While my blogging here has been firmly within historical linguistics, every once in a while I do go poking around self-styled formal linguistics blogs too. [1] This tends to be a frustrating exercise though. By now, supposedly deep problems discussed around such parts tend to strike me as, frankly, dumb questions that only exist due to particular “theoretical commitments”, and which could be trivially resolved or avoided within better-grounded frameworks of understanding language. People stuck in generativist bubbles in particular, however, seem to be often unaware that any other types of approaches would exist at all.
As I’m rather more informed about the ground-level facts of phonology than e.g. syntax, this is going to be the more profitable area for me to comment on in any real detail, though generative syntax has also struck me as having foundational flaws roughly analogous to the foundational flaws of generative phonology. (I presume open-minded syntacticians should be even able to figure out these, ahem, analogies themselves, without me having to do all their work for them.)
At any rate, a good majority of questions attracting protracted debate in phonological theory that I have seen are immediately solved under the traditional non-generativist approach: “phonological processes” or “deep structures” do not exist as such. They are only grammatographical shorthand; rules of thumb, not rules of Grammar. [2] Where non-allophonic “phonological alternations” actually exist is within the lexicon, not within phonology.
A standard counterargument to this seems to be the fairly simple observation that loads of obviously non-allophonic alternations are, in fact, still productive to this or that extent in loads of languages. Checkmate, lexicalists?
No, of course not. This simply shows a particularly pernicious systematic failure of generative linguistics — a lack of understanding of language change, particularly that language change, including linguistic creativity, does not take place solely inside a box of “Grammar”, but also within the lexicon. Phonological alternations are easy to approach in this fashion, as they are generally not actually productive in the sense of immediate, universal applicability (as they say in Generativistland, they can be opaque). Moreover quite typically they are “productive in spats”, creating new forms one by one, now and then in the speech of particular speakers, not everywhere constantly. And the range of applicability for any one process is very finite really: while everyone creates novel noun phrases practically daily, I would wager that most people do not create any entirely novel strong verb forms over their entire life. [3] In historical and historically-informed linguistics, our default assumption is to attribute these kind of changes to the process of lexical analogy, and understanding it is vital to understanding patterns that arise and exist in language.
What we can actually observe is that any arbitrarily deep alternations can indeed inspire the coinage of new instances of the same, and therefore they can remain “productive”. If desired, I can readily coin all sorts of cases like long ∶ length ∷ oblong ∶ oblength or sing ∶ sung ∷ wing ∶ wung. But then nothing stops me from creating folk-etymological examples either, say choose ∶ choice ∷ snooze ∶ snoice. These also fade organically into snowcloneish blends, e.g. thanks, ants ∶ thants ∷ hello, horses ∶ hellorses; spelling pronunciations, e.g. tentacles ∶ /ˈtɛntəkəlz/ ∷ Pericles ∶ /ˈpɛɹɪkəlz/; or (mis)etymological nativization, e.g. English wrong ∶ Swedish vrång ∷ En. to wring ∶ Sw. vringa. Crucially, what needs to be noted is that this is an extralinguistic cognitive skill that should not have any bearing on the development of purely linguistic theory. Already etymological nativization refuses to respect the confines of a single language, and I think most theories of mental grammar would likewise not attempt to account for spelling pronunciations. We can also easily advance loads of more or less formal analogies in areas that have nothing to do with language, from mathematics (2 ∶ 20 ∷ 5 ∶ 50; square ∶ cube ∷ triangle ∶ tetrahedron) to the natural world (nitrogen ∶ ammonia ∷ oxygen ∶ water; the Congo ∶ leopards ∷ the Amazon ∶ jaguars) and human society (evolution ∶ Darwin ∷ relativity ∶ Einstein; punks ∶ pop punk ∷ ravers ∶ happy hardcore). This, I think, demonstrates beyond reasonable doubt that analogy in fact is a general skill that humans possess, and hence there’s no point in trying to reduce its applications in language into some kind of specifically linguistic primitives.
(Note BTW that while all my examples above are phrased as classic proportional analogies, this also should not be assumed to be the only possible or even the main mechanism of analogy.)
Once we accept the existence of analogy as an explanation for some cases of morphophonological productivity, this provides also a direct path into rich gains in parsimony. My linguistic examples above have been chosen to be on the “clever” side, i.e. building on only marginal precedents, partly to be sure that they’re indeed novel (at minimum to me!), partly to make it seem more convincing that they should not be modelled by inserting additional epicycles into English (morpho)phonology. But the mechanism of analogy works perfectly well also on any pedestrian phonological alternations out there. What is, say, the plural of oblength? It’s clearly oblengths — but then we could model this conclusion as having been drawn purely on the analogy of lengths, or also tenths, shibboleths, Beths, etc., without needing to assume any distinct, exclusively linguistic machinery behind this. The putative outcome oblengthes, just like also morphologically clearly different options like oblengthim or oblengtha, can be predicted to be unlikely already due to the lack of bases of analogy that could lead to them. [4] That all sorts of other coinages also follow the same pattern could be likewise explained already by the extremely strong precedent for the English plural marker to be -s. In principle even the regular phonologically conditioned allomorphy between -s and -es could then turn out to be simply emergent within the English lexicon, if we enrich it with sufficiently many plural forms stored as lexemes. This approach allows cutting out a hefty amount of costly theoretical complexity assigned to phonology in theories that fail to recognize that analogy exists.
Spending one further moment within philosophy of science, there is certainly also an apparent countercost of presuming the existence of some words like lengths as separate from length (or sung from sing, etc.). However, given that lexicons already indisputably exist, and contain many, many thousands of items anyway (and that, given the phenomenon of suppletion, these indisputably can be syntactically specified as particular inflected forms, etc.), just a few hundreds more to “seed” it with generators of morphophonology should be unambiguously considered the superior solution. Extra stuff is free.
It would be indeed possible to go further still and to propose that e.g. even the realization of oblengths as specifically /ɒblɛŋθs/ with /-s/ (and not /-z/) will be inferred by analogy from other English plural forms. It’s hard to rule out that this could not be the case for some people. [5] But I do grant that this at least is not an approach that could be fully generalized. Analogy generally allows for multiple solutions, some of them perhaps much less probable but still possible (e.g. if we take a cube as a prism with a square base, not as a polyhedron entirely made of squares, then the triangle analogue will be a triangular prism, not a tetrahedron; and maybe it should be heorses /hɛəɹsɪz/ rather than hellorses). Allophony by contrast is, by all appearences, subconscious enough that speakers find it difficult to create or perceive forms departing from it, and it clearly calls for a different kind of cognitive machinery.
[1] That’s the {self-styled formal linguistics} blogs; what they call themselves is, apparently, just “linguistic blogs”, with the common if vaguely cultish stance that only their branch of work actually constitutes Real Linguistics.
[2] As far as I can tell, a lot of trouble indeed comes already from the failure to fully distinguish descriptive grammar from mental grammar. Much of the early history of morphology and syntax quite transparently consists of attempts to formulate rigorous definitions for concepts of traditional Greco-Latinate grammatography like “subject” or “word”, but with little attention paid on if this even should be done: a priori there is no reason to expect mental grammar to have any building blocks at all in common with traditional descriptive grammar (much like how, say, biochemistry is not under the obligation to follow any views of Aristotelean natural philosophy). Modern theory of phonological processes indeed also looks like as if it largely amounts to applying the same mistake ultimately to Pāṇini’s descriptive (morpho)phonology of Sanskrit, although the road from there to Chomsky & Halle is not clear to me.
[3] i.e. “novel to English (or German, etc.) as a whole”. E.g. (a soup has been) wung might be a new creation for me just two days ago (‘prepared without a prior plan or recipe’, if you must know), but even before checking I am certain that others have stumbled on this same territory before. — Oh yes, no question about it: it’s even on Wiktionary already, with attestations going back to 1881.
[4] But, of course, not impossible. As e.g. advanced linguistics students faced with the wug test will readibly demonstrate, sufficiently large numbers of contrarian smartasses will eventually end up creating any form imaginable, no matter how “ungrammatical”. Almost nothing in language is actually impossible. This is perhaps the most clearly so when a phenomenon is “impossible” (rather, inacceptable) in one language variety but business as usual in another.
[5] Definitely not for me though. As an L2 speaker whose native language has no voiced fricatives, I ended up adopting the English plural marker(s) as just /-(i)s/ back in the day, and though I can by now make conscious effort to use [z] instead, I will be still quite content to speak of [windous], [siːliŋs], [hɑusis], [tʃʰiːzis], [nɑiʋs], [dɔgs], etc…
Freelance reconstruction 
Very interesting post, which raises the crucial question of what a “rule (of grammar)” actually is. The specific issue here has to do with morphophonological alternation rules, but essentially the same would also apply to rules of morphology and syntax alike.
I would not subscribe to the view that “non-allophonic “phonological alternations” [i.e., “morphophonological rules”] actually exist […] within the lexicon, not within phonology”. At least when such alternations are fully regular (as they are in many languages), it actually does not make much sense to claim that they exist in the lexicon only; in a similar vein, one could claim e.g. that individual case forms of nouns exist within the lexicon, not within morphology. (Irregular alternations that are not subject to almost any level of generalization, like English long : length, are of course a different issue.)
I think the problem is that one must distinguish between what the “rule” actually is and how the “rule” is acquired. When one considers language acquisition, it is indeed quite clear that analogy is the main mechanism – and perhaps almost the only mechanism – for acquiring morphophonological rules (and also other grammatical rules). But I suppose that a rule, once it has been acquired, is no longer an instance of analogical reasoning, but instead a norm – more precisely, a social norm shared by the speech community. For example, in the Finnish speech community there is a social norm to the effect that in consonant gradation the weak grade of -kk- is -k-, and if one fails to adhere to this social norm and declines Mikko : Mikkon instead of Mikko : Mikon, then other members of the speech community will maintain that the rule-breaker speaks incorrect Finnish. But in this context it would not seem that rules (social norms) regarding morphophonological alternations could be conceptualized as just some kind of perpetual analogy based on the behavior of individual lexical items like Mikko, nakki, kukka, etc. In fact, this would be almost like assuming that rules (social norms) regarding speed limits are just some kind of complex analogy based individual instances of following the speed limit, breaking it, getting pulled over and fined, etc. Or have I somehow misunderstood what was implied, or missed something obvious here?
One limit I tried to draw on the discussion in the post was, as per the title, to focus on specifically phonological rules, not the general concept of rules, which certainly would be a bigger question. Rules in the sense of social norms and conventions would be a good starting point for that topic. Perhaps we do want to consider these to be distinct from analogy, and even invoke them for explaining some phenomena within language. Though, at the same time, they again demonstrate a cognitive skill that is not exclusively lingustic, i.e. cannot be assigned as just a part of a “grammatical module” within the brain.
For alternations like Finnish consonant gradation, I would take a stance that despite still appearing somewhat phonologically conditioned, these are instead primarily morphological by now (whatever the real nature of morphology ends up being; and I do find the construction grammar proposal that also much of morphology exists within the “extended lexicon” at least worth exploring). This seems to be well demonstrated by how geminates can appear in short closed syllables just fine. This is basically universal in forms like Mikkomme, jotten, ukkospilvi, appellatiivi; additionally dialectal or idiolectal in forms like kappalten, uppos ‘upposi’, nukkus ‘nukkuisi’, mittar(j), kuppar-Mikko; also variable in cases like Trollhättan(i), (Nikke :) Nikken, cappuccino (plus in the last one variants like /kaputsiino/ or /kappučiino/ could be explained, instead of by gradation, e.g. as reflecting the English rather than Italian pronunciation).
As you know, in generative phonology the answers to counterevidence like this are to claim that they manage to exist due to being created by higher-ranked rules or constraints, or phonology making direct reference to morphology, or due to “loanword phonology”. But this goes fast into at least one of positing somewhat ad hoc and seemingly unlearnable underlying forms, requiring more exclusively phonological machinery than I am comfortable assuming, and requiring unrealistic amounts of cognitive processing. (For the last point, bear in mind the boundary condition that the human brain only operates at about 10 Hz. Highly serial derivation of anything at all is probably experimentally disprovable in most cases.)
On the other hand, while the distribution of strong and weak grade forms probably should be accounted for via some kind of grammatical rule(s), it does seem entirely possible to me to consider the existence of the two grades Mikko- : Miko- (or any other recent cases like netti : neti-) to be lexicalized and originally analogical. Most likely not one-on-one proportional analogy though (this would fail to explain why geminate gradation remains far more productive than qualitative gradation), as much as something like overarching root-and-pattern analogy, a process that must be surely invoked at least to explain the origin of completely unetymological gradation patterns like blogata : bloggaa (and yet still lagata : lagaa, etc.) These and qualitative gradation likewise establish that at least some weak/strong grade pairs in Finnish are lexicalized anyway.
All this is about at least marginally opaque rules though. Entirely surface-faithful phonological rules surely could be still modelled as basically just allophonic. I believe this puts me close to e.g. Donegan & Stampe’s theory of Natural Phonology or Manaster Ramer’s Broad Phonology. — Do you perhaps mean to suggest the existence of phonological rules that are fully regular but also not allophonic?
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