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

Philosophy E156: Philosophy of Mind

Week 2: The Chomskyan Revolution

My example of a Poverty of the Stimulus Argument,

Revisited

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.

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.

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?

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.

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)

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

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.

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?

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)

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.

The Chomskyan Revolution

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:



• 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”;




“interlocking parts”; – (b) perhaps offering a synoptic perspective;




“interlocking parts”; – (b) perhaps offering a synoptic perspective;– (c) distinct from preceding science




“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;




“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)

Science Creation and Scientific Revolutions (cont.)


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


• 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





– (c) implications for other fields; unity of science– (d) a readiness within and outside linguistics for

these new results, and the recruitment that results

Interlocking Parts of the New Paradigm


• (1) Formal limitations of standard grammars


• (1) Formal limitations of standard grammars • (2) Transformational generative grammar – could say things not sayable

before, existence of discoveries, and rigor



before, existence of discoveries, and rigor• (3) Methodological change – intuitions vs. corpora



before, existence of discoveries, and rigor• (3) Methodological change – intuitions vs. corpora• (4) Conception of science – explanatory adequacy, etc.; behaviorism;

description vs. explanation




description vs. explanation• (5) Mentalism




description vs. explanation• (5) Mentalism• (6) Autonomy of syntax, eschewing explanation use (the Bloomfield sort)




description vs. explanation• (5) Mentalism• (6) Autonomy of syntax, eschewing explanation use (the Bloomfield sort)• (7) Creative character of language




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




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”




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




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




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

Books by Chomsky I Will Refer To


• Logical Structure of Linguistic Theory [LSLT] (1955)



• Syntactic Structures (1957)



• Syntactic Structures (1957)• Aspects of the Theory of Syntax (1965)



• Syntactic Structures (1957)• Aspects of the Theory of Syntax (1965)• Cartesian Linguistics (1966)

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



• “Chomsky hierarchy” of formal languages• Hierarchy of formal languages that

computational models or automata can generate or recognize

Chomsky’s Mixed Feelings about Mathematical Work


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


• 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.”


• 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….”


• 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.”

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



• 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

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

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


• 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.

Another Finite State Language

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 man comesThe old man comes



The man comesThe old man comesThe old old man comes, etc



The man comesThe old man comesThe old old man comes, etcThe men come



The man comesThe old man comesThe old old man comes, etcThe men comeThe old men come



The man comesThe old man comesThe old old man comes, etcThe men comeThe old men comeThe old old men come, etc



The man comesThe old man comesThe old old man comes, etcThe men comeThe old men comeThe old old men come, etc

• It produces a finite state language that is infinite.

A Problem

A Problem

• Problem: Is English a finite state language?

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.

A Problem


and its grammar’s mathematical properties.• Chomsky took the linguist Charles Hockett to

consider English to be a finite state language.

A Problem



consider English to be a finite state language.• Not: Is there is a finite state grammar that

generates only English sentences? Answer: Yes

A Problem



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?

The Corresponding Problem for the Propositional Calculus


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


• 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?

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?




• 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

Inadequacy of Finite State Grammars


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



(p ∨ q)



(p ∨ q)(p ( ∨ p ∨ q))



(p ∨ q)(p ( ∨ p ∨ q))( ( p ∨ q ) ( ∨ p ∨ q ) …



(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.



(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.

English Not a Finite State Grammar

English Not a Finite State Grammar• This illustrates why Chomsky asserts that English is also not a

finite state language.


finite state language.• There are many fragments of English that can be generated

by a finite state grammar.



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.






(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.”

The Proof

The Proof

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

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.

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 go beyond finite state grammars

• Phrase structure grammars can do things that finite state grammars cannot do

A Phrase Structure Grammar for the Propositional Calculus


• Consider this phrase structure grammar for the propositional calculus.


• Consider this phrase structure grammar for the propositional calculus.– S → ( S ◦ S )


• Consider this phrase structure grammar for the propositional calculus.– S → ( S ◦ S )– ◦ → ∨, ∧


• Consider this phrase structure grammar for the propositional calculus.– S → ( S ◦ S )– ◦ → ∨, ∧ – S → ¬ S


• Consider this phrase structure grammar for the propositional calculus.– S → ( S ◦ S )– ◦ → ∨, ∧ – S → ¬ S– S → p, q, r, …

Derivation of a Formula of the Propositional Calculus

FORMATION RULESS → ( S ◦ S )◦ → ∨, ∧ S → ¬ SS → p, q, r, …

Notice that in each case the symbol before the arrow is “singular”




SAMPLE DERIVATION




SAMPLE DERIVATION S




SAMPLE DERIVATION S ( S ◦ S )




SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S )




SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S ) (¬S S )∨




SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S ) (¬S S )∨ (¬p S )∨




SAMPLE DERIVATION S ( S ◦ S ) (¬S ◦ S ) (¬S S )∨ (¬p S )∨ (¬p q )∨

Derivations of This Sort Correspond to Tree Diagrams

Propositional Calculus Case Chomsky’s English Example






PROBLEM: Can such rules of this form be “associative,” placing parentheses around all logically connected pairs of S’s except the most inclusive pair?


Answer to Problem

Answer to Problem

• The answer is no

Answer to Problem

• The answer is no• In order to generate a string or formula like –

S ∨ S, orS S∧

Answer to Problem

• The answer is no• In order to generate a string or formula like –

S ∨ S, orS 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

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 –




• In the present context, a rule that would work is –# ( S ◦ S ) # → # S ◦ S #





• where “#” indicates a boundary for the most inclusive string.





• where “#” indicates a boundary for the most inclusive string.

• Call a grammar with such rules context-sensitive.

Context-Sensitive Rules in English


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



• Consider The man hits the ball



• Consider The man hits the ball• Chomsky offers rule (8) not of the “ X→y” form:

(8) NPsing + Verb → NPsing + hits



• 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

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 Chicagothe scene – of the play – was in Chicagothe 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.

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 Chicagothe scene – of the play – was in Chicagothe 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 Chicagothe scene – that I wrote – was in Chicagothe scene – of the movie and that I wrote – was in Chicago

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 ..).

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.”



• 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.

Transformational generative grammar


• Here, Chomsky introduces transformations


• 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):




• Some distinctions (pp. 35f):– The cycle




• Some distinctions (pp. 35f):– The cycle– Obligatory and optional transformations




• Some distinctions (pp. 35f):– The cycle– Obligatory and optional transformations– The kernel

Passivization

Passivization

• Structural description and structural change

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)

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 formNP1 – Aux – V – NP2,

then the corresponding string of the formNP2 – Aux + be + en – V – by + NP1

is also a grammatical sentence (p. 34)

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



• Could say things not sayable before• Existence of discoveries



• Could say things not sayable before• Existence of discoveries• Rigor

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

Documents

grammatical rule b

b slide

chomskyan revolution

revisited slide

negative sentences

kims happy grammatical

corresponding sentence

language organ slide