Abstract
Linguistics as a science has rapidly changed during the course of a relatively short period. The mathematical foundations of the science, however, present a different story below the surface. In this paper, I argue that due to the former, the seismic shifts in theory over the past 80 years opens linguistics up to the problem of pessimistic meta-induction or radical theory change. I further argue that, due to the latter, one current solution to this problem in the philosophy of science, namely structural realism (Ladyman in Science 29(3):403–424, 1998; French in Proc Aristot Soc 106:167–185, 2006), should be viewed as especially enticing for linguists, as their field is a largely structural enterprise. I discuss particular historical instances of theory change in generative syntax before investigating two views on the nature of structural properties and eventually proposing an approach in terms of invariance (Johnson in Mind Lang 30(2):162–186, 2015) as a grounding for structural realism in the history and philosophy of linguistics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Here my focus will largely be on the formal history of generative syntax. A broader view could take the present methodology and extend it beyond generative grammar to the so-called ‘structuralist’ movement of Harris, Bloomfield, and Hockett. See Joseph (1999) and Matthews (2001) for the direct connections between this latter paradigm and contemporary linguistics. See also Nefdt (2019b) for a related account.
A related, more ontological, question is if the grammars of linguistics are scientific theories (as Chomsky and others have insisted over the years), then what are the objects being explained by these grammars? The radical theory change question has received very little attention, while this latter question has received perhaps too much. For instance, Chomsky (1986a) details the received or psychological take on the ontology of linguistics, Katz and Postal (1991) offers a Platonist interpretation, Devitt (2006) a non-psychological physicalist view, and Stainton (2014) a mixture of all the above.
There are such instrumentalist theories on the market. See van Fraasen (1980) constructive empiricism as one prominent example. A general problem for such views is that they tend to make miraculous the explanatory and predictive successes of scientific theory. Van Fraasen’s response to these sorts of worries is to appeal to an analogy with evolutionary theory such that only the fittest theories survive (where ‘fittest’ means something like ‘latching on to actual regularities in nature’) (van Fraasen 1980: p. 40).
I attempt to follow Pullum and Scholz (2007) throughout in slaloming my way through the minefield of the distinctions between ‘formalisation’, ‘formal’, and ‘Formalism’. The senses expressed here are related to ‘formal’ as a term used for systems which abstract over meaning and ‘formalisation’ as a tool for converting statements of theory into precise mathematical representations. Early generative grammar can be seen as a theory which aimed to achieve both distinct goals.
Of course, the term dates back to Lenneberg (1967) who introduced these issues to the generative linguistics community.
Matters are not as simple as suggested here. As Bickerton (2014) stresses, the peculiarity of the situation in linguistics is that the field at present still contains scholars working in various versions of the generative programme concurrently.
Basically, regular grammars can’t handle constructions like centre embeddings such as The boy the girl loved left. These latter constructions form part of a larger class of non-serial dependencies which are inaccessible to regular languages.
‘Ordering paradoxes’ here refer to the situation in which there are equally valid reasons for orderings from X to Y and Y to X despite the grammar requiring a particular order to pertain.
I more or less follow the standard story here but see Kornai and Pullum (1990) for a series of convincing arguments to the effect that the X-bar formalism lacks substance in terms of illuminating phrase structure properties without significant restructuring (which they provide).
There are some linguists who resist this claim. Instead they claim theoretical continuity between the programmes. For instance, Horstein (2009) offers two reasons for the theoretical continuity between Minimalism and GB.
First, MP starts from the assumption that GB is roughly correct. It accepts both the general problems identified for solution (e.g. Plato’s Problem) and the generalizations (“laws”) that have been uncovered (at least to a good first approximation). The second way that MP continues the GB program is in its identification with the Rationalist research strategy that sits at the core of Chomskyan enterprise in general and GB in particular (178).
This might indeed be the case but in my view can best be described as a theoretical orientation rather than theoretical commitment. Many very different theories can be described as “rationalist” in this broad sense. I also worry about the veracity of the first reason but further discussion will take us into exegetical territory.
Technically, as Langendoen (2003) notes ‘Merge is not a single operation, but a family of operations. To belong to the merge family, an operation must be able to yield an infinite set of objects from a finite basis’ (307). However, by this definition, the phrase structure rules with recursive components would also be included. The structural similarities of various versions of this infinity requirement on grammars will be discussed in the next section.
The practice of taking ideas or insights in some disguised form from early frameworks is not uncommon. For example, the binding theory of Government and Binding is very close (if not identical) to principles governing anaphora (like the Ross-Langacker constraints) that were first articulated in the 1960’s. Similarly, the trace theory of movement is closely tied to the earlier idea of global derivational constraints.
Compare this metaphorical language to a similar caution in Pullum (2013: p. 496), ‘[t]he fact that derivational steps come in a sequence has encouraged the practice of talking about them in procedural terms. Although this is merely a metaphor, it has come to have a firm grip on linguists thinking about syntax’.
Of course, the immediate predecessor of phases can be found in barriers. See Chomsky (1986b) for more details on the general framework.
Hence the furious debates around the foundations of quantum physics and Heisenberg’s uncertainty principle.
Of course, van Fraasen (1980) and others (such as Wray 2007) disagree with the very idea that this empirical success is in need of explanation or at least the kinds of explanations realists provide. Laudan (1981) himself argues that is is possible to have approximate truth without empirical success, as well as successful reference without empirical success.
I thank an anonymous reviewer for pointing this worry out to me.
Another reason one might favour a paradigmatic understanding of generative linguistics is provided in Tomalin (2010) who adapts Kuipers’ (2007) taxonomy of scientific research categories. At the top are (1) research traditions, e.g. generative linguistics itself (including phonology, syntax etc.), which are instantiated by (2) research programmes such as generative grammar (further subdivided into Standard and Extended Standard Theory, Minimalism etc.) or the parallel architecture which in turn have (3) core theories (such as the autonomy of syntax or recursion) and finally (4) specific theories of particular phenomena which share core theoretical tenets. “This seems reasonable since the phrase ‘generative grammar’ is standardly used to refer to different theories of generative syntax that have been proposed during the period 1950s-present, and, given this, it would be misleading to classify GG as being simply a ‘theory”’ (Tomalin 2010, p. 317).
There is an interesting possible connection here between what Shapiro (1997) calls “working realism” in which mathematicians act as if some sort of Platonism is true (or even should do so) and the case of generative linguists who assume that some sort of mental realism is true. Of course such a position would be too weak to defeat anti-realism. I thank an anonymous reviewer for suggesting the connection.
What I find interesting is that despite questioning the cognitive scientific link, many of the philosophical critics of generative grammar have similarly insisted on realist interpretations of their views. Katz and Postal (1991) move from talk of Platonism to describing their view as ‘Linguistic Realism’. Devitt (2006) too considers himself a non-mentalist realist (in a more nominalistic sense). Thus, scientific realism seems to be a commonly held position within the foundations of linguistics across the philosophical spectrum.
At this point, one can glean how such a picture might enter into the debate concerning the ontological foundations of linguistics mentioned earlier. Unlike Platonists who claim among other things that languages are individual abstract objects like sets or mentalists who claim they are psychological or internal states of the brain, a structuralist might argue that languages are complex structures in part identified by abstract rules and physical properties. See Nefdt (2018) for a similar view.
In fact, these equivalences go beyond the generative grammars. Minimalist Syntax (or the Stabler 1997 version), Phrase-Structure grammars, Tree-substitution grammars, Head-Driven Phrase Structure grammars, and Dependency grammars have been shown to share weak generative capacity. See Mönnich (2007). Contrast this with ‘strong generative capacity’ in which a grammar assigns the same structural descriptions, e.g. Context-Free Grammars (CFGs) assign trees to each sentence. Thus, dependency grammars are not strongly equivalent in this sense to CFGs (or phrase-structure grammars) since they assign rooted acyclic graphs to sentences and not rooted binary trees.
As pointed out to me by an anonymous reviewer, semi-decidability would work for recursive enumerability as well. For instance, first order logic is not decidable but its validity is recursively enumerable (although I should add that the complement of the validity problem, i.e. determining whether a given formula \(\phi \) is not valid, is not recursively enumerable).
He goes on to ‘suspect’ that the adoption of the derivational approach is more than expository and might indeed be ‘correct’.
This scenario is guaranteed by Beth’s theorem which states (of classical logic) that a non-logical term T is implicitly defined by the theory (or generated by the rules) iff an explicit definition of the term is deducible from the theory (as in the case of constraint-based or model-theoretic grammars). This effectively connects the proof theory of the logic to the model theory. I thank an anonymous reviewer for directing me towards the applicability of Beth’s theorem here.
English speakers do make use of a form of understatement called “litotes” which also involves double negation but not always for the sake of retrieving a strong positive reading as in the example above. Litotes is largely pragmatic.
In addition, more technically, this agree relation is a Multiple Agree relation which means that multiple [uNeg] elements can be c-commanded by one element bearing [iNeg] in the feature checking.
The analysis is supported by the impossibility of double negation in Czech (and similar languages) and the cross-linguistic typology of possible negative configurations put forward by Zeijlstra and others. But of course nothing here rests on the ultimate truth of this particular account, it is merely meant to show the overall structural thinking involved in generative linguistic analysis.
The literature of WH-movement, for instance, is vast and can be found is almost all textbooks on syntax. Interestingly, for our purposes, the early trace theory is structurally identical to the later Minimalist copy theory of movement. The latter serves an additional theoretical purpose of limiting the proliferation of objects in the ontology such as the indices required for traces.
I thank an anonymous reviewer for pressing me on this point.
One may be tempted to consider these to be two identical or converging ways of carving up the same turkey. But according to Korbmacher and Schiemer (2018), once we move from the informal to the formal characterisations of these concepts, their differences become more apparent. See below.
Hard but not impossible. In his dissertation, Meier (2015) compares Bloomfield on substitutes and Harris’ kernel sentences toward an intertheoretical account of structural continuity. He defines a metatheoretical notion of theory reducibility for this purpose (i.e. Bloomfield is reducible to Harris and Harris to early Chomsky). Thus, he shows that the internally defined aspects of a theory are amenable to structural analysis and comparison. In this case, however, he is limited to epistemic structural realism which takes no stance on the properties of the objects of the structures in question.
Substitution involves replacing a non-terminal leaf in a tree with a new tree whose root node is labelled with the same non-terminal in order to create larger trees. Adjunction allows insertion of auxiliary trees within larger trees at various points. TAGs incorporate both mechanisms. See Rambow and Joshi (1997) for more details.
References
Awodey, S. (1996). Structure in mathematics and logic. A categorical perspective. Philosophia Mathematica, 3(4), 209–237.
Benacerraf, P. (1973). Mathematical truth. The Journal of Philosophy, 70(19), 661–679.
Biberauer, T., & Zeijlstra, H. (2012). Negative concord in Afrikaans: Filling a typological gap. Journal of Semantics, 29, 345–371.
Bickerton, D. (2014). More than nature needs: Language, mind, and evolution. Cambridge, MA: Harvard University Press.
Boyd, R. (2010). Scientific realism. The Stanford Encyclopedia of philosophy. Retrieved from https://plato.stanford.edu/archives/sum2010/entries/scientific-realism/.
Büchi, R. (1960). Weak second-order arithmetic and finite automata. Zeitschrift für mathematische Logik und Grundlagen derMathematik, 6, 66–92.
Bueno, O., & Colyvan, M. (2011). An inferential conception of the application of mathematics. Nous, 45(2), 345–374.
Chakravartty, A. (2011). Scientific realism. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy. Stanford: Stanford University.
Chomsky, N. (1956). Three models for the description of language. IRE Transactions on Information Theory, 2, 113–123.
Chomsky, N. (1957). Syntactic structures. The Hague: Mouton.
Chomsky, N. (1959). Review of skinner’s verbal behavior. Language, 35, 26–58.
Chomsky, N. (1964). Current issues in linguistic theory. The Hague: Mouton.
Chomsky, N. (1965). Aspects of a theory of syntax. Cambridge, MA: MIT Press.
Chomsky, N. (1970). Remarks on nominalization. In R. Jacobs & P. Rosenbaum (Eds.), Readings in English transformational grammar (pp. 184–221). Waltham, MA: Ginn.
Chomsky, N. (1972). Studies on semantics in generative grammar. The Hague: Mouton.
Chomsky, N. (1975). The logical structure of linguistic theory. Dordrecht: Springer.
Chomsky, N. (1983). Some conceptual shifts in the study of language. In L. S. Cauman, I. Levi, C. D. Parson, & R. Schwartz (Eds.), How many questions? Essays in honor of Sidney Morgenbesser. Indianapolis: Hackett.
Chomsky, N. (1986a). Knowledge of language: Its nature, origin, and use. New York: Praeger.
Chomsky, N. (1986b). Barriers. Cambridge: MIT Press.
Chomsky, N. (1995). The minimalist program. Cambridge, MA: MIT Press.
Chomsky, N. (1998). Minimalist inquiries: The framework. MIT Occasional Papers in Linguistics 15.
Chomsky, N. (2000). Minimalist inquiries. In R. Martin, D. Michaels, & J. Uriagereka (Eds.), Step by step: Essays on minimalist syntax in honor of Howard Lasnik (pp. 89–155). Cambridge, MA: MIT Press.
Chomsky, N. (2008). On phases. In R. Freiden, C. P. Otero, & M. Zubizarreta (Eds.), Foundational issues in linguistic theory (pp. 133–166). Cambridge, MA: MIT Press.
Cowie, F. (1999). What’s within? Nativism reconsidered. Oxford: Oxford University Press.
Culicover, P. (2011). Core and periphery. In P. Hogan (Ed.), The Cambridge encyclopedia of the language sciences, 227–230. Cambridge: Cambridge University Press.
Devitt, M. (2006). Ignorance of language. Oxford: Oxford University Press.
Freidin, R. (2012). A brief history of generative grammar. In G. Russell & D. Fara (Eds.), The Routledge companion to philosophy of language (pp. 895–916). New York: Routledge.
French, S. (2006). Structure as a weapon of the realist. Proceedings of the Aristotelian Society, 106, 167–185.
French, S. (2011). Shifting the structures in physics and biology: A prophylactic promiscuous realism. Studies in History and Philosophy of Biological and Biomedical Sciences, 42, 164–173.
French, S., & Ladyman, J. (2003). Remodelling structural realism: Quantum physics and the metaphysics of structure. Synthese, 136, 31–56.
Frigg, R., & Votsis, I. (2011). Everything you always wanted to know about structural realism but were afraid to ask. European Journal for Philosophy of Science, 1(2011), 227–276.
Gabig, C. (2013). Telegraphic speech. In F. Volkmar (Ed.), Encyclopedia of autism spectrum disorders (pp. 125–139). New York, NY: Springer.
Horstein, N. (2009). A theory of syntax: Minimal operations and universal grammar. Cambridge: Cambridge University Press.
Jackendoff, R. (1977). X’ syntax. Cambridge, MA: MIT Press.
Jackendoff, R. (2002). Foundations of language: Brain, meaning, grammar, evolution. Oxford: Oxford University Press.
Jäger, G., & Rogers, J. (2012). Formal language theory: Refining the Chomsky hierarchy. Philosophical Transactions of the Royal Society B: Biological Sciences, 367, 1956–1970.
Johnson, K. (2015). Notational variants and invariance in linguistics. Mind & Language, 30(2), 162–186.
Joseph, J. (1999). How structuralist was “American structuralism”? Henry Sweet Society Bulletin, 33, 23–28.
Katz, J., & Postal, P. (1991). Realism vs. conceptualism in linguistics. Linguistics and Philosophy, 14(5), 515–554.
Kincaid, H. (2008). Structural realism and the social sciences. Philosophy of Science, 75(5), 720–731.
Korbmacher, J., & Schiemer, G. (2018). What are structural properties? Philosophia Mathematica, 26(3), 295–323.
Kornai, A., & Pullum, G. (1990). The X-bar theory of phrase structure. Language, 66(1), 24–50.
Kuipers, T. (2007). General philosophy of science: Focal issues. Amsterdam/London: Elsevier/North Holland.
Ladyman, J. (1998). What is structural realism? Studies in the History and Philosophy of Science, 29(3), 403–424.
Ladyman, J. (2011). Structural realism versus standard scientific realism: The case of phlogiston and dephlogisticated air. Synthese, 180, 87–101.
Landry, E. (2007). Shared structure need not be shared set-structure. Synthese, 158(1), 1–17.
Langendoen, T. (2003). Merge. In A. Carnie, H. Hayley, & M. Willie (Eds.), Formal approaches to function in grammar: In honor of Eloise Jelinek (pp. 307–318). Amsterdam: John Benjamins.
Lappin, S., Levine, R., & Johnson, D. (2000). The structure of unscientific revolutions. Natural Language and Linguistic Theory, 18(3), 665–671.
Laudan, L. (1981). A confutation of convergent realism. Philosophy of Science, 48, 19–49.
Leitgeb, H., & Ladyman, J. (2008). Criteria of identity and structuralist ontology. Philosophia Mathematica, 16, 388–396.
Lenneberg, E. (1967). Biological foundations of language. New York: Wiley.
Lobina, D. (2017). Recursion: A computational investigation into the representation and processing of language. Oxford: Oxford University Press.
Ludlow, P. (2011). Philosophy of generative grammar. Oxford: Oxford University Press.
Matthews, P. (2001). A short history of structural linguistics. Cambridge: Cambridge University Press.
Meier, T. (2015). Theory change and structural realism. A general discussion and an application to linguistics. Dissertation, Ludwig-Maximilians-Universität München.
Mönnich, U. (2007). Minimalist syntax, multiple regular tree grammars, and direction preserving tree transducers. In Rogers, J. & Kepser, S. (Eds.), Model theoretic syntax at 10. ESSLLI’ 07 workshop proceedings (pp. 68–95). Berlin: Springer.
Moss, L. (2012). The role of mathematical methods. In G. Russell & D. Fara (Eds.), The Routledge companion to philosophy of language (pp. 533–553). New York: Routledge.
Miller, G. (2003). The cognitive revolution: A historical perspective. TRENDS in Cognitive Science, 7(3), 141–144.
Muller, F. (2010). The characterisation of structure: definition versus axiomatisation. In Stadler, F. (Eds.), The present situation in the philosophy of science. The philosophy of science in a European perspective (Vol. 1). Dordrecht: Springer.
Nefdt, R. (2018). Languages and other abstract structures. In C. Christina & M. Neef (Eds.), Essays on linguistic realism (pp. 139–184). Amsterdam: John Benjamins.
Nefdt, R. (2019a). Infinity and the foundations of linguistics. Synthese, 196(5), 1671–1711.
Nefdt, R. (2019b). Linguistics as a science of structure. In J. McElvenny (Ed.), Form and formalism in linguistics (pp. 175–196). Berlin: Language Sciences Press.
Newmeyer, F. (1996). Generative linguistics: A historical perspective. New York: Routledge.
Poole, G. (2002). Syntactic theory. Great Britain: Palgrave.
Postal, P. (1964). ‘Constituent structure: a study of contemporary models of syntactic description’. International Journal of American Linguistics 30.
Pullum, G. (1983). How many possible human languages are there? Linguistic Inquiry, 14(3), 447–467.
Pullum, G. (2011). The mathematical foundations of syntactic structures. Journal of Logic, Language and Information, 20(3), 277–296.
Pullum, G. (2013). The central question in comparative syntactic metatheory. Mind & Language, 28(4), 492–521.
Pullum, G. & Scholz, B. (2001). On the distinction between model-theoretic and generative enumerative syntactic frameworks. In de Groote, P., Morril, G., & Retoré, C. (Eds.), Logical aspects of computational linguistics: 4th international conference (pp. 17–43). Berlin: Springer.
Pullum, G., & Scholz, B. (2007). Tracking the origins of transformational generative grammar. Journal of Linguistics, 43(3), 701–723.
Putnam, H. (1975). Mathematics, matter and method. Cambridge: Cambridge University Press.
Pylyshyn, Z. (1991). Rules and representations: Chomsky and representational realism. In A. Kasher (Ed.), The Chomskyian turn (pp. 231–51). Cambridge, MA: Blackwell.
Quine, W. (1972). Methodological reflections on current linguistic theory. In D. Davidson & G. Harman (Eds.), Semantics of natural language (pp. 442–454). Dordrecht: D. Reidel.
Rambow, O., & Joshi, A. (1997). A formal look at dependency grammars and phrase structure grammars, with special consideration of word-order phenomena. In L. Wanner (Ed.), Recent trends in meaning-text theory (pp. 167–190). Amsterdam, Philadelphia: John Benjamins.
Rogers, J. (1998). A descriptive characterization of tree-adjoining languages. In Proceedings of the 17th international conference on computational linguistics (COLING’ 98) and the 36th annual meeting of the association for computational linguistics (ACL’98).
Ross, J. (1967). Constraints on variables in syntax. Ph.D. dissertation. MIT.
Rowbottom, D. (2019). Scientific realism: What it is, the contemporary debate, and new directions. Synthese, 196, 451–484.
Santana, C. (2016). What is language? Ergo, 3(19), 501–523.
Shapiro, S. (1997). Philosophy of mathematics: Structure and ontology. Oxford: Oxford University Press.
Stabler, E. (1997). Derivational minimalism. In C. Restoré (Ed.), Logical aspects of computational linguistics (pp. 68–95). Berlin: Springer.
Stainton, R. (2014). Philosophy of linguistics. In Oxford Handbooks Online.
Stokhof, M., & van Lambalgen, M. (2011). Abstractions and idealisations: The construction of modern linguistics. Theoretical Linguistics, 37(1/2), 1–26.
Thatcher, J., & Wright, J. (1968). Generalized finite automata theory with an application to a decision problem of second-order logic. Mathematical Systems Theory, 2(1), 57–81.
Tomalin, M. (2006). Linguistics and the formal sciences. Cambridge: Cambridge University Press.
Tomalin, M. (2010). Migrating propositions and the evolution of Generative Grammar. In D. Kibbee (Ed.), Chomskyan (r)evolutions (pp. 315–337). Amsterdam: John Benjamins Publishing Company.
Van Fraasen, B. (1980). The scientific image. Oxford: Oxford University Press.
Worall, J. (1989). The best of both worlds? Dialectica, 43(1/2), 99–124.
Wray, B. (2007). A selectionist explanation of the success and failures of science. Erkenntnis, 67(1), 81–89.
Zeijlstra, H. (2004). Sentential negation and negative concord. Ph.D. dissertation, University of Amsterdam.
Acknowledgements
I would like to thank Geoff Pullum and Michael Kac for their insights into the historical and technical linguistic details as well as Steven French for offering guidance on the structural realist aspects of the paper. I am also grateful to two anonymous reviewers of this journal for their excellent comments on both the philosophical and technical elements of the work. All remaining errors are my own.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Nefdt, R.M. Structural realism and generative linguistics. Synthese 199, 3711–3737 (2021). https://doi.org/10.1007/s11229-020-02952-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-020-02952-1