains-meaning view also works, one is likely to conclude that the language-contains-meaning view may be a useful approximation up to a point but is pretty sure to break down under stress. A number of us here seem to be inclined to this conclusion, so I suspect we're using this assumption rather than the other.

I speak in general about carrying menaing, holding meaning, or being the subject of a sentence built with the verb "to mean". But I don't think that I assume any particular origin for that meaning.

If there is meaning, I think that it is clear that there must be 2 recognizable forms involved: the form that means, and the form that is the meaning. When there is self-reference, both forms would be the same. Meaning establishes some kind of association or correspondence between those 2 forms. That association happens in our minds, and is determined by our minds and the minds of our social relatives, and at the same time determines those minds in weird ways that I am not willing to consider. I would object to the idea that language has meaning outside our minds, though.

And I think I am not assuming any agent or form that establishes that association, that meaning. I am just asking whether that association is completely arbitrary, i.e., whether there is a set of forms that mean, and a set of forms that can be meaning (which may intersect or coincide), and there is a map from the first to the second that is independent of the forms that mean, or whether there is some pre-semantic algebra, that provides the forms that mean, and affect how they mean, are somehow a variable in that map (even though its forms can then become meaning themselves, and be semantically changed).

I speak of sets in the previous paragraph. The things that mean, in NL, certainly form a set: there is a finite set of words, and combinations of them are enumerable. The things that can be meaning, however, are certainly not a set. But we might limit ourselves to the things that have ever been meaning, which is a set.

I speak in general about carrying [meaning], holding meaning, or being the subject of a sentence built with the verb "to mean". But I don't think that I assume any particular origin for that meaning.

This is, indeed, the distinction I was attempting to convey. Your apparent starting point is to suppose that meaning resides in the text. When you say it doesn't matter how it got there (I hope that's a fair paraphase), that emphasizes that you are treating it as residing there. I'm not saying there mightn't be some earlier stage, I'm saying that you're choosing to suppose that any earlier stage can be disregarded. An alternative supposition is that meaning arises from the process by which the sapient reader interprets the text. If meaning arises during interpretation, then conceivably the meaning cannot be usefully deposited in the text; it might then be possible to neatly package up the meaning in a way that could be readily depicted as deriving from the text, but then again, it might not be possible to do that.

[...] meaning arises from the process by which the sapient reader interprets the text. If meaning arises during interpretation, then conceivably the meaning cannot be usefully deposited in the text;

I must disagree with this. I don't see why a formal theory and a formal interpretation wouldn't fit in that process. But you don't disagree with with my disagreement:

it might then be possible to neatly package up the meaning in a way that could be readily depicted as deriving from the text, but then again, it might not be possible to do that.

That's the question :)

In the end, you have 2 things: a form that means -the text- and its meaning -perhaps provided by sapience. We can now abstract from whatever has been in the origin of that "association", and concentrate on possibl estructural relationships between both. Hence my question: is there any?

And here, I am accepting the possibility of there being none. Your proposed intervention of sapience is, in my opinion (and strictly as regards the matter we are discussing) equivalent to thinking about neural networks. We might give a name to this option, the semanticist option, as opposed to the syntacticist option that presupposes a syntactic core.

So far, the semanticist option seems to me mainly supported by historical arguments, by "if no one's found it, it surely doesn't exist". Once accepted, the possible scenarios where such option would be correct are presented as proofs - but, generally, nothing in those scenarios negates the possibility of the synctacticist option.

I tend to see some evidence in support of the syntacticist option, as I've made clear in other comments, but it doesn't seem enough to settle the question. So, there doesn't seem to be much more to say on this topic, right? it seems quite unresolved and probably unsolvable - unless by providing a candidate for the formal core...

It's seemed to me that your position is built into your initial assumptions. That's pretty usual, of course. But it can be useful to know what one is assuming, even if one then decides to stick with it once known, hence my struggles to articulate when I think I'm seeing. A few thoughts, here.

If meaning arises during interpretation, then conceivably the meaning cannot be usefully deposited in the text; [...]

[...] I don't see why a formal theory and a formal interpretation wouldn't fit in that process.

One possibility I'm trying to leave open here — perhaps not the only such, but one — is that the meaning cannot be effectively described by a value. We're used to the idea of first-class functions, of behavior reduced to a self-contained thing, and indeed all formal systems are like this; the whole formal behavior of the system is a value, expressed in the form of a Turing machine or whatever. But by the time you've assumed that, it seems you're already most of the way to the (as you put it) syntacticist option. Gödel's result presumably applies to systems of this sort. What if the interpreting behavior can't be packaged up neatly as a value, like that? It might be effectively impossible to reduce the behavior that way; some people have even suggested it's theoretically impossible to reduce the behavior that way (didn't David Bohm dabble in some weird ideas like that? not that I bought those ideas, but it's clearly possible to conceive of such a possibility). As I've mentioned, I prefer to treat the behavior of the sapient observer as an unknown, and that means not committing on whether the behavior can be represented as a self-contained value. Hence my reckoning that if you start with a value representing the behavior, you're already most of the way to deriving meaning from text, whereas if you start with the behavior in the form of stuff happening, you are still uncommitted on whether or not it can be reduced from happening to value.

Your proposed intervention of sapience is, in my opinion (and strictly as regards the matter we are discussing) equivalent to thinking about neural networks.

That seems an unnecessary assumption. Neural networks might be, again at a minimum, not effectively useful for describing the phenomenon. I maintain (and really, really need to get out the door my draft blog post on this) that we have no freaking clue how sapience works. Neural networks are in vogue atm.

"if no one's found it, it surely doesn't exist"

Perhaps we can agree that's a caricature of the rational position. How about, "if no one's found it, and a lot of smart people have been looking for it, we ought not to assume it does exist".

One possibility I'm trying to leave open [...] is that the meaning cannot be effectively described by a value.

In a conceptual framework in which meaning cannot be described by a value, my question would not make sense, or at least, would be clearly answered in the positive: yes there is proof that no formal core is possible, since there really is no permanent or repeatable form at all as regards meaning, so no form to consider as formal.

The dicotomy, however, would not be whether it can or cannot be effectively described by value. It may also be whether just some aspect(s) of it can be described by value. What I would offer as evidence for that possibility is something like negation, that modifies meaning. Whatever sentence there is that you hold true, when negated, you will hold untrue - if you don't change the meaning with semantic tricks, which would be perfectly acceptable and common. So, the semantic difference between NL sentences and their negations, in general or by default, can be seen as boolean.

if you start with the behavior in the form of stuff happening, you are still uncommitted on whether or not it can be reduced from happening to value.

I think there are 3 different things here. One is the question I pose: whether it is meaningful and can -or must- have an answer. Another is any answer I may believe I have for that question. And a third is how my belief on that answer might be determining the question I pose.

About this I would say that you seem to agree that there is an open question here, since you say something like:

"if no one's found it, and a lot of smart people have been looking for it, we ought not to assume it does exist".

I worded the question something like: "is there some proof that there is no formal core in NL?" And I am trying to maintain here the position of devil's advocate for that question, and so, trying to keep my possible answer out of the discussion. Of course I may have not succeded, I won't argue it :)

However, I am ready to accept that my answer is determining the way I pose the question, and in this sense, I would be interested in seeing it posed alternatively. Well, actually, it might perhaps be said that you are posing it alternatively: Is meaning in NL in any way typable^H^H^H^H representable by a value?

You run around with a set in your head?

with many :)

Yeah, well. All jokes aside, that's just not how a brain works. Not even close.

given that NL is all about truth

If there is a basic syntactic core (BSC) in NL, it must be present in scientific NL. Of course there is no exact definition of scientific NL, but if you take a book on QM, and remove dedicatories, historic notes, prologues, etc., you might have a sample. And, also of course, being a sample is not well defined. But in any sample, the BSC should be present.

Now, is there anything more significant in scientific NL than a paradox? Well, yes, a valid theory about some aspect of reality. But a paradox, being one of the main and worse things that can destroy a "valid" theory, is very significant. Is it in any way special, as a destroyer of theories? I would argue that it is; that it is the only syntactic way. All others I can think of are related to the meaning of the theory.

[Edited to add: In "street and family NL", of course, paradoxes are the norm. But we have already agreed (I think) that NL has more than enough semantic tricks to deal with paradoxes.]

Just to check that I am on correct ground speaking of "fexprs in NL", and also for the meta-laugths. Anders Horn spotted something in my original post as false. He was right. However, in the last line of my post, I warned about poetic licenses; Would this last line be doing some kind of "fexpr'ing"? Would it be changing the semantics of the "wrong" line, from false to hyperbole? In that case, the fexpr (the last line) should be able to pick as "arguments" any previous piece of the discourse, arbitrarily, of course, to disposses them of any already acquired meaning and provide them with any new one.

Or would you require some constraints on the order of fexprs and arguments?

Hm. If NL passages can change each other's processing by reference regardless of order (and why not?), how about this:

The following sentence is true.
The preceding sentence is false.

("Now actually, that is not the answer that I had in mind because the book that I got this problem out of wants you to do it in base eight." — Tom Lehrer)

Periods seem like natural conjunctions. My preferred simple solution to the Liar paradox is that every sentence asserts its own truth (Arthur Prior's solution), so the above translates to:

It is true that the following statement is true and it is true that the preceding statement is false

Which yields a simple contradiction and hence is simply false. There are some detailed elaborations and variations on this.

1) Either your translation is buggy (never mentioning 'preceding') or I don't understand your idea. 2) Even if the translation was just buggy, I don't see how this idea resolves the paradox. Can you explain?

Sorry, clearly responding on a phone after a long flight is inadvisable. I've revised and posted a reference.

I don't find this approach of treating the period as a conjunction at your link. You just deny that the subterms of the conjunction are propositions? What do 'following' and 'previous' reference then?

I prefer the resolution that self-referential statements are only valid propositions (that need be either true or false) when the chains of referents are well-founded.

The periods as conjunctions are something I posited, since it seems a natural interpretation. I believe I only said the interpretation of the liar paradox was due to Prior. Apologies if that was confusing too.

There are certainly many valid resolutions of the paradox, each with their own tradeoffs. Prior's solution just seems to fit in this discussion of purely syntactic reasoning. Others seem to require some semantic baggage which many seem to want to avoid in this discussion if I've understood correctly.

Thanks. I misread the attribution to Prior and thought that it would be found at the link.

I can see how you'd want to interpret periods as conjunctions if you like Prior's resolution. That seems like it needs to be generalized (e.g. "the statement on the opposite side of this card is false/true").

I agree there are multiple ways to "solve" it.

This seems eerily similar to the claim that typed programming languages are subsets of untyped languages? There are arguments expressing the contrary.

I'm no expert in natural languages so perhaps this analogy breaks down somehow.

I see difficulty in taking a subsetting view of the relationship at all. A formal language has (Platonically speaking) precise rules for mapping terms to semantic values. A natural language is used by sapient beings for communicating with each other. A natural language does not even have a fixed meaning; each speaker has their own idiolect, making the language as a whole a moving target at best and making dead languages extraordinarily difficult (at best) to resurrect. And the purpose of the language is not to identify a specific point in a precise and fixed semantic domain but rather to induce changes in the mental state of other sapient beings, based on the speaker's expectations about how their audience will respond to their utterance. Obligatory xkcd.

Even the supposition that we're dealing with formal terms is a bit oversimplified too. Our pets certainly don't understand all we say to them; there was a celebrated case of a horse that supposedly could do arithmetic, and on investigation it was found the horse was picking up cues from its handler (Clever Hans) — but our pet cat sometimes shows an uncannily accurate reaction to things we say in its presence, and I find it sobering to realize that in these cases, unlike the horse doing arithmetic, subtle cues are allowed, in fact they're a normal part of the way we communicate with each other, and the loss of them is, for example, why internet communication is laden with emoticons.

our pet cat sometimes shows an uncannily accurate reaction to things we say in its presence

Yes definitely. But we might structure 2 different discourses, one speaking about having to leave the bitch in a pet home during holidays abroad, and another speaking about some QM event; and even though they are semantically very unequal, we might imagine that, by chance or by artifice, both discourses have the same structure, the same number and form of sentences. The bitch will very clearly react to the first discourse and not to the second. But the property I am enquiring about will be identical in both discourses.

I totally agree with all you say. However, I also sense that there is some chance of saying something like "eppur si muove". For example, Darwin, in "The origin of the species", presents an argument that is perfectly consistent, understandable, discussable, and does not depend on any formal framework extraneous to the natural languages.

For natural languages to have a simple mathematical model you need a mathematical model for feelings.

I would say that that is only true if you want to use the NL to speak about feelings. Why would you need a mathematical model for feelings to write a book on QM?

Even most math is that informal that it mostly conveys feelings. The 'feeling' from some function 'f' going from some poorly imagined 'A' to 'B'. And that's a good thing!

Of course there is a formal system. Well actually MANY such systems. One for each person. Its called a human brain. Although perhaps human is a poor choice, considering a comparison of various animals such as my canine friends, and certain politicians ...