Recursion

8 Key excerpts on "Recursion"

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  Linguistics and Psychoanalysis

  A New Perspective on Language Processing and Evolution

  • Thomas Paul Bonfiglio(Author)
  • 2023(Publication Date)
  • Routledge

    (Publisher)

  2 Recursion and metacognition

  DOI: 10.4324/9781003180197-3

  One of the central concepts in the attempt to define human language pivots around the concept of Recursion. In linguistics, Recursion refers to the phenomenon of imbedding syntactic parts within other syntactic parts, as in the case of relative clauses, e.g.: “The cat that ate the bird that ate the worm that ate…”, which, in theory, could continue indefinitely. In the minimalist program of universal grammar, Recursion is seen as the nuclear faculty that generates the universe of linguistic possibilities, an atomic algorithm of infinite potential.

  In 2002, Hauser, Chomsky, and Fitch published “The Faculty of Language: What Is It, Who Has It, and How Did It Evolve”?, in which they reduce human language to a “narrow language faculty” that “only includes Recursion and is the only uniquely human component of the faculty of language” (Hauser et al., 2002 , p. 1569). Pinker and Jackendoff offer a succinct definition of Recursion along with a comment on the article by Hauser et al.: “Recursion refers to a procedure that calls itself, or to a constituent that contains a constituent of the same kind. In the article itself, the starkness of this hypothesis is mitigated only slightly” (Pinker & Jackendoff, 2005 , p. 203). Hauser et al. also simply assume this narrow language faculty a priori and say that it is independent of other cognitive systems. One begins to sense here echoes of the ghost in the machine.

  In The Recursive Mind: The Origins of Human Language, Thought, and Civilization, Michael Corballis brilliantly contextualizes the issue of Recursion. Corballis begins in a recursive manner by commenting on the satirist Ambrose Bierce’s ironic comment on Descartes: “Cogito cogito ergo cogito sum—‘I think I think, therefore I think I am.’” He then concocts “a not-too-serious dictionary definition: ‘Recursion (rĭ-kûr’-zhən) noun. See Recursion’” (Corballis, 2011

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  Cultural Psychology of Recursive Processes

  • Zachary Beckstead(Author)
  • 2009(Publication Date)
  • Information Age Publishing

    (Publisher)

  Wilhem von Humboldt echoed this notion by stating that only humans have the capacity to “make infinite em- ployment of finite means” in language (1836/1999, p. 91). Breaking with the behaviorist model of language, Noam Chomsky famously argued that human thought and language originated from operations applied recur- sively. Simple units of words can be merged and embedded with other units to form larger entities, and this process can be extended in increasing com- plexity and hierarchical organization. For instance, noun phrases can be created from other noun phrases as they are recursively embedded: “One can create new noun phrases by placing the word beside between any pair: the dog beside the tree, the cat beside the lake” (Chomsky, 1957, p. 6). Furthermore, linguists in the tradition of Saussure (1916/2011) point out that words and utterances derive their meaning from their relationship to other words and groups of words. Recursivity, in this sense, is related to the interrelationship of symbols and the meta-reflexive ability of the human mind to discover and grasp meaning and higher-order relationships and interconnections between parts (see Perinat, 2007). Human beings, then, can not only “decode” language, but reflect upon it. Psychology and Recursion Recursion, recursivity, and similar ideas typically enter into the field of psychology through the field of linguistics. As previously mentioned, it is re- cursion that is seen as the distinguishing faculty of human beings. Recently, the question of whether all human languages are fundamentally recursive has been a hot topic in psychology and anthropology (see Everett, 2005 for a discussion on Piraha language). This controversy emerged when a young missionary turned atheist visited a small Brazilian tribe and discov- ered that they live in the present moment and do not reference the past or future. Hence, they have no creation myths or sense of history. They

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  Segmental Structure and Representations

  • Jeroen van de Weijer(Author)
  • 2023(Publication Date)
  • De Gruyter Mouton

    (Publisher)

  that you liked so much]]]]). This does not exist in phonological structure: a syllable, for instance, cannot be embedded in another syllable.” (italics in original)

  Before anything may be said about Recursion, we must define what we are talking about.1 Coolidge, Overmann and Wynn (2010: 547) recall that “there is no single, universally accepted definition of Recursion. Its definition varies across disciplines (e.g., mathematics, logic, computer science, and linguistics), and it varies within these disciplines, particularly within linguistics”. Tomalin (2011: 298) adds that “the notion of ‘Recursion’ was fundamentally ambiguous when it began to be used by linguists in the 1950s, and [. . .] these ambiguities have persisted to the present day. This unfortunate (and needless) perpetuation of imprecision has had a deleterious impact upon recent discussions of the role of Recursion in linguistic theory.” In concluding his historical survey, Tomalin (2011: 307) identifies nine distinct interpretations of “Recursion” that were running in the adult sciences by the time Syntactic Structures appeared (1957). Lobina (2014a , 2014b , 2014c ) distinguishes “four distinct senses of the term Recursion that can appropriately be applied, or so it will be argued here, to four well-defined theoretical constructs of the cognitive sciences” (Lobina 2014c : 151). In fact there are two much debated questions: 1) what is the actual definition of Recursion in the formal (adult) sciences (namely mathematics and computer science), and 2) how do linguistic (in fact: syntactic) phenomena and theorizing relate to that? The former question is addressed in Watumull et al. (2014) and Lobina (2014a)

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  Psychology of Language

  A Critical Introduction

  • Michael A Forrester(Author)
  • 1996(Publication Date)
  • SAGE Publications Ltd

    (Publisher)

  In order to guard against an understandable resistance to engaging with what might appear to be unnecessary detail, this section begins by outlining, as clearly as possible, the essential ideas within Chomsky's theory. Let us start with the issue of grammatical competence and our apparently intuitive ability to recognise 20 Psychology of Language when a sentence is grammatical, and when it is not. Remember, syntactic theory is relevant in a cognitive sense because the main task of any syntactic theory within psycholinguistics is 'to model the system that enables us to know which sentences are part of our language . . . and which are noise' (Stillings et aI., 1987, p. 242). In other words, speakers know the patterns of their language, and the argument is that these patterns are represented as a set of rules that define what is a permissible sentence, and what is not. This account can provide us with one explanation for the inherent creativity of language, an issue whic h seriously undermined a strictly behaviourist account of language . Chomsky's (1957) theory of syntax rests essentially on the assumption that the mind is some kind of recursive computational entity. To recur commonly means describing a situation where something comes back or comes around again. The process of Recursion is where an algorithm or procedure which involves reference to itself (re)occurs in a repetitive fashion. Many programming operations in computers involve procedures (sections of code) which 'call themselves' when activated. This is a paradoxical, yet very important, idea for understanding theories of syntax. Recursion is the main reason why people have argued that the human mind has the capacity to recognise and produce an inf in ite number of sentences, even though our brains are clearly finite entities.

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  What Makes You Clever: The Puzzle Of Intelligence

  The Puzzle of Intelligence

  • Derek Partridge(Author)
  • 2014(Publication Date)
  • World Scientific

    (Publisher)

  3 Statement on p. 1573 of the paper referenced in Endnote 15. 4 The 2002 paper referenced in Endnote 15 can be taken as the modern benchmark for the accepted status of Recursion as the core of the human language facility. It has generated many commentary papers, which take issue with various elements of its claims, but they all accept a recursive basis of human language. A link between recur-sion and human language has been floating through the linguistic sciences ever since Chomsky proposed recursive components for grammars in the 1950s. The 2002 paper (which has Chomsky as a co-author) restates the relationship more forcefully and has become established as the basis for comment and criticism. D What Makes You Clever E 320 5 Michael C. Corballis’ article “Recursion, Language, and Starlings” in Cognitive Science , vol. 31 in 2007, pages 697–704. 6 “Working memory: a cognitive limit to non-human primate recursive thinking prior to hominid evolution” by Dwight W. Read in Evolutionary Psychology, vol. 6, no.4, in 2008, pages 676–714. 7 There is a good deal of confusion with respect to whether a language production, e.g., a sentence in English, can be said to be “recursive” (in general, this is incorrect). A large measure of this confusion is caused by loose usage of the term “Recursion”. We will enter into these intricacies only as far as is absolutely unavoidable. 8 An example is Recursion hypothesis considered as a research program for cognitive sci-ence , Pauli Brattico in Minds & Machines in 2010, vol. 20, pages 213–241. Another example is The recursive mind: the origins of human language, thought, and civiliza-tion by Michael C. Corballis (Princeton University Press, 2011). He “argues that what distinguishes us in the animal kingdom is our capacity for Recursion: the ability to embed our thoughts within other thoughts”.

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  Recursion and Human Language

  • Harry van der Hulst(Author)
  • 2010(Publication Date)
  • De Gruyter Mouton

    (Publisher)

  One that is consistent with much current work in linguistics is that of Pinker and Jackendo¤ (2005: 4), whereby a recursive structure is characterized as ‘‘a constituent that contains a constituent of the same kind’’. Recursive structures are indeed pervasive cross-linguistically. A closer look at the variety of such structures that occur, however, indicates that Recursion may not be the fixed, fundamental, hard-wired property envisioned. Much as languages vary in their distribution of structural complexity across the domains of morphology and syntax, they also vary in their dis-tribution of Recursion. The most common recursive structures involve noun phrases embedded inside of other noun phrases ( the neighbor’s cat’s habits ) and clauses embedded inside of other clauses, the type cited by Hauser, Chomsky, and Fitch ( Mary believes that S ). As will be seen, such constructions are not uniform cross-linguistically, nor are they static within individual languages. The variability in space and time calls into question the status of Recursion as the basic design feature of human lan-guage. It suggests, rather, that recursive structures are epiphenomenal, the product of combinations of a variety of cognitive processes. 2. Central Alaskan Yup’ik Languages of the Eskimo-Aleut family contain numerous syntactic con-structions containing clause Recursion. Examples cited here are drawn from Central Alaskan Yup’ik, a language of southwestern Alaska. 2.1. Yup’ik complement clauses The single structure cited by Hauser, Chomsky, and Fitch as an example of Recursion is complementation: Mary believes that S . Yup’ik counter-parts to this English construction are formed with dependent clauses in the Subordinative mood. The Subordinative mood su‰x -lu-on the sec-ond verb in (1) marks the clause ‘that you are well’ as dependent. (1) Yup’ik complement counterpart: Elizabeth Ali, speaker p.c.

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  Proceedings of the Fourteenth Annual Conference of the Cognitive Science Society

  • Cognitive Science Society (US) Conference(Author)
  • 2014(Publication Date)
  • Psychology Press

    (Publisher)

  1

  It is often noted that the prima facie existence of Recursion in NL behaviour poses serious problems for connectionist approaches to NL processing (e.g., Fodor & Pylyshyn, 1988) since Recursion— qua computational mechanism—is defined as being essentially symbolic. However, the existence of Recursion in NL presupposes that the grammars of linguistic theory correspond to real mental structures, rather than mere structural descriptions of NL per se . Yet, there are no a priori reasons for assuming that the structure of the observable public language necessarily must dictate the form of our internal representations (van Gelder, 1990b). Still, many linguists and psychologists (e.g., Chomsky, 1986; Frazier & Fodor, 1978; Kimball, 1973; Pickering & Chater, 1992; Pulman, 1986) take grammars as corresponding to in-the-head representations that are manipulated by computational processes. But, since human NL behaviour is limited under normal circumstances, a distinction is typically made between the bounded observable performance and an infinite competence inherent in the internal grammar.

  In what follows, I start off by arguing from a methodological perspective that the alleged distinc-tion between linguistic competence and actual NL performance must be rejected if linguistic theories are to encompass representational claims regarding the human NL mechanism. Then, I drive a wedge between the (quasi-) recursive nature of NL, as described in most current linguistic theories, and the actual NL processing mechanism. In particular, I suggest that Recursion is a conceptual artifact of the competence/performance distinction (C/PD), instead of a necessary characteristic of the underlying computational mechanism.2 In this light, the problemfacing connectionist models of NL processing is not whether they can implement some kind of recursive mechanism, but whether they will be able to account for the (limited) recursive structure

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  Syntax with oscillators and energy levels

  • Sam Tilsen(Author)
  • 2019(Publication Date)
  • Language Science Press

    (Publisher)

  Tis convention derives from conceptualizing linguistic units as objects which occupy space – without the metaphor, there is simply no basis for the conventions. Defnitional Recursion is also problematic because the concept o f a “de fni-tion” is quite vague. What constitutes a defnition? Te phrase structure rewrite rules above are “defnitions” o f a sort, but if one were to elaborate on how or why rewrite rules are defnitions, and what that could even mean, one would inevitably resort to many of the concepts which underlie procedural Recursion. 5.2.2 Procedural Recursion and the merge s cema Te deeper notion of Recursion is procedural: Recursion is a temporal pa tern in which the output of a function (or “procedure”, or “process”, or “transformation”, etc.) can be the input to that same function. Tis favor o f Recursion also applies to the directly and indirectly recursive rewrite rules above, where the arrow is the function and the symbols at its head/tail are inputs/outputs. To reason about functions we commonly use object-transformation schemas of the sort in Fig-ure 5.3. In the object-transformation schema, a function is a container, an object struc-ture goes into the container, the object is transformed, and a new object structure comes out. For rewrite rules, the transformation is o fen such that some object in the input structure is split into new objects which are connected to it. Te operations “external merge” and “internal merge” are also object-transformation schemas. External merge takes two input objects, creates a new object (which is always a phrasal category), and connects them to the new object, as in Fig-ure 5.4. Internal merge, as shown in Figure 5.5, transforms a structure of objects 149 5 Infnity and Recursion Figure 5.3: Rewrite rules and the object-transformation schema.

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