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Philosophy E156: Philosophy of Mind Week 2: The Chomskyan Revolution

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My example of a Poverty of the Stimulus Argument, Revisited

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Grammatical Rule (A) (1) I will have a cold if I don’t dress warmly (2) Will I have a cold if I don’t dress warmly Grammatical Rule (A): If a sentence like (1) is grammatical, then the corresponding sentence like (2) is grammatical.

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Grammatical Rule (B) (3) I will have a cold if I don’t dress warmly (4) I’ll have a cold if I don’t dress warmly Grammatical Rule (B): If a sentence like (3) is grammatical, then the corresponding sentence like (4) is grammatical.

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Is The Sentence Below Grammatical? (5) Will I’ve a cold if I don’t dress warmly First, do you think that (5) is grammatical? Second, do you think that others in the room will say that (5) is grammatical?

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Two-Part Hypothesis First, that everybody in the room thought that the sentence was ungrammatical. Second, that everybody in the room thought that everybody else in the room would judge the sentence to be ungrammatical.

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POS Argument: No Evidence, Positive or Negative Sentences just like (5) are never produced by the child Thus, there could not be “negative evidence” for the child about the ungrammaticality of sentences like (5) Nor do adult speakers ever produce sentences just like (5) on their own or comment on them But there is some evidence from sentences somewhat like (5) – and it is that sentences like (5) are grammatical, because of rules (A) & (B)

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From David Lightfoot’s “Plato’s Problem, UG and the Language Organ”

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Grammatical Rule (C) (6) Kim is happy (7) Kim’s happy Grammatical Rule (C): If a sentence like (6) is grammatical, then the corresponding sentence like (7) is grammatical.

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Is The Sentence Below Grammatical? (8) Kim’s happier than Tim’s First, do you think that (8) is grammatical? Second, do you think that others in the room will say that (8) is grammatical?

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POS Argument: No Evidence, Positive or Negative Lightfoot cites empirical evidence that sentences like (8) are never produced by the child Thus, there could not be “negative evidence” for the child about the ungrammaticality of sentences like (8) Nor do adult speakers ever produce sentences like (8) on their own or comment on them The only evidence the child has is that sentences like (8) are grammatical And intuitions are robust, perhaps unlike with (5)

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Other Cases Where Contraction is Impermissible (9) I wonder where the party’s tonight (10) What I want’s to go (11) What’s bothering Jack’s your behavior See Ellen Kaisse, “The Syntax of Auxiliary Reduction in English,” Language 59 (March 1983), pp. 93-122. (12) Who do you wanna promise to leave? Answer: I wanna promise to leave John. Answer: I wanna promise John to leave. #Answer: I want John to promise to leave.

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The Chomskyan Revolution

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Science Creation and Scientific Revolutions

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We often hear of “the Chomskyan revolution” – but what was so revolutionary in Chomskyan linguistics?

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Science Creation and Scientific Revolutions We often hear of “the Chomskyan revolution” – but what was so revolutionary in Chomskyan linguistics? If it was revolutionary, we would expect to find certain elements in common with familiar scientific revolutions, like the Newtonian revolution:

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Science Creation and Scientific Revolutions We often hear of “the Chomskyan revolution” – but what was so revolutionary in Chomskyan linguistics? If it was revolutionary, we would expect to find certain elements in common with familiar scientific revolutions, like the Newtonian revolution: – (a) paradigm of method and discovery with many “interlocking parts”;

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Science Creation and Scientific Revolutions We often hear of “the Chomskyan revolution” – but what was so revolutionary in Chomskyan linguistics? If it was revolutionary, we would expect to find certain elements in common with familiar scientific revolutions, like the Newtonian revolution: – (a) paradigm of method and discovery with many “interlocking parts”; – (b) perhaps offering a synoptic perspective;

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Science Creation and Scientific Revolutions We often hear of “the Chomskyan revolution” – but what was so revolutionary in Chomskyan linguistics? If it was revolutionary, we would expect to find certain elements in common with familiar scientific revolutions, like the Newtonian revolution: – (a) paradigm of method and discovery with many “interlocking parts”; – (b) perhaps offering a synoptic perspective; – (c) distinct from preceding science

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Science Creation and Scientific Revolutions We often hear of “the Chomskyan revolution” – but what was so revolutionary in Chomskyan linguistics? If it was revolutionary, we would expect to find certain elements in common with familiar scientific revolutions, like the Newtonian revolution: – (a) paradigm of method and discovery with many “interlocking parts”; – (b) perhaps offering a synoptic perspective; – (c) distinct from preceding science – (d) solves outstanding problems of earlier paradigm or pre- revolutionary science, which perhaps led to crisis;

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Science Creation and Scientific Revolutions We often hear of “the Chomskyan revolution” – but what was so revolutionary in Chomskyan linguistics? If it was revolutionary, we would expect to find certain elements in common with familiar scientific revolutions, like the Newtonian revolution: – (a) paradigm of method and discovery with many “interlocking parts”; – (b) perhaps offering a synoptic perspective; – (c) distinct from preceding science – (d) solves outstanding problems of earlier paradigm or pre- revolutionary science, which perhaps led to crisis; – (e) non-Baconian, but unified and providing what Chomsky calls “intellectual justification” (Selected Readings, p. 7)

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Science Creation and Scientific Revolutions (cont.)

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Other elements (from Thomas Kuhn’s The Structure of Scientific Revolutions):

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Science Creation and Scientific Revolutions (cont.) Other elements (from Thomas Kuhn’s The Structure of Scientific Revolutions): – (a) posing of all-new problems within linguistics and successes in solving them or at least in creating of testable hypotheses;

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Science Creation and Scientific Revolutions (cont.) Other elements (from Thomas Kuhn’s The Structure of Scientific Revolutions): – (a) posing of all-new problems within linguistics and successes in solving them or at least in creating of testable hypotheses; – (b) creation of a new “normal science,” with textbooks that codify results

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Science Creation and Scientific Revolutions (cont.) Other elements (from Thomas Kuhn’s The Structure of Scientific Revolutions): – (a) posing of all-new problems within linguistics and successes in solving them or at least in creating of testable hypotheses; – (b) creation of a new “normal science,” with textbooks that codify results – (c) implications for other fields; unity of science

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Science Creation and Scientific Revolutions (cont.) Other elements (from Thomas Kuhn’s The Structure of Scientific Revolutions): – (a) posing of all-new problems within linguistics and successes in solving them or at least in creating of testable hypotheses; – (b) creation of a new “normal science,” with textbooks that codify results – (c) implications for other fields; unity of science – (d) a readiness within and outside linguistics for these new results, and the recruitment that results

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Interlocking Parts of the New Paradigm

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(1) Formal limitations of standard grammars

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora (4) Conception of science – explanatory adequacy, etc.; behaviorism; description vs. explanation

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora (4) Conception of science – explanatory adequacy, etc.; behaviorism; description vs. explanation (5) Mentalism

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora (4) Conception of science – explanatory adequacy, etc.; behaviorism; description vs. explanation (5) Mentalism (6) Autonomy of syntax, eschewing explanation use (the Bloomfield sort)

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora (4) Conception of science – explanatory adequacy, etc.; behaviorism; description vs. explanation (5) Mentalism (6) Autonomy of syntax, eschewing explanation use (the Bloomfield sort) (7) Creative character of language

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora (4) Conception of science – explanatory adequacy, etc.; behaviorism; description vs. explanation (5) Mentalism (6) Autonomy of syntax, eschewing explanation use (the Bloomfield sort) (7) Creative character of language (8) Deep structure and surface structure

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora (4) Conception of science – explanatory adequacy, etc.; behaviorism; description vs. explanation (5) Mentalism (6) Autonomy of syntax, eschewing explanation use (the Bloomfield sort) (7) Creative character of language (8) Deep structure and surface structure (9) “Uniting the best parts of universal grammar and structuralism”

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora (4) Conception of science – explanatory adequacy, etc.; behaviorism; description vs. explanation (5) Mentalism (6) Autonomy of syntax, eschewing explanation use (the Bloomfield sort) (7) Creative character of language (8) Deep structure and surface structure (9) “Uniting the best parts of universal grammar and structuralism” (10) Making linguistics part of psychology & biology

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora (4) Conception of science – explanatory adequacy, etc.; behaviorism; description vs. explanation (5) Mentalism (6) Autonomy of syntax, eschewing explanation use (the Bloomfield sort) (7) Creative character of language (8) Deep structure and surface structure (9) “Uniting the best parts of universal grammar and structuralism” (10) Making linguistics part of psychology & biology (11) Cognitive science

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Interlocking Parts of the New Paradigm (1) Formal limitations of standard grammars (2) Transformational generative grammar – could say things not sayable before, existence of discoveries, and rigor (3) Methodological change – intuitions vs. corpora (4) Conception of science – explanatory adequacy, etc.; behaviorism; description vs. explanation (5) Mentalism (6) Autonomy of syntax, eschewing explanation use (the Bloomfield sort) (7) Creative character of language (8) Deep structure and surface structure (9) “Uniting the best parts of universal grammar and structuralism” (10) Making linguistics part of psychology & biology (11) Cognitive science (12) Nativism

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Books by Chomsky I Will Refer To

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Logical Structure of Linguistic Theory [LSLT] (1955)

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Books by Chomsky I Will Refer To Logical Structure of Linguistic Theory [LSLT] (1955) Syntactic Structures (1957)

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Books by Chomsky I Will Refer To Logical Structure of Linguistic Theory [LSLT] (1955) Syntactic Structures (1957) Aspects of the Theory of Syntax (1965)

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Books by Chomsky I Will Refer To Logical Structure of Linguistic Theory [LSLT] (1955) Syntactic Structures (1957) Aspects of the Theory of Syntax (1965) Cartesian Linguistics (1966)

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Chomsky’s Work in Logic and Mathematics

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Similarly, Chomsky did groundbreaking work in the part of computation theory known as automata theory

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Chomsky’s Work in Logic and Mathematics Similarly, Chomsky did groundbreaking work in the part of computation theory known as automata theory “Chomsky hierarchy” of formal languages

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Chomsky’s Work in Logic and Mathematics Similarly, Chomsky did groundbreaking work in the part of computation theory known as automata theory “Chomsky hierarchy” of formal languages Hierarchy of formal languages that computational models or automata can generate or recognize

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Chomsky’s Mixed Feelings about Mathematical Work

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Chomsky in the 1973 introduction to LSLT on 1950’s

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Chomsky’s Mixed Feelings about Mathematical Work Chomsky in the 1973 introduction to LSLT on 1950’s On computers: “A technology of machine translation, automatic abstracting, and information retrieval was put forward as a practical prospect. It was confidently expected … that automatic speech recognition would soon be feasible.”

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Chomsky’s Mixed Feelings about Mathematical Work Chomsky in the 1973 introduction to LSLT on 1950’s On computers: “A technology of machine translation, automatic abstracting, and information retrieval was put forward as a practical prospect. It was confidently expected … that automatic speech recognition would soon be feasible.” “As for machine translation and related enterprises, they seemed to me pointless as well as … hopeless. [I]nterested in linguistics, logic, and philosophy, I could not fail to be aware of the ferment and excitement. But I felt myself no part of it….”

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Chomsky’s Mixed Feelings about Mathematical Work Chomsky in the 1973 introduction to LSLT on 1950’s On computers: “A technology of machine translation, automatic abstracting, and information retrieval was put forward as a practical prospect. It was confidently expected … that automatic speech recognition would soon be feasible.” “As for machine translation and related enterprises, they seemed to me pointless as well as … hopeless. [I]nterested in linguistics, logic, and philosophy, I could not fail to be aware of the ferment and excitement. But I felt myself no part of it….” “I have been surprised since to read repeated and confident accounts of how work in generative grammar developed out of an interest in computers, machine translation, and related matters. At least as far as my own work in concerned, this is quite false.”

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Point of Chomsky’s Work in Automata Theory Negative

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“Shortly after LSLT was completed I did become interested in some of these questions and made several attempts to clarify the issues.”

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Point of Chomsky’s Work in Automata Theory Negative “Shortly after LSLT was completed I did become interested in some of these questions and made several attempts to clarify the issues.” However, the point was purely negative – to show that the simple machine models of the mind that were much discussed were inadequate as models of natural language processors

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Point of Chomsky’s Work in Automata Theory Negative “Shortly after LSLT was completed I did become interested in some of these questions and made several attempts to clarify the issues.” However, the point was purely negative – to show that the simple machine models of the mind that were much discussed were inadequate as models of natural language processors The goal is to show by increasingly elaborate models what sort of grammar is required for natural language

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Finite State Grammars

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Chomsky takes a grammar to be a set of rules, or a machine that operates by the rules.

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Finite State Grammars Chomsky takes a grammar to be a set of rules, or a machine that operates by the rules. A finite state grammar is a collection of states paired with symbols; it moves between states by producing symbols.

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Finite State Grammars Chomsky takes a grammar to be a set of rules, or a machine that operates by the rules. A finite state grammar is a collection of states paired with symbols; it moves between states by producing symbols. Consider the finite state grammar modeled by the state diagram on the right.

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Finite State Grammars Chomsky takes a grammar to be a set of rules, or a machine that operates by the rules. A finite state grammar is a collection of states paired with symbols; it moves between states by producing symbols. Consider the finite state grammar modeled by the state diagram on the right.

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Finite State Grammars Chomsky takes a grammar to be a set of rules, or a machine that operates by the rules. A finite state grammar is a collection of states paired with symbols; it moves between states by producing symbols. Consider the finite state grammar modeled by the state diagram on the right. Sentences are paths

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Finite State Languages

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If it is a so-called “Markov” (i.e., random) process, operating probabilistically, the finite state grammar will produce two English sentences, each corresponding to a path: (1) The man comes (2) The men come

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Finite State Languages If it is a so-called “Markov” (i.e., random) process, operating probabilistically, the finite state grammar will produce two English sentences, each corresponding to a path: (1) The man comes (2) The men come By definition, the language consisting of just these two sentences, (1) and (2), is a finite state language because it can be generated by a finite state grammar.

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Another Finite State Language

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The state diagram on the right presents a finite state grammar that produces an infinite sequence of sentences of the form:

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Another Finite State Language The state diagram on the right presents a finite state grammar that produces an infinite sequence of sentences of the form: The man comes

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Another Finite State Language The state diagram on the right presents a finite state grammar that produces an infinite sequence of sentences of the form: The man comes The old man comes

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Another Finite State Language The state diagram on the right presents a finite state grammar that produces an infinite sequence of sentences of the form: The man comes The old man comes The old old man comes, etc

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Another Finite State Language The state diagram on the right presents a finite state grammar that produces an infinite sequence of sentences of the form: The man comes The old man comes The old old man comes, etc The men come

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Another Finite State Language The state diagram on the right presents a finite state grammar that produces an infinite sequence of sentences of the form: The man comes The old man comes The old old man comes, etc The men come The old men come

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Another Finite State Language The state diagram on the right presents a finite state grammar that produces an infinite sequence of sentences of the form: The man comes The old man comes The old old man comes, etc The men come The old men come The old old men come, etc

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Another Finite State Language The state diagram on the right presents a finite state grammar that produces an infinite sequence of sentences of the form: The man comes The old man comes The old old man comes, etc The men come The old men come The old old men come, etc It produces a finite state language that is infinite.

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A Problem

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Problem: Is English a finite state language?

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A Problem Problem: Is English a finite state language? If it is, we can have a good grasp of some of it and its grammar’s mathematical properties.

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A Problem Problem: Is English a finite state language? If it is, we can have a good grasp of some of it and its grammar’s mathematical properties. Chomsky took the linguist Charles Hockett to consider English to be a finite state language.

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A Problem Problem: Is English a finite state language? If it is, we can have a good grasp of some of it and its grammar’s mathematical properties. Chomsky took the linguist Charles Hockett to consider English to be a finite state language. Not: Is there is a finite state grammar that generates only English sentences? Answer: Yes

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A Problem Problem: Is English a finite state language? If it is, we can have a good grasp of some of it and its grammar’s mathematical properties. Chomsky took the linguist Charles Hockett to consider English to be a finite state language. Not: Is there is a finite state grammar that generates only English sentences? Answer: Yes But: Is there is a finite state grammar that generates all and only English sentences?

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The Corresponding Problem for the Propositional Calculus

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Consider what might seem to be a simpler problem: Is the propositional calculus a finite state language?

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The Corresponding Problem for the Propositional Calculus Consider what might seem to be a simpler problem: Is the propositional calculus a finite state language? That is, Is there is a finite state grammar that generates all and only the well- formed formulae of the propositional calculus, or of some fragment of the propositional calculus?

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The Problem Posed for a Fragment

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Consider the well-formed formulae which can be constructed out of the following symbols: – (, ) – ∨, ∧, ¬ – p, q, r, … (infinite set of propositional variables)

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The Problem Posed for a Fragment Consider the well-formed formulae which can be constructed out of the following symbols: – (, ) – ∨, ∧, ¬ – p, q, r, … (infinite set of propositional variables) For example, (p ∨ q) – “p or q” (p ∧ ( p ∧ q)) – “p and ( p and q )” ¬ ( ( p ∧ q ) ∨ ( p ∧ r ) ) – “not true that, p and q, or p and r”

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The Problem Posed for a Fragment Consider the well-formed formulae which can be constructed out of the following symbols: – (, ) – ∨, ∧, ¬ – p, q, r, … (infinite set of propositional variables) For example, (p ∨ q) – “p or q” (p ∧ ( p ∧ q)) – “p and ( p and q )” ¬ ( ( p ∧ q ) ∨ ( p ∧ r ) ) – “not true that, p and q, or p and r” Is the infinite set of such formulae a finite state language?

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The Problem Posed for a Fragment Consider the well-formed formulae which can be constructed out of the following symbols: – (, ) – ∨, ∧, ¬ – p, q, r, … (infinite set of propositional variables) For example, (p ∨ q) – “p or q” (p ∧ ( p ∧ q)) – “p and ( p and q )” ¬ ( ( p ∧ q ) ∨ ( p ∧ r ) ) – “not true that, p and q, or p and r” Is the infinite set of such formulae a finite state language? On p. 22 of Syntactic Structures (in a part not reprinted in Selected Readings), Chomsky says no

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Inadequacy of Finite State Grammars

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Finite state grammars do not allow dependencies of certain later symbols on certain earlier symbols.

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Inadequacy of Finite State Grammars Finite state grammars do not allow dependencies of certain later symbols on certain earlier symbols. (p ∨ q)

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Inadequacy of Finite State Grammars Finite state grammars do not allow dependencies of certain later symbols on certain earlier symbols. (p ∨ q) (p ∨ ( p ∨ q))

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Inadequacy of Finite State Grammars Finite state grammars do not allow dependencies of certain later symbols on certain earlier symbols. (p ∨ q) (p ∨ ( p ∨ q)) ( ( p ∨ q ) ∨ ( p ∨ q ) …

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Inadequacy of Finite State Grammars Finite state grammars do not allow dependencies of certain later symbols on certain earlier symbols. (p ∨ q) (p ∨ ( p ∨ q)) ( ( p ∨ q ) ∨ ( p ∨ q ) … The placement of propositional variables and logical connectives is unproblematical, but the placement of parentheses creates problems because placement of later parentheses depends upon earlier ones.

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Inadequacy of Finite State Grammars Finite state grammars do not allow dependencies of certain later symbols on certain earlier symbols. (p ∨ q) (p ∨ ( p ∨ q)) ( ( p ∨ q ) ∨ ( p ∨ q ) … The placement of propositional variables and logical connectives is unproblematical, but the placement of parentheses creates problems because placement of later parentheses depends upon earlier ones. There is no finite state diagram that is suitable.

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English Not a Finite State Grammar

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This illustrates why Chomsky asserts that English is also not a finite state language.

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English Not a Finite State Grammar This illustrates why Chomsky asserts that English is also not a finite state language. There are many fragments of English that can be generated by a finite state grammar.

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English Not a Finite State Grammar This illustrates why Chomsky asserts that English is also not a finite state language. There are many fragments of English that can be generated by a finite state grammar. But there are many fragments that cannot be, where later parts depend on earlier parts (as in what Chomsky calls “mirror image” cases).

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English Not a Finite State Grammar This illustrates why Chomsky asserts that English is also not a finite state language. There are many fragments of English that can be generated by a finite state grammar. But there are many fragments that cannot be, where later parts depend on earlier parts (as in what Chomsky calls “mirror image” cases). A finite state grammar, e.g., cannot insert then or or, since their appearances depend on the earlier appearances of if and either:

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English Not a Finite State Grammar This illustrates why Chomsky asserts that English is also not a finite state language. There are many fragments of English that can be generated by a finite state grammar. But there are many fragments that cannot be, where later parts depend on earlier parts (as in what Chomsky calls “mirror image” cases). A finite state grammar, e.g., cannot insert then or or, since their appearances depend on the earlier appearances of if and either: (11) (i) If S1, then S2. (ii) Either S3, or S4.

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English Not a Finite State Grammar This illustrates why Chomsky asserts that English is also not a finite state language. There are many fragments of English that can be generated by a finite state grammar. But there are many fragments that cannot be, where later parts depend on earlier parts (as in what Chomsky calls “mirror image” cases). A finite state grammar, e.g., cannot insert then or or, since their appearances depend on the earlier appearances of if and either: (11) (i) If S1, then S2. (ii) Either S3, or S4. As Allen & Van Buren state: “the set of all such sentences cannot be described by a finite state grammar.”

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The Proof

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In Syntactic Structures, Chomsky himself declines to present the mathematical proof, although he footnotes another paper in which he does it.

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The Proof In Syntactic Structures, Chomsky himself declines to present the mathematical proof, although he footnotes another paper in which he does it. What he does instead is to list forms of languages that are provably not finite state and to indicate how fragments of English are like them.

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Phrase Structure Grammar

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A phrase structure grammar, or context-free grammar, is a grammar with rules only of the form “ X → y,” where X is a singular, “nonterminal” symbol.

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Phrase Structure Grammar A phrase structure grammar, or context-free grammar, is a grammar with rules only of the form “ X → y,” where X is a singular, “nonterminal” symbol. Phrase structure grammars go beyond finite state grammars

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Phrase Structure Grammar A phrase structure grammar, or context-free grammar, is a grammar with rules only of the form “ X → y,” where X is a singular, “nonterminal” symbol. Phrase structure grammars go beyond finite state grammars Phrase structure grammars can do things that finite state grammars cannot do

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A Phrase Structure Grammar for the Propositional Calculus

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Consider this phrase structure grammar for the propositional calculus.

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A Phrase Structure Grammar for the Propositional Calculus Consider this phrase structure grammar for the propositional calculus. – S → ( S ◦ S )

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A Phrase Structure Grammar for the Propositional Calculus Consider this phrase structure grammar for the propositional calculus. – S → ( S ◦ S ) –◦ → ∨, ∧

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A Phrase Structure Grammar for the Propositional Calculus Consider this phrase structure grammar for the propositional calculus. – S → ( S ◦ S ) –◦ → ∨, ∧ – S → ¬ S

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A Phrase Structure Grammar for the Propositional Calculus Consider this phrase structure grammar for the propositional calculus. – S → ( S ◦ S ) –◦ → ∨, ∧ – S → ¬ S – S → p, q, r, …

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … Notice that in each case the symbol before the arrow is “singular”

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … Notice that in each case the symbol before the arrow is “singular” SAMPLE DERIVATION

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … Notice that in each case the symbol before the arrow is “singular” SAMPLE DERIVATION S

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … Notice that in each case the symbol before the arrow is “singular” SAMPLE DERIVATION S ( S ◦ S )

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … Notice that in each case the symbol before the arrow is “singular” SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S )

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … Notice that in each case the symbol before the arrow is “singular” SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S ) (¬S ∨ S )

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … Notice that in each case the symbol before the arrow is “singular” SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S ) (¬S ∨ S ) (¬p ∨ S )

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … Notice that in each case the symbol before the arrow is “singular” SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S ) (¬S ∨ S ) (¬p ∨ S ) (¬p ∨ q )

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Derivations of This Sort Correspond to Tree Diagrams Propositional Calculus CaseChomsky’s English Example

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S ) (¬S ∨ S ) (¬p ∨ S ) (¬p ∨ q )

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Derivation of a Formula of the Propositional Calculus FORMATION RULES S → ( S ◦ S ) ◦ → ∨, ∧ S → ¬ S S → p, q, r, … PROBLEM: Can such rules of this form be “associative,” placing parentheses around all logically connected pairs of S’s except the most inclusive pair? SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S ) (¬S ∨ S ) (¬p ∨ S ) (¬p ∨ q )

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Answer to Problem

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The answer is no

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Answer to Problem The answer is no In order to generate a string or formula like – S ∨ S, or S ∧ S

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Answer to Problem The answer is no In order to generate a string or formula like – S ∨ S, or S ∧ S – where two sentences are connected by ‘ ∨ ’ or ‘ ∧ ’ but lack parentheses, a formulation rule of a form different from the formulation rules of phrase structure grammars is required

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Context-Sensitive Grammars

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A rule is necessary that contains more to the left of the arrow than a single symbol

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Context-Sensitive Grammars A rule is necessary that contains more to the left of the arrow than a single symbol That is because application of the formulation rule only obtains in certain contexts

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Context-Sensitive Grammars A rule is necessary that contains more to the left of the arrow than a single symbol That is because application of the formulation rule only obtains in certain contexts In the present context, a rule that would work is –

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Context-Sensitive Grammars A rule is necessary that contains more to the left of the arrow than a single symbol That is because application of the formulation rule only obtains in certain contexts In the present context, a rule that would work is – # ( S ◦ S ) # → # S ◦ S #

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Context-Sensitive Grammars A rule is necessary that contains more to the left of the arrow than a single symbol That is because application of the formulation rule only obtains in certain contexts In the present context, a rule that would work is – # ( S ◦ S ) # → # S ◦ S # where “#” indicates a boundary for the most inclusive string.

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Context-Sensitive Grammars A rule is necessary that contains more to the left of the arrow than a single symbol That is because application of the formulation rule only obtains in certain contexts In the present context, a rule that would work is – # ( S ◦ S ) # → # S ◦ S # where “#” indicates a boundary for the most inclusive string. Call a grammar with such rules context-sensitive.

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Context-Sensitive Rules in English

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Number agreement in English might seem to require context-sensitive rules

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Context-Sensitive Rules in English Number agreement in English might seem to require context-sensitive rules Consider The man hits the ball

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Context-Sensitive Rules in English Number agreement in English might seem to require context-sensitive rules Consider The man hits the ball Chomsky offers rule (8) not of the “ X→y” form: (8) NP sing + Verb → NP sing + hits

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Context-Sensitive Rules in English Number agreement in English might seem to require context-sensitive rules Consider The man hits the ball Chomsky offers rule (8) not of the “ X→y” form: (8) NP sing + Verb → NP sing + hits Chomsky calls (8) a rule of a “phrase structure grammar,” even though we often distinguish now between context-sensitive grammars and phrase structure grammars

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Interlocking Part (2): An Inadequacy in Phrase Structure Grammars Chomsky suggests that we cannot treat English conjunction adequately even in terms of (context-sensitive) phrase structure grammars the scene – of the movie – was in Chicago the scene – of the play – was in Chicago the scene – of the movie and of the play – was in Chicago If sentences of the first two sorts are grammatical then sentences like the third are.

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Interlocking Part (2): An Inadequacy in Phrase Structure Grammars Chomsky suggests that we cannot treat English conjunction adequately even in terms of (context-sensitive) phrase structure grammars the scene – of the movie – was in Chicago the scene – of the play – was in Chicago the scene – of the movie and of the play – was in Chicago If sentences of the first two sorts are grammatical then sentences like the third are. Contrast that with these, where this is not true. the scene – of the movie – was in Chicago the scene – that I wrote – was in Chicago the scene – of the movie and that I wrote – was in Chicago

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The Generalization about Conjunction Chomsky suggests that to capture this fact, one, in some sense, needs a rule like (16): If S 1 and S 2 are grammatical sentences, and S 1 differs from S 2 only in that X appears in S 1 where Y appears in S 2 (i.e. S 1 =.. X.. and S 2 =.. Y..), and X and Y are constituents of the same type in S 1 and S 2 respectively, then S 3 is the result of replacing X by X + and + Y in S 1 (i.e. S 3 =.. X+ and +Y..).

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What Chomsky Says about Simplicity Chomsky writes: “Even though additional qualification is necessary here, the grammar is enormously simplified if we set up constituents in such a way that (16) holds even approximately. “That is, it is easier to state the distribution of ‘and’ by means of qualifications on this rule than to do so directly without such a rule.”

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What Chomsky Says about Simplicity Chomsky writes: “Even though additional qualification is necessary here, the grammar is enormously simplified if we set up constituents in such a way that (16) holds even approximately. “That is, it is easier to state the distribution of ‘and’ by means of qualifications on this rule than to do so directly without such a rule.” We are not told here why it matters that “the grammar is enormously simplified” or that the distribution of “and” is “easier to state.”

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What Chomsky Says about Simplicity Chomsky writes: “Even though additional qualification is necessary here, the grammar is enormously simplified if we set up constituents in such a way that (16) holds even approximately. “That is, it is easier to state the distribution of ‘and’ by means of qualifications on this rule than to do so directly without such a rule.” We are not told here why it matters that “the grammar is enormously simplified” or that the distribution of “and” is “easier to state.” Perhaps he means there are no missing generalizations; perhaps Chomsky himself is unclear.

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Transformational generative grammar

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Here, Chomsky introduces transformations

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Transformational generative grammar Here, Chomsky introduces transformations A transformation, he writes, “operates on a given string (or, as in the case of (16), on a set of strings) with a given constituent structure and converts it into a new string with a new derived constituent structure” (page 35).

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Transformational generative grammar Here, Chomsky introduces transformations A transformation, he writes, “operates on a given string (or, as in the case of (16), on a set of strings) with a given constituent structure and converts it into a new string with a new derived constituent structure” (page 35). Some distinctions (pp. 35f):

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Transformational generative grammar Here, Chomsky introduces transformations A transformation, he writes, “operates on a given string (or, as in the case of (16), on a set of strings) with a given constituent structure and converts it into a new string with a new derived constituent structure” (page 35). Some distinctions (pp. 35f): – The cycle

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Transformational generative grammar Here, Chomsky introduces transformations A transformation, he writes, “operates on a given string (or, as in the case of (16), on a set of strings) with a given constituent structure and converts it into a new string with a new derived constituent structure” (page 35). Some distinctions (pp. 35f): – The cycle – Obligatory and optional transformations

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Transformational generative grammar Here, Chomsky introduces transformations A transformation, he writes, “operates on a given string (or, as in the case of (16), on a set of strings) with a given constituent structure and converts it into a new string with a new derived constituent structure” (page 35). Some distinctions (pp. 35f): – The cycle – Obligatory and optional transformations – The kernel

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Passivization

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Structural description and structural change

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Passivization Structural description and structural change “To specify a transformation explicitly we must describe the analysis of the strings to which it applies and the structural change that it effects on the strings.” (SR, p. 39)

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Passivization Structural description and structural change “To specify a transformation explicitly we must describe the analysis of the strings to which it applies and the structural change that it effects on the strings.” (SR, p. 39) (24) If S is a grammatical sentence of the form NP 1 – Aux – V – NP 2, then the corresponding string of the form NP 2 – Aux + be + en – V – by + NP 1 is also a grammatical sentence (p. 34)

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What Made Transformations Attractive

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In Syntactic Structures, they are said to satisfy the “need” for simplicity, whatever that turns out to be

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What Made Transformations Attractive In Syntactic Structures, they are said to satisfy the “need” for simplicity, whatever that turns out to be Could say things not sayable before

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What Made Transformations Attractive In Syntactic Structures, they are said to satisfy the “need” for simplicity, whatever that turns out to be Could say things not sayable before Existence of discoveries

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What Made Transformations Attractive In Syntactic Structures, they are said to satisfy the “need” for simplicity, whatever that turns out to be Could say things not sayable before Existence of discoveries Rigor

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Three Generative grammars

Three Generative grammars

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