Philosophy E156: Philosophy of Mind

1
Philosophy E156 Philosophy of Mind
Week 2 The Chomskyan Revolution
2
My example of a Poverty of the Stimulus
Argument, Revisited
3
Grammatical Rule (A)
(1) I will have a cold if I dont dress
warmly (2) Will I have a cold if I dont 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 dont dress
warmly (4) Ill have a cold if I dont 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 Ive a cold if I dont 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.

7
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)

8
From David Lightfoots Platos Problem, UG and
the Language Organ
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Grammatical Rule (C)
(6) Kim is happy (7) Kims 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) Kims happier than Tims 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 partys tonight (10) What
I wants to go (11) Whats bothering Jacks 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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Science Creation and Scientific Revolutions

• We often hear of the Chomskyan revolution but
  what was so revolutionary in Chomskyan
  linguistics?

16
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

17
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

18
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

19
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

20
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

21
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)

22
Science Creation and Scientific Revolutions
(cont.)
23
Science Creation and Scientific Revolutions
(cont.)

• Other elements (from Thomas Kuhns The Structure
  of Scientific Revolutions)

24
Science Creation and Scientific Revolutions
(cont.)

• Other elements (from Thomas Kuhns 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

25
Science Creation and Scientific Revolutions
(cont.)

• Other elements (from Thomas Kuhns 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 Kuhns 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

27
Science Creation and Scientific Revolutions
(cont.)

• Other elements (from Thomas Kuhns 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

29
Interlocking Parts of the New Paradigm

• (1) Formal limitations of standard grammars

30
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

31
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

32
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

33
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

34
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)

35
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

36
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

37
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

38
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

39
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

40
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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Books by Chomsky I Will Refer To

• Logical Structure of Linguistic Theory LSLT
  (1955)

43
Books by Chomsky I Will Refer To

• Logical Structure of Linguistic Theory LSLT
  (1955)
• Syntactic Structures (1957)

44
Books by Chomsky I Will Refer To

• Logical Structure of Linguistic Theory LSLT
  (1955)
• Syntactic Structures (1957)
• Aspects of the Theory of Syntax (1965)

45
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)

46
Chomskys Work in Logic and Mathematics
47
Chomskys Work in Logic and Mathematics

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

48
Chomskys 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

49
Chomskys 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

50
Chomskys Mixed Feelings about Mathematical Work
51
Chomskys Mixed Feelings about Mathematical Work

• Chomsky in the 1973 introduction to LSLT on 1950s

52
Chomskys Mixed Feelings about Mathematical Work

• Chomsky in the 1973 introduction to LSLT on
  1950s
• 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.

53
Chomskys Mixed Feelings about Mathematical Work

• Chomsky in the 1973 introduction to LSLT on
  1950s
• 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. Interested 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.

54
Chomskys Mixed Feelings about Mathematical Work

• Chomsky in the 1973 introduction to LSLT on
  1950s
• 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. Interested 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.

55
Point of Chomskys Work in Automata Theory
Negative
56
Point of Chomskys 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.

57
Point of Chomskys 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

58
Point of Chomskys 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

59
Finite State Grammars
60
Finite State Grammars

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

61
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.

62
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.

63
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.

64
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

65
Finite State Languages
66
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

67
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.

68
Another Finite State Language
69
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

70
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

71
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

72
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

73
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

74
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

75
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

76
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.

77
A Problem
78
A Problem

• Problem Is English a finite state language?

79
A Problem

• Problem Is English a finite state language?
• If it is, we can have a good grasp of some of it
  and its grammars mathematical properties.

80
A Problem

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

81
A Problem

• Problem Is English a finite state language?
• If it is, we can have a good grasp of some of it
  and its grammars 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

82
A Problem

• Problem Is English a finite state language?
• If it is, we can have a good grasp of some of it
  and its grammars 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?

83
The Corresponding Problem for the Propositional
Calculus

84
The Corresponding Problem for the Propositional
Calculus

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

85
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?

86
The Problem Posed for a Fragment
87
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)

88
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

89
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?

90
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

91
Inadequacy of Finite State Grammars
92
Inadequacy of Finite State Grammars

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

93
Inadequacy of Finite State Grammars

• Finite state grammars do not allow dependencies
  of certain later symbols on certain earlier
  symbols.
• (p ? q)

94
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))

95
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 )

96
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.

97
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.

98
English Not a Finite State Grammar

99
English Not a Finite State Grammar

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

100
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.

101
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).

102
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

103
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.

104
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.

105
The Proof
106
The Proof

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

107
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.

108
Phrase Structure Grammar
109
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.

110
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

111
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

112
A Phrase Structure Grammar for the Propositional
Calculus
113
A Phrase Structure Grammar for the Propositional
Calculus

• Consider this phrase structure grammar for the
  propositional calculus.

114
A Phrase Structure Grammar for the Propositional
Calculus

• Consider this phrase structure grammar for the
  propositional calculus.
• S ? ( S ? S )

115
A Phrase Structure Grammar for the Propositional
Calculus

• Consider this phrase structure grammar for the
  propositional calculus.
• S ? ( S ? S )
• ? ? ??, ? ?

116
A Phrase Structure Grammar for the Propositional
Calculus

• Consider this phrase structure grammar for the
  propositional calculus.
• S ? ( S ? S )
• ? ? ??, ? ?
• S ? S

117
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, ?

118
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
119
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
120
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
121
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 )
122
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 )
123
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 )
124
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 )
125
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 )
126
Derivations of This Sort Correspond to Tree
Diagrams
Propositional Calculus Case
Chomskys English Example
127
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 )
128
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 Ss except the most inclusive pair?
SAMPLE DERIVATION S
( S ? S ) (S ? S )
(S ? S ) (p ? S )
(p ? q )
129
Answer to Problem
130
Answer to Problem

• The answer is no

131
Answer to Problem

• The answer is no
• In order to generate a string or formula like
• S ? S, or
• S ? S

132
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

133
Context-Sensitive Grammars
134
Context-Sensitive Grammars

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

135
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

136
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
  

137
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

138
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.

139
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.

140
Context-Sensitive Rules in English
141
Context-Sensitive Rules in English

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

142
Context-Sensitive Rules in English

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

143
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) NPsing Verb ? NPsing hits

144
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) NPsing Verb ? NPsing 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

145
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.

146
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

147
The Generalization about Conjunction

• Chomsky suggests that to capture this fact, one,
  in some sense, needs a rule like (16)
• If S1 and S2 are grammatical sentences, and S1
  differs from S2 only in that X appears in S1
  where Y appears in S2 (i.e. S1 .. X .. and S2
  .. Y ..), and X and Y are constituents of the
  same type in S1 and S2 respectively, then S3 is
  the result of replacing X by X and Y in S1
  (i.e. S3 .. X and Y ..).

148
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.

149
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.

150
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.

151
Transformational generative grammar
152
Transformational generative grammar

• Here, Chomsky introduces transformations

153
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).

154
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)

155
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

156
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

157
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

158
Passivization
159
Passivization

• Structural description and structural change

160
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)

161
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
• NP1 Aux V NP2,
• then the corresponding string of the form
• NP2 Aux be en V by NP1
• is also a grammatical sentence (p. 34)

162
What Made Transformations Attractive
163
What Made Transformations Attractive

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

164
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

165
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

166
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