In response to “The Recovery of Case” (Vol. 2, No. 3).

To the editors:

In their article, “The Recovery of Case,” David Berlinski and Juan Uriagereka speak of Jean-Roger Vergnaud’s “desire to see beneath the infernal arbitrariness of description to the place where unity prevails.” That this could even be possible may be contrasted with the viewpoint of the later Ludwig Wittgenstein for whom the label “language” lumps together activities by reason of their overlapping similarities, their family resemblances.1 Wittgenstein saw no need to suppose any prevailing hidden unity. Noam Chomsky dismissed Wittgenstein’s view succinctly: “it is of the nature of bits of evidence to be fragmentary, confusing, partial, loosely related, lacking sharp boundaries, etc., that is, to exhibit only ‘family resemblances.’”2

Berlinski and Uriagereka note that this attempt to find underlying unity is a strategy of Galilean style. Discussing Edmund Husserl’s reflections upon the sciences and objectivity, Aron Gurwitsch observed that the concern with “being as it really is in itself” “finds its expression in the work of Galileo.”3 The scientific revolution required “a notion of objectivity which is of central importance for the mathematico-physical sciences of Galilean style.”4 Shortly after Vergnaud’s discovery, Chomsky elaborated upon the Galilean style:

Can we hope to move beyond superficiality by a readiness to undertake perhaps far-reaching idealization and to construct abstract models that are accorded more significance than the ordinary world of sensation, and correspondingly, by readiness to tolerate unexplained phenomena or even as yet unexplained phenomena or even as yet unexplained counterevidence to theoretical constructions that have achieved a certain degree of explanatory depth in some limited domain …5

If “significance” is understood as truth or approximation to truth, then the Galilean style is quite remote from Wittgenstein’s viewpoint, circa 1930. Wittgenstein proposed a view that came to be of tremendous influence in the philosophy of science, namely that “An hypothesis is a law for forming propositions. You could also say: An hypothesis is a law for forming expectations.”6 These would be expectations of sensations, as “phenomenology would be the grammar of the description of those facts on which physics builds its theories.”7 In other words, a scientific theory is a kind of machine or program for producing descriptions of sensations, and one judges a theory according to how well the descriptions agree with the sensory experiences. One could not even say that a theory is true or false, but only that it is more or less reliable as a kind of instrument for engineering. Much of Chomsky’s work, on a philosophical level, can be understood as a rebellion against this instrumentalist view of scientific theories.

Vergnaud’s contribution of Galilean style, as Berlinski and Uriagereka discuss in admirable detail, concerned grammatical case.8 Consider a language, such as Turkish, in which a noun or determiner will have different endings according to its part of speech. The Turkish word “bura” means “here” or “this place,” but it is seldom pronounced simply as “bura.” Typically, there is a case ending attached to it. Here are three Turkish sentences featuring “bura,” each followed by an English translation:

  1. Burası güzel. (“This place is lovely.”)
  2. Burayı seviyorum. (“I love this place.”)
  3. Buraya gel. (“Come here” or “Come to this place.”)

In (1), “bura” is in nominative case, as it must be to serve as the subject of a finite clause. In 2, “bura” is in accusative case, since it is the object of the verb. In 3, “bura” is in adpositional case, since the case is assigned by an adposition (such as the preposition “to” in English or the postposition “ya” in Turkish). “Bura” receives a different ending in each sentence to reflect its different cases. English differs: “this place” is pronounced the same in all three instances. There is almost no case morphology in English, other than a few vestiges: “him” versus “he,” “them” versus “they,” “us” versus “we,” “whom” versus “who.” There is even less case morphology in Mandarin, if any. Here we have apparent variety, not only between languages, but also within English itself: “them” has case, while “that” appears not to have it.

Vergnaud suspected that in English, and of course in his own native French, even when there is no morphological indication of case, case is present nonetheless. Consider English. Vergnaud noted that the determiner phrase in the subject position of an infinitival phrase, if it is pronounced must be assigned accusative case. This is done either by its immediately following a transitive verb, or immediately following the preposition “for” which serves here as a clause introducer, a “complementizer.” (For each of the sample sentences, the infinitival phrase is in brackets, and its subject, if pronounced is italicized.)

  1. We want for [them to succeed].
  2. For [them to succeed] would be desirable.
  3. We very much want [them to succeed].

Even relocating the modifier “very much” so that it stands between the transitive verb and the subject of the infinitive results in an ungrammatical sentence. The verb cannot assign case when something stands in its way.

  1. * We want very much [them to succeed].

The subject of the infinitive, if pronounced, cannot be in nominative case.

  1. * We want for [they to succeed].
  2. * For [they to succeed] would be desirable.
  3. * We very much want [they to succeed].

The constituent preceding the subject of the infinitive must either be a transitive verb or the transitive preposition “for.” Otherwise, accusative case is not assigned to the subject of the infinitive phrase.

  1. * [Them to succeed] would be desirable.
  2. * I agreed [them to leave].

Now compare (7), (11), and (12) with the following three sentences:

  1. * We want very much [the children to succeed].
  2. * [The children to succeed] would be desirable.
  3. * I agreed [the children to leave].

Vergnaud noticed that one could explain the similarity in pattern between (7), (11), and (12) and (13), (14), and (15) by assuming that “the children” also requires accusative case assignment. What is remarkable about this is that the determiner phrase “the children” has no morphological case. It evidently has case, but it has it on some psychological level not reflected in the morphology. In Turkish, the word “çocukları” is the word for “children” or “the children,” followed by a suffix indicating accusative case: çocuklar + ı. In English, “the children” also has case, even though it is morphologically invisible. When the subject of the infinitival phrase is not pronounced, null case is assigned by the infinitive particle “to,” as reflected by the fact that a transitive verb or transitive preposition is no longer needed to assign case to the subject.

  1. We want very much [to succeed].
  2. [To succeed] would be desirable.
  3. I agreed [to leave].

In other words, we have a kind of case which lies beneath the level of appearances: Abstract Case. Chomsky and Howard Lasnik had postulated filters for screening out sentences like (13), (14), and (15).9 But the filters seemed a bit like arbitrary rules as to when to use a complementizer and when not. As Berlinski and Uriagereka put it, “It might even seem … as if the system’s filters were an adventitious afterthought, something that grammarians added to the system to tie up a few loose ends.” But now Vergnaud had found an underlying order in what had looked arbitrary.

Vergnaud’s theory of Abstract Case was a crucial step toward checking theory, an attempt to explain the general phenomenon of how constituents fit together to form phrases and sentences.10 Checking theory explains how the mind constructs a sentence by embedding phrase within phrase within phrase. In other words, Vergnaud’s work was a step toward an understanding of recursion in language. Hence, Berlinski and Uriagereka’s discussion of the infinity of language also illustrates the power of Vergnaud’s discovery. Going deeper than the surface has resulted in greater explanatory power, helping us to understand the infinity of language.

Vergnaud found order beneath apparent randomness, not only explaining a seemingly arbitrary aspect of English and French, but also finding that these two languages, on some deeper level, resemble languages in which there is a morphologically elaborate case system. English and French turn out to be more like Turkish, Latin, and Sanskrit than one would have thought from, say, studying grammar in high school. Given that recursion is a feature of all natural languages, Case appears to be a general feature of natural language. Apparent differences between languages are revealed to be more superficial than one might have suspected. Simplex sigillum veri: simplicity is the sign of truth.

There is another lesson in Berlinski and Uriagereka’s article, a lesson which has the potential to be more surprising than Simplex sigillum veri. It concerns the nature of evidence. Consider the numbered sentences above. Some are intuitively grammatical to native speakers and some are not, the latter marked by an asterisk. Berlinski and Uriagereka appeal to the same sort of evidence in their paper, as is commonly done in generative linguistics. Peruse Chomsky’s book The Minimalist Program, and one will find hundreds of sentences and phrases used as illustrations, some with asterisks and some without. They are a major part of the evidence base of Chomsky’s book, and the remaining evidence consists of citations of other works that also appeal to such sentences.

Speaking more carefully, one’s intuitions about sentences are the evidence. One has the intuition that “I sincerely want puppies to have good homes” is better formed than “I want sincerely puppies to have good homes.” The intuition is evidence, but it is not a sensation. The intuition may be triggered by the sensory experience of seeing the words written on paper or appearing on a computer screen, but the intuition itself is not sensory. Even the sensory trigger is not necessary, since one could have the intuitions just by thinking about the sentences. This is not to say that other forms of evidence are not welcome in linguistics. In fact, investigation of brain activity during sentence parsing is an important source of corroboration.11 But it is to say that scientific evidence need not always have a sensory component. Theorizing must be constrained by how the world is. Otherwise, it would only be fantasy, except with some wildly good luck. Sensation, however, is not, strictly and in every case, the only way for the world to act as a constraint. There are non-sensory scientific experiments. This is a further strike against the instrumentalist view of science discussed earlier: the point of science is to understand the world, not to predict patterns of sensations.

As Jerry Fodor noted “An experiment is a gadget that’s designed (not to cause you to have certain experiences but) to cause the state of your mind to correspond to the state of the world.”12 To assume that evidence always consists of sensation is to place an unwarranted restriction on what sorts of gadgets are possible. One may be skeptical of some of his more nihilistic positions, but Paul Feyerabend got it right when he said that “some knowledge resides in the individual brain without ever having entered it” and hence that some scientific evidence is not sensory.13 Given the neurological nature of language, one has access to a range of linguistic phenomena simply by virtue of having a normally functioning faculty of language.

The linguist Geoffrey Sampson begs to differ. In protesting the widespread appeal to intuitions in generative linguistics, he writes that

The data of ‘intuitions’ may be abundant, but they are hopelessly unreliable. In the Middle Ages, theories about the subject-matter that we now call physics were in many cases founded on intuitions. For instance, the Sun, Moon and planets were held to move in circles, because the circle was obviously the only shape perfect enough to be associated with a celestial body. But, once the matter was treated as open to empirical testing, it turned out that circles were incompatible with the data of observation; the orbits of the Moon and planets are in fact ellipses (and the Sun does not move).14

But this is to confuse intuitions about sentences with intuitions about theories. One’s intuition that (15) is ungrammatical, is quite a different thing from the widespread intuition that “Language is people talking and writing. It is a concrete, tangible aspect of human behavior.”15 The appeal to intuitions about grammaticality belong to generative methodology, but the appeal to intuitions about theories do not, and should not.

Or so one might think. Berlinski and Uriagereka’s discussion of what they call Gedankenblitze leaves me feeling uncertain as to whether they would agree. Referring to Vergnaud, they write that

His letter had some of the effect commonly assigned to heat lightning. It lit up the scene. There should be a name for events of this sort. Perhaps the German Gedankenblitz will do.
In 1956, Francis Crick discovered transfer RNA by what amounted to a transcendental deduction. Given the chemical discrepancy between the nucleic acids and the proteins, something must mediate between them. He was entirely correct. He had been guided to this conclusion by nothing more than his uncanny intuition.

Now, just what is a Gedankenblitz? The example of Vergnaud’s letter suggests that it is a unitary analysis, or the introduction of a unitary analysis into a field. That was, after all, the effect of his letter to Chomsky and Lasnik. But the second illustration is different: it illustrates an intuition about a theory. In fact, it is not even clear that Vergnaud experienced a Gedankenblitz in the second sense. The case of Crick brings to mind the famous story, perhaps apocryphal, of August Kekulé’s hypnogogic hallucination of the ouroboros, leading to his insight regarding the structure of benzene. Also note that the word Gedankenblitz seems to suggest a sudden intuitive flash of insight.

I am concerned that linking such sudden flashes of insight to “the Galilean undertaking,” as the authors apparently do, could create a distorted perception of how research in generative linguistics is conducted. The intuitions of a native speaker about sentences should constitute a reasonably reliable set of data. But a sudden flash of insight regarding an hypothesis? Would this too count as a firm datum? Perhaps, by definition, any insight is true. But then how does one distinguish genuine insights from counterfeit ones, the latter having the subjective feel of an insight but being, sadly, misleading?

Some philosophers of science distinguish the context of discovery from the context of justification.16 Quoting Imre Lakatos, “It does not matter at all what actually triggered off Copernicus’s imagination. We are not now concerned with the psychological causes of Copernicus’s achievement, but with its appraisal.”17 If one accepts the distinction, then intuitions about theories would presumably belong on the discovery side, with intuitions about sentences belonging to the context of justification. Perhaps Berlinski and Uriagereka reject the distinction between the two contexts. In fact, some philosophers have questioned it.18 Or perhaps the authors are using the term “Gedankenblitz” as a synonym for “unitary analysis,” in which case all is well. A clarification would be a most welcome addendum to their fine article.

John Bolender

Juan Uriagereka replies:

John Bolender’s letter was very informative to me, particularly since among my many educational lacunae, philosophy is probably the most salient. I find myself agreeing with all of John’s lines of reasoning, particularly inasmuch as they question a broadly Wittgensteinian nihilism (I am probably using the wrong term) when it comes to the study of language. Of course, if one listens to what philosophers have often said about, say, the foundations of physics, one also wonders to what extent the nihilism expressed in such terrains has affected the development of the modern synthesis. To my knowledge, physicists do what they do, they use the math they use, and they happily march along making crazy predictions that, well, work… It is for much better minds than mine to understand why they do. I can only say this: it is a necessary property of a piece of the sort David and I wrote that it should be reasonably intelligible to a sophisticated, yet not professional, audience. Had we gone into the subtleties that we could have, aside from cutting our audience in half with each new bit of formalism (a necessary condition to be precise about it all), things would be much (and I mean MUCH) weirder. For those who care to understand what this means, I for one am convinced that the only way to seriously formalize long-range correlations in language involves going into a Hilbert space built from lexical dependencies. I believe it can be shown that this is doable in very strict and standard terms, stemming from a vectorial treatment of Chomsky’s 1974 approach to categories as sets of features, which we cite in the article: those feature matrices can be seen as linear operators. I know I am laughed at when making such claims, but that does not keep me from then proceeding to show how such an admittedly bizarre move predicts some observables. Point is: that should be the metric, whether philosophers like it or not. And I read John’s letter as agreeing with this, if I have followed.

John also asks about the Gedankenblitz remarks in our paper. While the term is David’s (when he suggested it I thought of responding Gesundheit!, as my German is only a bit worse than my English), I think I agree with the spirit it conveys and how it relates to the Galilean undertaking. To me, it reminds me of that famous phrase, applied to many entities by different authors, that “you don’t know what X is until you see one.” John speaks of these “things” in the case of science leading to unification. I agree with that—without the ensuing unification, they would sound merely cute. But unification does not seem to me enough: you could achieve that with painful work over the eons. What makes a Gedankenblitz one is the almost mystical response one gets upon experiencing it subsidiarily. I know this will get me in trouble, particularly if I speak of “abductive reasoning” in science, but take it as coming from an unsophisticated peasant, who in addition knows very little about mysticism or even spirituality. I do know, however, that I feel something strange when hearing certain passages by Beethoven or Wagner, or absorbing some paintings by Goya or Pollock, to name something concrete. Pretty much that sort of feeling is triggered in me when understanding the scope of a Gedankenblitz in science, sheer joy that makes me feel vulnerable and one with a community of thinkers—not because of anything original in my mind (I certainly have never experienced producing one of these) but because of “capturing” other folks’ originality. That is not the word either, but the ineffability of it all also relates to why I am calling this virtually mystical. I agree: I do not know what I am talking about.

David Berlinski replies:

In the Philosophical Investigations (§65–71), Wittgenstein argued that what coordinated various games was more a family resemblance than anything they had in common. It was not an argument calculated overmuch to worry Plato. Or anyone else. To say that games share a family resemblance is hardly to say that they have nothing in common. They have in common their family resemblance. It is easy enough to express this precisely in formal terms. Or in any which way. “Thus in syntax,” Noam Chomsky remarks, “crucial relations are typically local, but a sequence of operations may yield a representation in which locality [although preserved in each individual step] is obscured.”19

I am not sure, on the other hand, that Chomsky’s remarks about evidence add much to Bolender’s letter. “It is of the nature of bits of evidence,” Chomsky writes, “to be fragmentary, confusing, partial, loosely related, lacking sharp boundaries, etc., that is, to exhibit only ‘family resemblances.’”

The evidence in favor of the thesis that some pigeons can fly is a flying pigeon. There it goes. Nothing is fragmentary about this bit of evidence, nor is it confusing, partial, or lacking in sharp boundaries.

The pigeon has flown.

Bolender is surely correct in his assessment of the role played by intuitions in linguistics. Native speakers of English, or any other language, even those who might, under normal circumstances, be disposed to no more complicated an utterance than a grunt, demonstrate a refinement of linguistic intuition seen nowhere else in conscious life. Almost every English sentence occupies an isolated spot on the manifold of combinatorial possibilities. For all that, Joan Bresnan is right to stress that deviance is, in linguistics as well as the law, sometimes a matter of degree, and sometimes a matter of an implied context.20 A man may break his back by straining it, or his flashlight by dropping it; but simply sitting there, he cannot break. Or so intuition might suggest until some competitive intuition reveals that since he may be broken, he might then break. Broken? By interrogation, by pain, by sleeplessness, or by life itself, so that he broke makes perfect sense.

He broke, poor devil. We all do. In the end, we all break.21

The complexities are endless. I may elbow my way through a crowd, and often do, or shoulder my way through the same crowd—Out of my way you fat fools—but in a display of anatomical nicety, I find that I cannot knee or hip my way through, and while I can stick my nose into someone else’s business, it is left to crotch-bound Beagles to stick their nose into a crowd, thus producing a characteristic form of embarrassment for which the English language lacks a name. I can step into a crowd, and step out of it, too, but I cannot kick my way through a crowd, although under certain circumstances, I can imagine saying of someone that she high-kicked or high-stepped her way through a crowd, as when talking about Cyd Charisse, but not Angela Merkel.

Linguists know what I am talking about; but so does every speaker of the English language. For the French speakers out there—Bonjour, les mecs—there is tu parles de quoi, but je me demande de quoi tu parles, de quoi scuttling back from the caboose, something French speakers know at once, and without instruction.22

I think Geoffrey Sampson wrong in his remarks about intuition, and Bolender right in thinking Sampson wrong. Attaboy. On the other hand, when Bolender cites Jerry Fodor approvingly, I have no idea what either of them is talking about: “An experiment is a gadget that’s designed (not to cause you to have certain experiences but) to cause the state of your mind to correspond to the state of the world.”23 Wishing to inquire whether hubcaps can float, I toss a few into the bathtub. Some do, some don’t. That’s pretty much what I figured they would do. Whatever the correspondence between my state of mind and the world at large—zero, most often—nothing much has changed.

In his more general concerns, Bolender is concerned to set his face against an instrumental view of science—the idea that

[a] scientific theory is a kind of machine or program for producing descriptions of sensations, and one judges a theory according to how well the descriptions agree with the sensory experiences. One could not even say that a theory is true or false, but only that it is more or less reliable as a kind of instrument for engineering. Much of Chomsky’s work, on a philosophical level, can be understood as a rebellion against this instrumentalist view of scientific theories.

I am in favor of rebellions—all of them, in fact—but I am not sure that this one has been properly conceived.

Descriptions? Sensations may be named, but how described? What does it feel like, you imbecile? Drop a hammer on your toe. That’s what it feels like.

Predictions, perhaps? As when a computer program suggests that at the conclusion of the Stern-Gerlach experiment, I am apt to feel a tingle. Maybe. But what about you, sitting over there in obvious thick-lidded bewilderment? A tingle, too?

This is obviously absurd, and if this is what Bolender is saying, count me in.

On the other hand, it would seem to be an imperative of any scientific theory that it agree with sensory experience to the extent that sensory experience designates the ultimate result of experiment or observation. Theories require confirmation; and confirmation in the last analysis must involve a human being who sees in his instruments that gravitational waves, in an understandable hurry to get away from two merging black holes, are streaming in from the edge of space and time. No wonder those infernal things are called black.

Nor is it clear to me that the instrumental view and its denial are in a position of radical conflict. In control systems theory, it is useful to describe a system by means of a transfer function taking inputs to outputs. It is equally useful to describe the system in terms of a series of internal states. It is always possible in the linear case to go from one scheme to the other (although not uniquely), recovering either the transfer function or the states. The distinction between input-output and state-space systems remains; but it does not count for much.24

Not for me, in any event.

John Bolender is a professor in the Philosophy Department at Unisinos in São Leopoldo, Brazil.

Juan Uriagereka is a linguist at the University of Maryland.

David Berlinski is an American writer.

  1. Ludwig Wittgenstein, Philosophical Investigations, trans. G. E. M. Anscombe (London: Blackwell, 1953), §§65-7. 
  2. Noam Chomsky, “Some Empirical Assumptions in Modern Philosophy of Language,” in Philosophy, Science, and Method: Essays in Honor of Ernest Nagel, eds. S. Morgenbesser et al., (New York: St. Martin’s Press, 1969), 280. 
  3. Aron Gurwitsch, “The Last Work of Edmund Husserl,” Philosophy and Phenomenological Research 16, no. 3 (1956): 389. 
  4. Aron Gurwitsch, “The Last Work of Edmund Husserl,” Philosophy and Phenomenological Research 16, no. 3 (1956): 386. This is not to imply that Husserl fully endorsed the Galilean style. In fact, “At the root of the present crisis of philosophy, Husserl discerns the breakdown of objectivism,” as Gurwitsch observed, (p. 399). For a skeptical treatment of the Galilean style, see Paul Feyerabend, Conquest of Abundance: A Tale of Abstraction Versus the Richness of Being (Chicago and London: The University of Chicago Press). 
  5. Noam Chomsky, Rules and Representations (New York: Columbia University Press, 1980), 9-10. 
  6. Ludwig Wittgenstein, Philosophical Remarks, ed. Rush Rhees, trans. R. Hargreaves and R. White (Chicago: The University of Chicago, 1975), §228. 
  7. Ludwig Wittgenstein, Philosophical Remarks, ed. Rush Rhees, trans. R. Hargreaves and R. White (Chicago: The University of Chicago, 1975), §1. 
  8. Jean-Roger Vergnaud, Dépendences et Niveaux de Représentation en Syntaxe, Thèse de doctorat d’état, (Université de Paris VII, 1982); Jean-Roger Vergnaud, “Letter to Noam Chomsky and Howard Lasnik on ‘Filters and Control,’ April 17, 1977” in Foundational Issues in Linguistic Theory: Essays in Honor of Jean-Roger Vergnaud, eds. Robert Friedin et al. (Cambridge, MA: The MIT Press, 2008), 3–15. 
  9. Noam Chomsky and Howard Lasnik, “Filters and Control,” Linguistic Inquiry 8, no. 3 (1977): 425–504. 
  10. Noam Chomsky, The Minimalist Program (Cambridge, MA: The MIT Press). 
  11. For two recent examples, see Christophe Pallier et al., “Cortical Representation of the Constituent Structure of Sentences,” Proceedings of the National Academy of Sciences of the United States of America 108, no. 6 (2011): 2,522–27; Nai Ding et al., “Cortical Tracking of Hierarchical Linguistic Structures in Connected Speech,” Nature Neuroscience 19, no. 1 (2016): 158–64. 
  12. Jerry Fodor, “The Dogma That Didn’t Bark (A Fragment of a Naturalized Epistemology)” Mind 100, no. 2 (1991): 211. 
  13. Paul Feyerabend, Realism, Rationalism and Scientific Method: Philosophical Papers, Volume I (Cambridge: Cambridge University Press, 1981), 134. 
  14. Geoffrey Sampson, Empirical Linguistics (London and New York: Continuum, 2001), 2–3. 
  15. Geoffrey Sampson, Empirical Linguistics (London and New York: Continuum, 2001), 1. 
  16. Karl Popper, Logik der Forschung (Tübingen: J.C.B. Mohr, 1969). The distinction is sometimes credited to Hans Reichenbach. 
  17. Imre Lakatos, The Methodology of Scientific Research Programmes: Philosophical Papers, Volume I (Cambridge: Cambridge University Press, 1978), 182n. 
  18. Jutta Schickore and Friedrich Steinle, eds., Revisiting Discovery and Justification: Historical and Philosophical Perspectives (Dordrecht: Springer, 2006). 
  19. Noam Chomsky, The Minimalist Program (Cambridge, MA: MIT Press, 1995), 223, 224. 
  20. Joan Bresnan, “Linguistics: The Garden and the Bush,” forthcoming in Computational Linguistics, The MIT Press. 
  21. This is hardly a point unknown to traditional grammarians, who would have assigned verbs such as break a middle voice. 
  22. In our essay, we remarked of Google-translate that it got Ernest wants Bill to go all wrong. It now gets it all right. 
  23. Jerry Fodor, “The Dogma That Didn’t Bark (A Fragment of a Naturalized Epistemology),” Mind 100, no. 2 (1991): 211. 
  24. I seem to remember discussing all this in On Systems Analysis (Cambridge, MA: MIT Press, 1975).