Remember when I recently announced the publication of Paul Postal’s new book attacking Chomsky and generative grammar? Well, Slavo/bulbul has been reading it and getting increasingly grumpy, and Slavo’s grumpiness produces such eloquence I have no recourse but to quote his Facebook posts in extenso (I have added itals and blockquotes for clarity and fixed some OCR errors). From here:
Aaaand we are at a point where I am reminded that while Postal broke with Chomsky a long time ago and his criticism of Chomsky’s bullshit is 109% valid, Postal himself is a student of Chomsky and thus wholly compromised. Nowhere is this more apparent than in his discussion of NLs as generative systems and the type/token distinction. Postal (2025: 63) argues that
That renders use of NL sentences for communication impossible unless mental tokens of NL sentences are somehow connected to physical things perceptually available to others. It is the function of Expression systems to facilitate this connection. There are different types of known Expression system, the fundamental one evidently being that which links Core elements to the output of vocal tract behavior, that is, to pronunciations. This clearly has biological primacy in humans.
Suddenly we are dealing with Core and Expression systems, but ok, I can dig.
My view then is that while there is an inherent biological connection between the Cores of known NLs and human sound-producing vocal tract gestures, there is no inherent logical connection. I take the existence of the gesture Expression systems of the NLs of the deaf and orthographical Expression systems to justify that conclusion.
Minus five points for the misuse of ‘logical’, but ok. You get the point – the abstract NL can be instantiated as concrete/physical speech, writing or sign language. So far so good. But then:
While I will not be able to address these issues seriously, many linguistic works appear to treat spoken and written expressions as involving separate languages. For instance, De Swart 2010 makes the distinction throughout.
What is it that De Swart is talking about? The fact that spoken French now gets by with pas as the sole verbal negator while in written French, ne is still used!
This is the kind if bullshit this sort of theorizing will led you to. No discussion of the primacy of spoken language, not a syllable on writing as technology, not a beep about where this sort of thinking leads, since the quote from De Swart closes out the section.
From here:
Jesus Christ riding into town on a vintage V3S truck filled to the brim with ancient type molds, Postal is full of shit.
OK, OK, OK, so: we’re on page 79. Postal is still discussing the type/token distinction, this time with reference to what he calls “orthographies” and should properly be termed “graphical representation”. He’s discussing the idea of shape and gives the example below of the “massive variety of shapes” below from Wetzel 2009 who uses it to … Argue against shape theory or whatever (ex. 53), not important.
Postal argues against Wetzel and his argument is basically that one can subdivide those into upper-case and lower-case and then into printed and written. And then goes on to say:
It is at best only the four lowest level elements in the letter tree which need to receive shape definitions. I think this analysis already accounts for much of the variation in (53).
Some of the rest may well involve historical change of the shape definitions. But much of the variation is, I suggest, simply artistic distortion of standard shape definitions.
It seems impossible to me that anyone would use many of the shapes in Wetzel’s diagrams to actually compose serious text, either handwritten or printed.
Absolute ignorance of history or any other writing systems is one thing. It’s the arrogance of the ‘I can’t imagine it therefore it must not exist’ is what gets to me.
And from here (the quote is from Chomsky):
“We therefore take Merge (X,Y) = {X,Y}, where X and Y are either lexical items or syntactic objects in ws, already generated.”
I did not need Postal to remind me of this, I have read this – or equivalent formulations – many times. Each time I marveled at the seriousness of this incredibly inane statement and wondered how people cn take this seriously.
And today I finally realized what this is. It is the linguistic equivalent of Ayn Rand’s “A is A”, a simulacrum of scientific expression, an imitation of analytic thought, playacting at mathematics. Except Rand at least turned it into coherent philosophy.
Go get ’em, Slavo!
Gosh, those Trotskyites sure have some powerful critiques of Stalinism, yet something about their affirmative program somehow still seems a bit off …
Quite.
This reminded me that I had wanted to see if the NY Public Library had a circulating copy of the newer edition of Harris’ _The Linguistics Wars_, about inter alia Postal’s break w/ Chomsky. Answer: No, but it does have a recent science-fiction title called _Battle of the Linguist Mages_. Maybe that’s better? From the plot summary: ‘Isobel is the Queen of the medieval rave-themed VR game Sparkle Dungeon. Her prowess in the game makes her an ideal candidate to learn the secrets of “power morphemes”-unnaturally dense units of meaning that warp perception when skilfully pronounced. But Isobel’s reputation makes her the target of a strange resistance movement led by spellcasting anarchists, who may be the only thing stopping the cabal from toppling California over the edge of a terrible transformation, with forty million lives at stake.’
Merge (X,Y) = {X,Y}
{X,Y} is of course exactly the same set as {Y, X}. I had forgotten that Miracle Merge, the Key to All Languages, does not produce an ordered pair. It is even more vacuous as an “analysis” of the fundamental structure of Language than it seems at first.
This is not about word order: it’s that in the presumed fundamental structure of Language, there is no “head” element. Obviously ordered pairs can be defined in set theory, and Chomskyites do the equivalent. But to use the notation of set theory for this is simply mystification/obfuscation for its own sake. There is no explanatory value whatsoever in reinventing one of the most basic wheels of elementary set theory and claiming this as part of “linguistics.”
(Geoffrey Pullum is very good on Chomsky’s outright major mathematical errors in his supposedly foundational work, incidentally. The mathematics is basically all there to frighten non-mathematical linguists into agreement. Pullum, who knows more maths than Chomsky, looks behind the curtain.)
That renders use of NL sentences for communication impossible unless mental tokens of NL sentences are somehow connected to physical things perceptually available to others.
Seems that Postal has not heard about the (insuperable) problems with the
https://en.wikipedia.org/wiki/Picture_theory_of_language
Chomskyites are doctrinally incapable of dealing with the full implications of the fact that Language is a social construct.
The mathematics is basically all there to frighten non-mathematical linguists into agreement.
I had always assumed this.
The bizarre notion of written language as produced by a quite separate mechanism from spoken language reminds me of The Sound Pattern of English, which sets up underlying spoken-English forms to account for the relationship between e.g. /’krɪtɪk/ and /’krɪtɪsaɪz/, never so much as alluding to the possibility that the relationship might be connected with English spelling rules in some way. The idea of an interaction between speech and writing can’t be fitted into the ideology. It won’t fit in the “language organ.”
Except Rand at least turned it into coherent philosophy
Nah. Cargo-cult “philosophy.” Philosophers have been coming up with wrong answers ever since Plato, but Rand didn’t even understand the questions.
Aaaagh. Chapter 3 basically summarizes Postal’s old argument against the finite nature of lexicon which is basically just “We can say stuff like ‘And then the dude went KAPLOW!’ and KAPLOW is not a lexical item (or rather, is an untyped alexical item) in English, so checkmate!”. I mean like, fine, yes, great point, well done. But a) Postal has made it before, b) how many pages do you need to drive this home (100, fyi) and c) it is all couched in terms of formal language theory. Which, again, ok, it is interesting in itself, but it is muddled beyond all recognition, has had little relevance to Chomsky’s theory in decades and just goes to show how pointless the whole idea of natural languages as formal languages is. How pointless you ask? This pointless: the first time the idea of sentences conveying meaning is mentioned is page 130!!!
Re Merge: Postal refers to a recent (2023) paper by Chomsky and some other people on the mathematical properties of syntactic Merge: https://arxiv.org/pdf/2305.18278. You are welcome.
New Frontiers in Intellectual Autobinesis.
There is a cargo-cult aspect to this, too: wholly irrelevant mathematics in purported support of a dead-end misanalysis of the nature of natural language. The appearance of science is meant to substitute for genuine linguistic enquiry.
From p. 153:
The first author is a mathematical physicist; the third is a professor of computational linguistics who is evidently part of the Chomsky, er, movement:
https://direct.mit.edu/books/book/4464/Why-Only-UsLanguage-and-Evolution
This is a moderately interesting paper of the sort that trawls WALS for data, on the theme, basically, that at least some similarities between human languagues might reflect shared pan-human preverbal conceptual categories:
https://onlinelibrary.wiley.com/doi/full/10.1111/cogs.12332
to which one’s natural response is, of course, “Well, duh.”
Still, less likely to be bad for a typical Hatter’s blood pressure.
I was interested in the mass/count distinction stuff. In Kusaal, this works in a way so similar to English that I was worried initially that I was just imposing my own conceptual categories on Kusaal, but I’m pretty sure now that it just is very similar.
And, of course, just because something is obvious, it doesn’t necessarily mean it’s true. It’s interesting to see actual evidence that preverbal children actually do have some of the suggested concepts already.
Though I wonder about cherry-picking, and maybe a tendency to ascribe to human cognition things which are actually part of the logische Aufbau der Welt. (But that’s a whole nother can of worms anyway, and I kant claim to know much about it.)
I was interested in the mass/count distinction stuff. In Kusaal, this works in a way so similar to English that I was worried …
How many non-similar ways are there to make a mass/count distinction in a language? Semitic puts mass nouns in the plural; that’s hardly a dramatic difference.
Are there languages that make no grammatical distinction? How do they distinguish five pails (quantity) of milk vs five milk-pails (currently empty)?
The paper goes into that (the major complications are with languages like Chinese and Japanese where plurals are usually unmarked, but there are classifiers.)
Similarities between Kusaal and English here include things llike the fact that mass quantifiers are grammatical (yup) with count nouns (“less animals”) but count quantifiers can’t go with mass nouns (*”fewer water”), and that mass nouns can be used as count nouns in secondary senses (“three beers.”)
Kusaal mass nouns mostly either belong to one of the two specifically “mass” noun classes or are formally plural morphologically, but with plenty of exceptions; but regardless, they take singular agreement (again, as in English.)
There are differences: nouns referring to materials are mass, as in English, but they are referential when used as premodifiers, unlike in English:
salima la’ad nɛ o bʋtiis
gold items with his cups
“gold items and (gold) cups”
This was spontaneously offered to me by a language consultant as a correction of salima la’ad nɛ bʋtiis, which has to be taken as “[gold items] and cups” rather than “gold [items and cups].”
The animate singular pronoun o for referential inanimate li “it” is actually quite typical of unstudied informal speech: consultants “corrected” this if you drew their attention to it, for example by asking them to repeat what they’d just said. Salima “gold” is formally plural, but it takes singular agreement because it’s a mass noun. (The formal singular salim “piece of gold” turns up in the Bible translation once or twice.)
Semitic has lots of formally singular mass nouns.
In Bantu, historical sound changes have led to the prefix for the Volta-Congo “liquid” class (corresponding to the Kusaal class suffix -m, as in ku’om “water”) falling together with the prefix for the plural of the Bleek-Meinhof class pairing 5/6 (cognate with the Kusaal plural suffix -a, as in gɛla, plural of gɛl “egg”); so you get e.g. Swahili maji “water”, with the same prefix and agreements as mayai, plural of yai “egg.”
@david eddyshaw
“Geoffrey Pullum is very good on Chomsky’s outright major mathematical errors in his supposedly foundational work, incidentally.”
I’d be grateful if you have a reference for Pullum’s comment on this issue. Thanks
@Julian, On the mathematical foundations of Syntactic Structures [Pullum 2011]
[This is not the only example of Chomsky falling below academic standards: plagiarism, failure to deliver supporting evidence. The technical claims in SS rely on Chomsky’s previous paper ‘Three Models’ that was unpublished — indeed unavailable for several decades after SS; when it was finally forced out of him (and we don’t know how much he rewrote it first), it plain did not support the claims.]
You could also look at Pullum 2010 on Recursion.
The Hattery’s CHOMSKY’s FOREVER WAR would also supply voluminous discussion points.
@AntC,
yes exactly, throughout chapter 3 I kept wondering what all this is for when Pullum 2011 already covered Chomsky’s mathematical inadequacies.
The answer is of course is that Postal does not know enough math. He is like a giddy 12-year old* who just discovered X (in his case set theory) and derives his understanding of NL from it. To him, NLs are merely sets of sentences, all he cares about is the finite vocabulary vs infinite syntax distinction. He did not even get to the, um, Chomsky hierarchy and thinks all formal languages are the same.
* A similar story is told of de Saussure.
After the depressing ch. 3, ch. 4 is back to the fun stuff, i.e. tearing Chomsky a new one. Specifically, it focuses on Chomsky’s oft-repeated claim that if a Martian scientist were to study the languages on Earth, they would find that “with marginal, minor modifications, there is only one language” (Postal 2025: 152). Postal calls this “play acting at science” (hey, that’s my line!) (Postal 2025: 153) which is, of course, nonsense, it is just a baseless claim. But Postal is right in pointing out that the only way Chomsky can make this claim is by “systematic[ally] hedging”, e.g. the “minor modifications” above and also
a. very slight variation
b. in essentials
c. marginal minor modification
d. minor variants
e. peripheral variation
f. differences only at the margin
(Postal 2025: 153).
This hedging is one of the most stable characteristics of Chomsky’s style, something once you notice it (like I did back in January 2017 while working on my dissertation), you will never unsee it. Syntactic Structure and Aspects of the Theory of Syntax are full of “perhaps”, “can be regarded”, “for the present” and shit like the following:
“Furthermore, there is no reason to expect that reliable operational criteria for the deeper and more
important theoretical notions of linguistics (such as “grammaticalness” and “paraphrase”) will ever be forthcoming.”
The only reason Chomsky is considered to have established a ‘science’ of language is a) because he said so and b) all the scary mathematical notation. Motherfucker hedges and prevaricates all the fucking time in the way of the shiftiest of hucksters.
The ultimate problem with Postal is evidenced in his constant invocation of platonic linguistics (as opposed to Chomsky’s mentalist linguistics) and in off-hand comments like this:
Dixon is of course Robert M. W. Dixon whose work is of course a hundred times more valuable to modern linguistics than that of Chomsky and Postal combined. And you know why? Because Dixon actually went out and looked at how people speak!
I can’t believe this is the case in the year of our Lord 2025, but what we have here is just another iteration of the problem of the universals: Postal (and his buddy Katz) argue that languages exist as abstract objects, before they are written or spoken, with no connection to our physical reality. His problem with Chomsky is not that Chomsky also believes that languages are abstract entities, but that Chomsky also claims that they are in some way connected to the physical structures of the brain because, duh, they must be. Postal rightly points out that Chomsky completely fails to square that circle, because duh, you can’t, and also Chomsky is an incoherent idiot.
But that does not change the fact that they both believe in language as an abstract disembodied entity (or set, in Postal’s case) and actual speech or texts is just some – what did Postal call it? – oh yes, Expression system. Or, we called it back in the day, universalia ante rem. That at two points in the book (Postal 2025: 84, 128), Postal has the khutzphe to take William of Ockham’s name into his fucking mouth just takes the cake.
Anathema sint.
The commenter here
https://languagehat.com/chomskys-forever-war/#comment-4386589
links to a takedown by Julian Bradfield (an actual mathematician) of Langendoen and Postal’s The Vastness of Natural Languages.
https://www.julianbradfield.org/Research/vastness.pdf
(It’s quite accessible and surprisingly funny.)
As bulbul says, Postal is a full-bore Platonist who has mistaken his Platonic Idea of Language for the real thing. (This Platonic Form is, indeed, Vast. But that has no actual bearing on linguistics at all.)
It is, of course, quite untrue that R M W Dixon “claim[s] that linguistics could operate (exclusively) on the basis of speaker observation”, as the genuflection to Dixon’s “Basic Linguistic Theory” at the beginning of every other grammar by a decent field linguist shows. (Postal will not have read any such things, one imagines.) Or as is immediately clear from reading any of Dixon’s actual grammatical works. His 1972 Dyirbal grammar, for example, is actually pretty damn theory-heavy (being, among much else, a pioneering work on ergativity and its syntactic aspects.)
Dixon is a touch impatient with gratuitous flimflam in grammars. I like (in his Grammar of Boumaa Fijian) the remark on a previous Fijian grammar that the “grammatical analysis is original to that extent that, for him, Fijian has no unit word, no adjectives, no subject/predicate division, no prepositions and no passive (this last following on from a paper […] in which criteria for ‘what a passive is’ were not stated.)” The kicker is “original” …
[Bradfield] (It’s quite accessible and surprisingly funny.)
This made me laugh out loud
It was rather the vogue to be Intuitionist when I were a wee undergraduate.
@David,
thank you for the link to the Bradfield paper! He his the nail on the head on the first page:
Postal has no interest in the physical universe or its limitations. This is best seen in his muddled discussion of “orthography” – i.e. graphical representation – where Postal argues that orthographies are also infinite. The idea that for an orthography to be usable, people need to able to tell the individual characters apart easily, does not even occur to him. He only realizes this because Turing (1936: 246-250) makes an off-handed remark to that effect. Postal then begins to treat it as a huge discovery, even to the point of calling it “Turing’s theorem” (Postal 2025: 99)
I must say here that as far as I know, the possibility that the actual physical universe is infinite in space and time is and always has been consistent with cosmological theory and observations.
The problem is more radical than that. Postal’s concept of Language effectively incorporates the entire apparatus of ZFC, which implies infinities far beyond anything that has ever been postulated for the physical universe.
Geoffrey Pullum has a paper (with his then wife) exploring the view that actual languages* are in fact finite. (Very big, but that, of course, is something entirely different.)
https://archive.nytud.hu/szakcsoport/neuro/tanulmanyok/ujpullum.pdf
The Chomskyan dodge is to set up an apparatus of rules to generate all conceivable utterances by freely generalising from observed patterns in the finite data, and then to say that all the utterances that your system might generate, given infinite time and space, are the language. In other words, to identify the productions of analytic model with the actual data – or even to identify the model itself with the data, proclaiming that it is the language, and actual utterances are merely the shadows on the wall of the cave.
On a practical level, such systems both overgenerate (grotesquely, for example by declaring that hypothetical infinitely long sentences are a real part of a natural language) and undergenerate, because scholars committed to this approach routinely reject genuine utterances which cannot be generated by their systems as being ungrammatical. Theory trumps data.
But as a real linguist famously said, “All grammars leak.”
The entire approach is philosophically incoherent. It is ironic that Chomskyites regularly claim that their guru is a major “analytic philosopher.”
* “A language” is actually a vague concept: necessarily so, according to Pullum (nice quote about this on his WP page.) Here I mean more or less “all utterances in that language.”
@Jerry,
yes, the universe is most likely infinite. Things in it – human beings such as Postal and yourself – are not.
@David,
(emphasis mine)
Oh no, mon frère, this is not the Chomskyan dodge. This is a later – and still semi-heretical – development of the orthodoxy of the day, in direct contravention of Chomsky’s well-known dislike for data collection, cf. the ‘butterfly collecting’ remark Chomsky and Ronat 1979: 57).
The Chomskyan dodge was describing sitting down and inventing sentences in one’s brain, calling it experiments and comparing it to physics.
At a recent conference, I stumbled into a generativist session which featured exactly this kind of language “theorizing”. It was a very surreal experience.
Actually, the universe seems most likely to be finite, at least spatially. But the continuum implies another kind of infinity, of course. (Whether the real numbers actually correspond to the fine structure of the world itself or are just an extremely useful way for us to reason about it is another issue.)
Postal’s idea seems to be that you need real numbers to describe Language, and he thinks Chomsky is merely up to the countably infinite, and is therefore Wrong, Wrong, Wrong.
@David,
just a nitpick:
Geoffrey Pullum has a paper (with his then wife)
This to me implies they got divorced. She, in fact, passed (VP) while they were married, so maybe “late wife” would be better.
The Chomskyan dodge was describing sitting down and inventing sentences in one’s brain, calling it experiments and comparing it to physics.
Yes. I was a witness to this in the 1970s, and I am still recovering from the trauma.
@bulbul:
True. Read “late” for “then.” (The carelessness arose from introducing her as an afterthought while editing, which unfortunately reveals a further bad attitude on my part. Double apologies to the memory of Prof Scholz.)
http://www.lel.ed.ac.uk/~gpullum/about_barbara.html
@bulbul: yes, the universe is most likely infinite. Things in it – human beings such as Postal and yourself – are not.
Such a consideration is why I didn’t object to Bradfield’s “entities”. But since he used that word, I don’t see a way to read his “infinite space, time, and entities” other than saying that the physical universe is finite in space and time. If all he meant is that language-producing entities such as you and me are finite in space and time, he could have just written “infinite entities”.
That’s just a nitpick; I’m convinced by his paper to the extent that I understand it.
“Late wife” is ambiguous since Pullum has had three marriages, with both the second and third ending in his wife’s death. You can hardly expect readers to remember (or look up) who he was married to at what date, and it’s not relevant anyway. Just say “Pullum has a paper (with Barbara Scholz)”.
So ordered!
*bangs gavel*
@ktschwarz,
to me, “late wife” decidedly means they – meaning Mr. Smith and Dr. Jones, so as to leave the innocent out if this – were married at the time of Dr. Jones’s passing. Were it Dr. Macdonald whom Mr. Smith divorced before he married Dr. Jones who passed, she would be referred to as “the late former wife” of Mr. Smith. Death conserves some things.
Also, “ You can hardly expect readers to remember”. Not all readers, surely. But those of us interested in such matters certainly would.
@DE: Actually, the universe seems most likely to be finite, at least spatially
Did I miss something? This article from last year says the universe is usually taken to be flat, which AIUI means infinite in space and time, and says it’s not known whether the universe really is finite or infinite (since AIUI even the slightest overall positive curvature would mean it’s finite in space and time).
Hat’s version has my blessing. Barbara Scholz should not have been referred to anonymously as “his wife”, even though Pullum himself was more discourse-salient. I repent in dust and ashes.
bulbul, I agree with everything you said here and like how you said it. But — why did you put yourself through this? Did you think there was any chance of finding anything worthwhile in this book?
I’ve felt a bit like that reading Geoffrey Sampson on linguistics: he lays into Chomsky et al with gusto and makes numerous points I enthusiastically agree with. But it gets tiresome after a while.
And while he may be a lovely person for all I know, his politics are thoroughly repulsive.
https://www.theguardian.com/society/2002/may/14/politics.raceintheuk
It wasn’t when (some) people believed in the Big Crunch.
I, for one, have read some bad stuff just to make sure I don’t end up arguing against strawmen.
A noble pursuit …
I think the utility of doing that varies, though. There is nothing much to be gained from ploughing through even a masterly treatment of phlogiston. But with Chomskyans, you sometimes do need to read quite far before you can be quite sure that when they say “oxygen”, they actually mean “phlogiston.” Theirs is not a culture that values clarity.
Phlogiston was conceived of as the opposite of what we now know to be oxygen. It was believed to be released during combustion.
This, I was aware of.
I think whether the universe is finite or infinite is a (maybe perpetually) open question… but this is LanguageHat, not BigBangHat, so I’ll leave it at that. I’m really surprised at the viscerality of the argument which took me by surprise, but I remember I was viscerally in the anti- or rather exo-generative grammarian camp back when I shortly dabbled in these matters. To me at the time it was much more promising and satisfying to find and describe structures and build models that can explain such structures. Over the years I have become more and more agnostic about that enterprise, meaning I believe less and less that it makes sense to jump to mentalist conclusions and, as it were, jump into the ring and grab the microphone whenever I think I’ve ‘found something’, and declare triumphantly that now I know better how ‘Language’ with a capital ‘L’ works. Rather, I may have put together some data, then I made this cute little somewhat-functional paper model of it, an origami practice of sorts. Crucially, *that’s just a model*, and other models (infinitely many of them?) may also cover the same data but provide entirely different views on ‘how things work’. Doesn’t mean my model is wrong, or the other is. They may both be wrong, and almost certainly neither of them are complete. I’ve come to the point where I prefer ‘model’ and ‘point of view’ over ‘explanation’, and have come to suspect that all the entities that we stipulate, like “the phoneme /e/” or “adjectives” only ‘exist’ in any true sense in the model, *not* in language in a general and not in a specific language.
Circling back to the infinities as a programming person I am regularly confronted with the Entscheidungsproblem, and part of that is that Turing postulated a machine with a rather limited rule set but an infinitely long paper tape. So that is always presented with a caveat, as in “if we had an infinite tape” and so on. It seems to me the better way to understand the limitation—or lack thereof—is by saying ‘arbitrarily extendable’. So I don’t have to imagine infinitely long tapes, I only have to imagine a tape that, whenever I run out of it, I can get another role of tape and glue them together end to end, and go on computing.
I think sentences work like that. Sure, it’s easy to make fun of a theory that postulates the Real Language is infinite with infinitely long sentences, and actual languages are just their shadows on the walls of the cave. But then some literary works have extremely long punctuation-free convoluted colorless green ongoing […∞…] sentences in them, so where do you draw the line? You can’t, either…
The “infinite sentences” thing is not in itself the point; it’s more that it exemplifies a particular concept of what a language is (viz a quasi-mathematical Platonic Form.) “Infinite” is completely different conceptually from “very, very long”, as I’m sure you don’t need me to tell you. “Infinite” cannot be treated as simply not drawing a line when it comes to size. No finite set, for example, no matter how enormous, even, say, “all the atoms in the universe”, can be equinumerous with a proper subset of itself. (When Cantor realized this property of the set of all positive integers, he is supposed to have said “Je le vois, mais je ne le crois pas.”)
The vitriol isn’t just of the trite academic catfight kind, I think. It’s grounded in the behaviour of Chomsky himself towards opponents and dissidents, which has often gone well beyond reasonable acceptability. This attitude has been transmitted to many of his disciples. This is (alas) very well documented.
In other words, the Sturm und Drang is indeed not justified by the actual linguistic issues; but it is justified by the behaviour of (many, not all of) the Chomskyans. (They started it!)
In addition, I think a lot of Hatters (certainly including me) are triggered by pseudoscience, which explains some of the venom here. The Chomskyan idol really does have philosophical and methodological feet of clay. It’s galling to see this kind of thing securely ensconced in academia.
Yes, what DE said. (Also, the Chomskyan hostile takeover of linguistics is all too reminiscent of more recent trends in more important areas.)
Thanks for the input, that really helps to clear up some things for me.
@David Marjanović “people believed in the Big Crunch”—to me the origin and the fate of the universe is indeed an open question. By and large I “believe” in the Big Bang (with some reservations), and it does look, as far as I understand and can remember recent-ish cosmological general-audience level talks, rather flat with a very small margin of uncertainty. As well as we can tell until the next discovery is made (cf. faint red dots in the early universe discovered by the JWST which may or may not be primordial black holes). Not only that, we know something is wrong with our theories because we need the help of Obscure Elements (dark matter and dark energy) to make it add up, so to me that sounds like the Big Crunch is maybe bound for a comeback by tomorrow, who knows…
I’d totally be interested in BigBangHat.
Charles L Harness’s Firebird has the possibility – or not – of a Big Crunch as a central plot point.
It’s quite enjoyable. Some willing suspension of disbelief is called for when it comes to the physics, though. To put it mildly …
@David Eddyshaw: That quote from Cantor comes from a letter he wrote to Dedekind, who was also making important contributions to the set theoretic foundations of analysis at the time. (Dedekind’s construction of the real numbers from the rationals is more straightforward and elementary, but Cantor’s construction extends to the completion of any metric space. Dedekind also realized that properties like the one Cantor had found so surprising, that a line contains as many points as a plane, provide a good way of giving an abstract definition of an infinite set. A set is Dedekind infinite if it can be put in one-to-one correspondence with one of its proper subsets, although for that definition to be useful, the axiom of choice is also needed.) That raises the question of why the quote is in French. Was the whole letter in French, rather than German?
While Cantor is normally thought of as German, his family background was complicated. He probably had Danish, Austrian, Magyar, and Jewish; moreover, he was born and lived for much of childhood in Saint Petersburg. However, he lived the vast majority of his life in Germany, spoke German as his everyday language, and wrote mathematical articles in the language.
Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk …
I was just reading the WP article on Cantor, in which I discovered that he encountered criticism on religious grounds, for positing the existence of an infinity that was not God …
I’m with Wittgenstein on this: “he believed that Cantor’s diagonal argument conflated the intension of a set of cardinal or real numbers with its extension, thus conflating the concept of rules for generating a set with an actual set” (from the same WP page.)
Mind you, I gather that W’s ideas on the philosophy of mathematics have not impressed actual mathematicians one little bit (and not only because of the finitism: there seem to be other serious problems with his Remarks thereon too.)
https://en.wikipedia.org/wiki/Remarks_on_the_Foundations_of_Mathematics
But even if his finitist views on the whole of mathematics are anathema to all but a few cranky mathematicians, I think they’re spot-on when it comes to Chomskyan notions about the supposed infinity of languages: confusing the rules with the generated output is exactly what they do. The more remarkable, as the whole point of the rules is surely to avoid absurdities like “infinite” languages.
Here’s a mathematician discussing the series of letters and postcards between Cantor and Dedekind. He says the letter is in German except for the vois/crois sentence in French: “I don’t know whether this is because of the rhyme vois/crois, or because of the well-known phrase ‘voir, c’est croire,’ or for some other reason. I do not believe the phrase was already proverbial.” (Also, “one cannot fail to be impressed with the speed of the German postal service!”)
To be slightly fairer to the ur-Chomskyites, I think the idea is to deduce from the open-endedness of language (which seems apparent from sentences constructed in the privacy of one’s own mind) that in principle you could go on forever along the lines of e.g.
“Jack knows that Jill knows that Jack knows that Jill knows that …”
The only way to escape from “infinite language” is then to suppose that a sentence like this is not already present, floating in the noosphere somewhere, but can be produced “on demand” by rules that permit sentences to be constructed from other sentences by coordination, embedding or whatever. QED. (Subsequent fiddling with the notion of “rule”, successively bleaching it of more and more content until it becomes an irreduceable “merge”, doesn’t alter the basic principle; it just makes the complete edifice less and less transparent and farther from any real language data.)
However, even if you accept the introspective methodology, there is actually a thumping petitio principii in this: “could go on forever” assumes the conclusion that there actually is a rule that you could keep on following in this way. If you don’t make this circular argument, the only way you could show that such a sentence is possible would be to actually construct it. (I’ll wait: you don’t mind if I get on with a few other things in the meantime, do you?)
(Wittgenstein’s contribution to issues like this is to actually ask questions like, “What do we actually mean by ‘following a rule’?” “How can you tell that someone is following a rule?” But that’s a somewhat different issue.)
Chomsky, of course, took the further step of reifying the rule(s) as a physical thing in the brain, and speculated that the “organ” in question arose from a single genetic mutation …
The only real interest here is the question of what exactly had gone wrong with academia that led to this kind of thing being taken seriously.
Das waren noch Zeiten!
@David Eddyshaw—my assumption is that as with the rotary newspaper printing press, so with language. The rotary press is fed by a—conceptually!—endless band of paper. When a role (haha edit: roll) is finished, a new one drops and the machine manages to paste the ends together. There may be a few printed exemplars to be tossed, but that’s it: the speaker takes another sip from the water bottle and goes on, the audience is audibly breathing, whispering and clearing their throats, people start leaving. We can be sure the printing press cannot go on for-literally-ever because even if it were to recycle all the atoms from old newspapers and everything else in the universe it would still run out of thermal imbalances to harvest. But I think we still have a meaningful theory of the rotary press and know we can keep it running for five minutes or five days and not reach a hard limit. So to me it does not look like a theory of language that allows for sentences to run to infinity is unlikely to be realistic just because of this because I don’t see the alternative—somehow model the limited capacity of speakers and listeners? That doesn’t make sense except as a theory of the “surroundings”, the “ecosystem” of human language (the rotary press also needs this to account for the wear and tear on its gears, and especially the abrasive action on the printing form, but I’d say it should be external to the process of printing unless your printing form is jelly or potatoes, which is a thing).—I for one hope to have plausibly demonstrated that a text can go on for-almost-ever.
@David Eddyshaw: Interestingly, Wittgenstein wasn’t exactly wrong with that basic notion (although he took off from there in pretty much the wrong direction). The (downward) Löwenheim–Skolem theorem states that every infinite structure has models of every smaller infinite (e. g. countably infinite) size. These models can exist essentially because they take advantage of the distinction Wittgenstein was talking about—not just for the set produced by a diagonalization argument, but pretty much every infinite set in the model. Cantor’s Theorem and related results still hold, but one has to be very careful about interpreting what they mean. The diagonalization results state that certain bijections cannot exist, but a bijective correspondence is, at the most basic level, itself a set of ordered pairs. So if you have a countable interpretation of what is “normally” an uncountable theory, it is no surprise that many infinite sets that you might have wanted to construct do not actually exist in that theory.
@~flow:
The Chomskyites’ problems come from identifying the rotary press with all the newspapers that it could print – in infinite time – and/or indentifying the contents of the newspaper with the mechanism of the press.
I’ll say again that “infinity” is a wholly different thing from “going on almost for ever.” In fact it’s a really weird and highly counterintuitive concept: people tend not to notice just how weird because the term is familiar and people who are not mathematicians think of it informally as just “insanely big.” It’s not: it’s something qualitatively different from “very big indeed.”
In axiomatic set theory there is no way of deducing the existence of an infinite set from other axioms. You have to assert the existence of an infinite set as an axiom of its own. (And then you find that you’ve opened the door on a Lovecraft world where you are forced into having an infinity of infinities, all different …)
I don’t think your analogy is fundamentally different from the notion of an ideal Turing machine with a theoretically infinite tape. It’s a useful concept that has been a fruitful model for thinking about real machines, but you can’t ever actually build one – it’s not just impractical, it’s strictly impossible – and it would be ludicrous to describe a real computer as actually being an ideal Turing machine.
The Chomskyites mistake the model for the reality. (There’s a lot else wrong with their system too: it’s basically a radically inadequate bad model, which makes this confusion particularly lethal.)
@Brett:
I have some vague memory that Skolem was a hardcore constructivist, if not an actual finitist, so he presumably had skin in this game …
[Bestirred myself to consult WP: Yes, he was.]
He said “I’ll school ’em!”
“Legend has it that Thoralf Skolem, up until the end of his life, was scandalized by the association of his name to a result of this type, [the “upward” Löwenheim-Skolem theorem] which he considered an absurdity, nondenumerable sets being, for him, fictions without real existence.”
Skolem was certainly not disinterested when it came to the issue of higher infinities, but, whatever his personal philosophical hang-ups, no one doubts the correctness of the the theorem itself. In fact, neither Löwenheim nor Skolem ever proved the upward version of the theorem, but once you have the general downward version, the upward version is an almost trivial corollary. The proof can be summarized in a couple lines:
I discover that there is also
https://en.wikipedia.org/wiki/Ultrafinitism
which denies the existence of some finite numbers which are just too big.
(Actually, this makes more sense than my tendentious characterisation suggests; the WP article explains it a bit.)
I have to say that “ultrafinitist” sounds way cooler than “minimalist.” Perhaps I shall inaugurate an Ultrafinitist Programme in linguistics …
Actualism is another cool name.
Reminds me of David Lewis’ comment about objections to his own Modal Realism:
(From Counterfactuals, 4.1.)
@David Eddyshaw—”I don’t think your analogy is fundamentally different from the notion of an ideal Turing machine with a theoretically infinite tape. It’s a useful concept that has been a fruitful model for thinking about real machines, but you can’t ever actually build one – it’s not just impractical, it’s strictly impossible – and it would be ludicrous to describe a real computer as actually being an ideal Turing machine.”
So the way I mentally deal with that is simply that there are these theoretical infinite supplies of time and tape, whereas in physical reality there’s no such thing as infinity. But being finite is not part of the core model—the Turing machine T, a given computer C—but a property of the reality they’re embedded in.
As long as they’re embedded in my Gedankenexperiment I can at least *pretend* the tape goes on forever, or at least I don’t have to worry where to get the next roll of paper or how to attach more RAM onto my finite machine C; when we talk about real, physical machines though those are embedded in a reality where one print run can only consume so much resources before it becomes untenable. T ceases to be an ‘ideal’ Turing machine, and all of a sudden I have to deal with the fact that my computer will not be able to hold all digits of π in memory or on disk. That’s fine! In physics models work until they don’t, like Newton’s law when you approach c, that kind of stuff. Newton’s fine but gets worse under extreme conditions like Mercury’s orbital elements or when approaching a black whole, or GPS.
I *believe* I am also therefore exempt from contemplating the theoretical implications of infinitely many ways to obtain infinite sets and the relationship of ℵ₀ and ℵ₁. In practical computing they’re too big to be dealt with directly anyway. And because both T and C are both embeddable in both the Gedanken-Universe and reality alike while behaving similarly w.r.t. a number of essential properties, I do think the—shall we call it—’idealized’ Turing machine (not the ‘ideal’ one which cannot exist in this world) is actually a good model of what we would call a practical computing hardware C.
Since this is still going, I’ll overcome my natural shyness to offer a thought on the question that Bradfield –
https://www.julianbradfield.org/Research/vastness.pdf
– posed thus:
“Is the following string –
‘The numbers zero, two, four, ’ … ‘are called even.’ [where the ellipsis (outside quotation marks) indicates the indefinite continuation of the sentence in the obvious way]
– a sentence of English? ” [that is, a grammatically correct sentence, I think he means.]
I would probably answer:
“Your question implies that there’s a set of objects called ‘sentences’ which may be divided into complementary subsets of ‘grammatical sentences and ‘ungrammatical sentences’.” [not sure about this on reflection, but let’s go on]
“So before I can answer in respect of the particular point that you’re interested in I’ll need to know how you define ‘sentence’ generally.”
Let’s imagine that Bradfield says: “Whatever you think it is.”
I would then say:
“I would define sentence in the usual way with reference to grammatical rules, including relevantly “in a coordination [a list of grammatically similar items usually separated by pauses/commas or ‘and’], there’s no limit to the number of coordinates [the individual items].”
“With those rules, I would have to concede that the following are all grammatical sentences (whether or not anyone would ever utter them):
“1. The numbers 2 and 4 are called ‘even’.
2. The numbers 2, 4 and 6 are called ‘even’.
3. The numbers 2,4,6 and 8 are called ‘even’.
4. et cetera
“where ‘et cetera’ means ‘continuing in the same way as long as you like.'”
Suppose Bradfield says:
“What if we take ‘et cetera’ to mean ‘continuing in the same way until we’ve included all the even numbers’?”
I would probably then say:
“That’s an unproductive question, because it’s not possible to do that.”
If you’re concerned about item 4 above – the sentences encompassed by ‘et cetera’ – it really comes down to whether you accept that grammatical rule about coordinations, n’est-ce pas?
This line of reasoning is just about following the logical implications of definitions and rules. It’s not about pragmatics or comprehensibility or the limitations imposed by the finite future lifespan of the universe. Of course you’re welcome to argue in different ways that do consider those things.
Although Turing allowed for an infinite tape, plenty of subsequent people have thought about the implications of having only a finite amount of space to write. There are complexity classes defined by how much memory a program can use. However, they just turn out to be a lot less interesting than the complexity classes defined by running times. Savitch’s Theorem, that making a computation nondeterministic doesn’t change its memory complexity class (e. g. PSPACE = NPSPACE), is the biggest, but not the only, reason these classes are less interesting.
Prof. Postal has asked me to post a lengthy response to various comments, which I will do below; I will do my best to reproduce formatting, but I don’t promise perfection.
I take the liberty of commenting on remarks at LanguageHat Postal BS.
September 25, 2025. The underlying subject is my 2025 Brill monograph
Generative Grammar’s Grave Foundational Errors.
Bulbul
Postal himself is a student of Chomsky and thus wholly compromised.
First, I was never a literal student of Chomsky’s but rather a very junior
colleague. I was, when young, foolish and ignorant, quite influenced by
him. But I have had nothing to do with him for
well more than half a century.
What on earth is it supposed to mean that I am totally compromised, a
phrase usually used in contexts where someone is accused of some wrong
doing or illegal activity. In this case it seems to mean no more that there is
some point on which the author disagrees with me. By parity of
nonreasoning, I guess that means he is totally compromised.
Bulbul
Minus five points for the misuse of ‘logical.
The author points to no misuse and could not because there was none. A
glance at my text shows I used the word to indicate that there was no valid
inference from one state of affairs, the existence of natural language cores
and the fact that there is a biological connection between such cores and the
use of the human vocal system for expression of sentences. Valid inference
is of course a central logical notion.
Bulbul
This is the kind if bullshit this sort of theorizing will led you to. No
discussion of the primacy of spoken language, not a syllable on writing
as technology, not a beep about where this sort of thinking leads, since
the quote from De Swart closes out the section.
Something is called ‘bullshit’ but it is not even made clear what. The author
apparently did not like my raising the question of whether ‘written
languages’ and ‘spoken languages’ in the case of related systems like those
of French might actually be distinct languages.
While this is a complex and little studied matter, there are good arguments
for the point. Most obviously, there are written sentences which have no
spoken analogs, including say the following example (109) from Postal
2025 page 105.
Shin 2002: 27
To capture the meaning of this in spoken English would require lengthy
descriptions of the circles, their positions, etc. Not for nothing is there the
aphorism ‘a picture is worth a thousand words’.
I said the vocal mechanism is biologically determined. Is not that some sort
of primacy. What does the writer really want? Several things are cited
which I did not discuss, but no argument is given that they would be
relevant to the topic of my chapter. I was not obliged to write a different
book which the author might have liked better.
Apparently another author adds:
Jesus Christ riding into town on a vintage V3S truck filled to the brim
with ancient type molds, Postal is full of shit.
Ignoring more childish vulgarity, again the remark is entirely without
substance.
I wrote in my monograph:
It seems impossible to me that anyone would use many of the shapes in
Wetzel’s diagrams to actually compose serious text, either handwritten or
printed.
The critic says:
Absolute ignorance of history or any other writing systems is one thing.
It’s the arrogance of the ‘I can’t imagine it therefore it must not exist’ is
what gets to me.
I am accused of ignorance of something, but no specification of what or
how that supposed ignorance would be relevant to what I was talking about.
Then I am accused of arrogance. Granting the claim for argument, again
that is not a substantive point. The author could have tried to show my
speculation was false by providing documentation of modern use of the
orthographical variants at issue. But that would have been harder than
simple ad hominum insult.
Not much further along, the author adds:
I did not need Postal to remind me of this, I have read this – or
equivalent formulations – many times.
There is no reasonable reason why my name should have been mentioned
here. It seems not to have occurred to the author that the monograph was
not written for him or others fully cognizant of the quality of Chomsky’s
argumentation. The author seems to think his irrelevantly citing my name in
this context amounts to a criticism.
David Eddyshaw says:
Seems that Postal has not heard about the (insuperable) problems with the
https://en.wikipedia.org/wiki/Picture_theory_of_language
Let us grant I have not heard about these supposed problems. The author
does not attempt to spell out what they may be. So we have no reason to
accept that they are insuperable (and for what). Connection shown to my
monograph: zero.
He continues:
Chomskyites are doctrinally incapable of dealing with the full
implications of the fact that Language is a social construct.
The placement of this passage inevitably suggests, absurdly, that I am a
Chomskyite. That aside though, this is my favorite remark in the posts
about my book. How easy blog linguistics is; a one liner which establishes
the nature of language. No need for argument, evidence, references to such.
One can dismiss all different views via monographs written on postcards.
How foolish of me to have gone to so much trouble to write a whole book.
The incredible arrogance, dogmatism and question begging of Mr.
Eddyshaw’s remarks about social constructs reminds me of the the style of
the contribution to the Soviet linguistic controversy of the Georgian linguist
Iosif Vissarionovich Dzhugashvili (also known as Joseph Stalin). In contrast
to Mr. Dzhugashvili though, Mr. Eddyshaw (presumably) lacks thousands
of armed thugs prepared to enforce his linguistic views.
Back to commenter bulbul
it is interesting in itself, but it is muddled beyond all recognition,
This claim is not supported in any way.
has had little relevance to Chomsky’s theory in decades
This is grotesquely false as shown in the book by a multitude of relatively
recent Chomsky and Chomsky supporter comments.
and just goes to show how pointless the whole idea of natural languages
as formal languages is.
The claim that natural languages are formal languages is not clear here.
Would merely the claim that they are set-theoretical objects suffice?
How pointless you ask? This pointless: the first time the idea of
sentences conveying meaning is mentioned is page 130!!!
This is of course just a nonsequitur. No attempt to even connect the fact to
any aspect of the argument of the chapter.
Bulbul again:
The answer is of course is that Postal does not know enough math. He
is like a giddy 12-year old* who just discovered X (in his case set
theory) and derives his understanding of NL from it. To him, NLs are
merely sets of sentences, all he cares about is the finite vocabulary vs
infinite syntax distinction. He did not even get to the, um, Chomsky
hierarchy and thinks all formal languages are the same.
It is difficult to understand this bizarre mixture of ad hominum attack,
falsehood and nonsequitur. The claim that I did not discuss the Chomsky
hierarchy is true but there was not the slightest reason for me to do so.
Anyone interested in that can easily find a multitude of sources. The claim I
think all formal languages are the same is sheer make believe. I defy him to
cite a page in my book which says anything of the sort.
Bulbul again:
in off-hand comments like this:
Postal’s 1966 review of Dixon 1963 criticized that author’s claim that
linguistics could operate (exclusively) on the basis of speaker
observation.
Bulbul has nothing to say about my review of Dixon 1963. His only
discernable reason for citing it appears to be that it gives him a lead in to:
Dixon is of course Robert M. W. Dixon whose work is of course a
hundred times more valuable to modern linguistics than that of
Chomsky and Postal combined. And you know why? Because Dixon
actually went out and looked at how people speak!
I guess in Mr. Bulbul’s mind ‘looking at how people speak’ is awfully rare. I
suspect a few people have done it before RMW Dixon. I probably have
listened to one or two utterances myself.
Bulbul certainly likes his ad hominums. Also nonsequiturs. Let us suppose
he is correct in his evaluation of Dixon’s and my contributions to
linguistics. Let’s go further and grant that Dixon is the greatest linguist of
all time and that I am the worst. What could that possibly show about any
claim in my book??
Back to Mr. Eddyshaw:
As bulbul says, Postal is a full-bore Platonist
True
who has mistaken his Platonic Idea of Language for the real thing.
Ok fine, I am accused of having made a mistake. It wouldn’t be the first.
But in making an accusation of this type, one might expect from someone
serious at least a tiny bit of argument showing the mistake or some
references showing that or, in fact anything at all. But no, just another
arrogant dogmatic claim based on personal prejudice.
(This Platonic Form is, indeed, Vast. But that has no actual bearing on
linguistics at all.)
More unsupported dogma.
There is in fact a significant literature defending the platonic view of
natural languages.. Although nothing Mr. Eddyshaw has said really merits
the effort, I list some relevant works:
Katz, Jerrold J. 1981. Language and other abstract objects. Totowa, New
Jersey: Rowman and Littlefield.
Katz, Jerrold J. 1984. An outline of platonist grammar. In Bever,Thomas G.,
John M. Carrol and L.A. Miller (eds.). Talking minds: The study of
language in cognitive science. Cambridge, Massachusetts: The MIT Press.
Katz, Jerrold J. 1990. The Metaphysics of Meaning. Cambridge,
Massachusetts: The MIT Press.
Katz, Jerrold J.1996.The unfinished chomskyan revolution. Mind and
Language 11: 270–294.
Katz, Jerrold J. 1998. Realistic Realism. Cambridge, Massachusetts: The
MIT Press.
Katz, Jerrold J. and Paul M. Postal. 1991. Realism vs. Conceptualism in
Linguistics. Linguistics and Philosophy, Vol. 14, No. 5 pp. 515-554
Postal, Paul M. Remarks on the Foundations of Linguistics. 2003. The
Philosophical Forum, Vol XXXIV, Nos 3 and 4.
Of course, considering a reasonable portion of the argumentation in these
works and attempting in the face of them to justify the dogma presented
above would take a good deal of time and effort. Easier to just pontificate
on blogs.
Mr. Eddyshaw again:
September 27, 2025 at 10:51 am
The problem is more radical than that. Postal’s concept of Language
effectively incorporates the entire apparatus of ZFC, which implies
infinities far beyond anything that has ever been postulated for the
physical universe.
So what! If one is not talking about the physical universe, where is the
problem. To think that it is just a given that talking about natural languages
must be talking about some aspect of the physical universe is of course to
beg the question which a platonist view of language raises.
And anyway the recognition of infinities beyond…is due to Cantor not to
any linguist.
Geoffrey Pullum has a paper (with his then wife) exploring the view
that actual languages* are in fact finite. (Very big, but that, of course, is
something entirely different.)
This is wrong. Pullum’s repeated view is that model-theoretic grammars,
unlike generative grammars, make no claim about the size of languages and
are compatible with any size whatever.
Once more Mr. Eddyshaw
On a practical level, such systems both overgenerate (grotesquely, for
example by declaring that hypothetical infinitely long sentences are a
real part of a natural language)
As far as I know the claim that there were sentences of infinite length was
only made by T. Langendoen and I in our 1984 volume The Vastness of
Natural Languages.To suggest as here that this marginal idea is
characteristic of a mass of modern syntactic thought, most of which rejects
or ignores the idea, shows a vast ignorance of the domain.
and undergenerate, because scholars committed to this approach
routinely reject genuine utterances which cannot be generated by their
systems as being ungrammatical. Theory trumps data.
This dogmatic claim is not supported with a single piece of evidence, not a
single reference and yet is taken to be a general truth covering
hundreds/thousands of works.
Mr. Eddyshaw once more:
Postal’s idea seems to be that you need real numbers to describe Language, and he thinks Chomsky is merely up to
the countably infinite, and is therefore Wrong, Wrong, Wrong.
That is in effect precisely my idea. The evidence is that some sentences can
contain arbitrary nonlexical elements drawn from uncountable sets, e.g.
arbitrary squiggles, e.g. ‘The kid scribbled
[squiggle]
or pictures of cats, etc. as illustrated in the book. One notes that Mr.
Eddyshaw says nothing to ground rejecting these claims.
Mr Eddyshaw again:
Jack knows that Jill knows that Jack knows that Jill knows that …”
The only way to escape from “infinite language” is then to suppose that
a sentence like this is not already present, floating in the noosphere
somewhere, but can be produced “on demand” by rules that permit
sentences to be constructed from other sentences by coordination,
embedding or whatever. QED. (Subsequent fiddling with the notion of
“rule”, successively bleaching it of more and more content until it
becomes an irreduceable “merge”, doesn’t alter the basic principle; it
just makes the complete edifice less and less transparent and farther
from any real language data.)
However, even if you accept the introspective methodology, there is
actually a thumping petitio principii in this: “could go on forever”
assumes the conclusion that there actually is a rule that you could keep
on following in this way. If you don’t make this circular argument, the
only way you could show that such a sentence is possible would be to
actually construct it. (I’ll wait: you don’t mind if I get on with a few
other things in the meantime, do you?)
To see that what passes for reasoning here has no real force and is just
confused snark it suffices to see that the same remarks could equally be
applied to any infinite mathematical system.
The author says:
floating in the noosphere somewhere, but can be produced “on
demand” by rules that permit sentences to be constructed from other
sentences by coordination, embedding or whatever.
No one thinks though that the natural numbers have a finite cardinality or
that they are ‘floating in the noosphere’. Rather it is recognized that they are abstract objects which exist but cannot be found anywhere. To think that
existence entails position in time or space is again question begging.
For instance, does Mr. Eddyshaw believe that the principle of modus
ponens exists? If so, where in the physical universe is it???
One can search in all Mr. Eddyshaw’s many remarks and find no basis for
distinguishing the cardinality of integers from that of natural language
sentences.
In fact, could one not take the following just to be a bad representational
notation for the sequence of nonnegative integers, with Jane’s = 0 and each successive case of the form
[[X+ mother’s]], X not equal to Jane’s, equal in value to +1 of the
expression it immediately contains.
[[[[[[[[Jane’s] mother’s] mother’s] mother’s] mother’s] mother’s] mother’s]
mother’s]….
0 1 2 3 4 5 6 7
Bulbul says:
His problem with Chomsky is not that Chomsky also believes that
languages are abstract entities,
Any reading of my chapter 3 will show via quotes from Chomsky that there
is no sense in which he advances the idea that NLs are abstract entities. Not
content with his error, Bulbul repeats it:
But that does not change the fact that they both believe in language as an abstract disembodied entity (or set, in Postal’s case) and actual
speech or texts is just some – what did Postal call it? – oh yes,
Expression system.
The implication here is that the view roughly characterized is somehow
defective. But nothing is advanced to support that view.
Has Bulbul read even the first few pages of my chapter 2 whose (2) quotes
Chomsky as saying:
(2) Chomsky 1972: 169 n. 3
Since the language has no objective existence apart from its mental
representation, we need not distinguish between ‘system of beliefs’ and
‘knowledge’ in this case.
Bulbul adds:
That at two points in the book (Postal 2025: 84, 128), Postal has the
khutzphe to take William of Ockham’s name into his fucking mouth
just takes the cake.
I haven’t a clue as to what point Bulbul thinks he is making here. Rather,
this piece of contentless vulgar nastiness just makes me wonder whether he
might be advised to taper off his consumption of adult beverages and or
controlled substances. They are enemies of clear thinking and simple
civility.
Bulbul also says:
Postal has no interest in the physical universe or its limitations.
I have never met Bulbul or corresponded with him. How could he know so
definitively what my interests are? He couldn’t and doesn’t.
This is best seen in his muddled discussion of “orthography” –
i.e. graphical representation – where Postal argues that
orthographies are also infinite.
He does not give any ground to the claim that something is muddled. And
nowhere did I say orthographies are infinite. If Bulbul knows of an infiinite
orthography he would make a contribution by revealing its hitherto secret
developers and society where this curious system was used.
And his following passage is completely absurd:
The idea that for an orthography to be usable, people need to able to
tell the individual characters apart easily, does not even occur to him.
He only realizes this
So there is purportedly an idea which both does not even occur to me and
which I nonetheless realize. This sort of nonsense is the result of a very
strong desire to say something critical without having thought through any
actual objection.
Bulbul continues:
because Turing (1936: 246-250) makes an off-handed remark to
that effect. Postal then begins to treat it as a huge discovery,
even to the point of calling it “Turing’s theorem” (Postal 2025:
99)
This is complete distortion. Turing’s published paper was not an off-handed
remark, but a proof, as discussed in the paper by David Richeson I also
cited. Bulbul with no basis falsely makes it seem like I decided to call
Turing’s result a theorem. Again in his strange drive to criticize where there
is nothing to object to he falls into absurdity or worse.
Well, no doubt I have gone on too long. I am surely less than fully objective
about my own book. But the level of comment on it here, is in my opinion,
overall truly wretched. In one section of my 2004 monograph Skeptical
Linguistic Essays, I talked about and criticized what I called junk
linguistics. I regret to say that the comments on my monograph on the
relevant page of LANGUAGEHAT that I have responded to here rarely rise
to that quality level.
I note finally I am aware of two serious reviews of my book. One by an
Irish philosopher named Keith Begley appears at LINGUIST List 37.1565, Sun Apr 26 2026. The other by Geoffrey K. Pullum appears at
Historiographia Linguistica August 2026
DOI: 10.1075/hl.00199.pul
While there is much in these reviews I agree with, there are also
serious points where my views differ.
“In contrast to Mr. Dzhugashvili though, Mr. Eddyshaw (presumably) lacks thousands of armed thugs prepared to enforce his linguistic views.”
1. This is great, especially the (presumably). Are you sure Bulbul did not write this for you?
2. You are very brave considering that at this very moment thousands of armed thugs (or even one Bulbul) might be racing to intercept you.