I

STANFORD ARTIFICIAL INTELLIGENCE PROJZCT MEMOAIM-170

STAN-CS-72-289

• o CO 00

LAKOFF ON LINGUISTICS AND NATURAL LOGIC

BY

YORICKWILKS

SUPPORTED BY

ADVANCED RESEARCH PROJECTS AGENCY

ARPA ORDER NO. 457

JUNE 1972

Reproduced by

NATIONAL TECHNICAL INFORMATION SERVICE

U $ Department of Commtre* r-pnngfleld VA 22151

COMPUTER SCIENCE DEPARTMENT

School of Humanities and Sciences

STANFORD UNIVERSITY

■

i 4

^D D O

SEP 25 1972

15ED U E B

i

BBaBiHit

BEST AVAILABLE COPY

STANFORD ARTIFICIAL INTELLIGENCE PROJECT MEMC NO. AIK-170

CC^PUUR SCIENCE DEPARTMENT

RKPCHT NC, 289

•

LAKOFF ON LINGUISTICS AND NATURAL LOGIC

by

Yorick W||ks

APSTHACT

loole, i norn-a I ly oa^ef»a Sefefat i the theg

Layoff's ad abSL shows , recc'' i c li^c ist Intel I fg

:T*« log arg

nun v3 is ( not wop

rdu-i I naa er lc ence

paper lc an ue tha oarsto ber o senant of Gen att ona k nay

of t verten i ts ow enqu I r u syst

exam 0 of t the od I f po icS, erat t 1 va Ppov! ns d* tiy, n i nf y--.-

em.

Ines and a gene ralatio

s unclea ss lb le

I, argue Vü Semar1

r iant u* de a sar r ivatlon that o

erences that I

or i rat i'. nshlo r. DU Intnr furt

tics) Choin

v I cs a I oa nly can d s t

ti c I ses a seman of the

t 1 sug PretatI her tha is fal

skyan t In that rad!gm a syst o the J o say

Lakoff tics das se notl gest iIn ons of t on the se, unle heory, I it cons

cf moder em with ob that , only

' s no cr ibed ons t the c his

se I nt ss It argue time n I tng

the Lakoff

an

tlons In :

o !o ourse thes

erore be ta

, to sar ulst! «b! I sets "art

of a arms of gic as of the

Is of tat t ons ken as Of that eductlo es) and Ity to UP for

Ificlal

t

\

The viev,s and conclusions contained In this document ara those o* the agthop and should not be Interpreted as representing necessarily the official oollcles, elther expressed or Imciledi of the Advanced Research Projects Agency or the U.S.Government,

This research was supported

i DINTHUOUCTION

I

f

In tMs paper I want to examine George LaKoff's discussion cl natunl loolc In some detail, anc then to examine his, ciosely conntctad, thesis of Generative semantics CGS3, He writes:

"Generativ« semantics claims that the underlylno arammatlcai

structure of a sentence Is the logical form of that sentence, and consequently that the rules relating logical form to surface form are exactly the rules c.f grammar, "C16, p, 183

It "•ill De one o

this claim is fa I se , norrta | rrean I ngs ,

f the orinclpa

at leayt if tasKs of this oaoer to argue that

ts words have anything llKe their

Two Irrtrediate comments are appropriate about this general thesis: (a' about Its conseque'.ces; and, (b) about Its originality. The consequences of the thesis, if it Is true, seem to me not to have beer, sufficiently appreciated. For this tbesls of LaKoff's Is In a sense a reduct!o ad absJrdum of modern I InguI St Ics|in that it would be reduced tr a mepe handmaidan of logic or worse, whose only residual role would be tc provide the details of the translation of sentences Into logical form, which would then be the real, or oriirary, structure of language, If Lakoff Is right In this matter thar. ChomsKy's wno i e enterprise of the last 15 years, to construct a fortral linguistics Independent of logic, has been a raoloally Tisguioed one from t^e start, Some of us rould contemplate that Possibility perhaps» but not the other consequence of GS that there cannot be any other, non-Chorskyan, 'ingulstics Independent of logic either,

As to the orioinality of Lakoff's thesis, it seems to me Interesting

to point out that it Is not as novel or striking as Is sometimes as^t-med.-it consists |n taking seriously an Idea floated by BarHlllel in I9t)4[4j, and to which Chomsky replied in one of hlg earliest, least known, and best paparsC73,$$

In order to nake this ooint let me sketch briefly whet seems to me the flow of energies from logic to linguistics In this century, That there are differences between the analyses that grammarians and Icgiclars provide of the same sentences nas been remarked on for irlMenla, And much of what, in recen;. years, has been ceiled the difference between deeo and surface structures Is no more than a relabelling of that difference. The distinction took a sharper form wher. Russell and whjtehead provloed 9 notation In which to make oo'r.ts such as that "John loves'* and "John exists" hrve the samb gpa-rTatlcal forms, in some sense of those words, but diffarent logical forms: in that "loves" could be represented by some preclcate In the predicate calculus, while "exists" could not,

%$ i air Inde*-*

iry rotice,

to Prof,Julius Moravcsik for bringing th|» paper to

It is not necessary to agree with that oartlcular ooint gf Russall anc »Jhltehead's to accept that the high point of that whole way of thinking------that logic «as "deeper" than grammar---- was Carnap's Logical Syntax of Language, where he wrote C63:

"Oy the logical syntax of a language we mean the formal theory of the

linguistic forms of that languaga -----the systematic statement of the formal rules which govern It, together with the development of the consequences which follow from these rules, , , . The difference between syntactical rules In the narrower sense and the logical rules of oeductlon Is only the differenc" between FORMATION RULES and TRANSFORMATJOM RULES, both of w ch are completely formulable In syntactical terms. Thus we are Justified In designating as "jooical syntax" the system which comprises the rules of formation and transf oriiat Icn",

For Carnap the formation rulas of the logical syntax of a LOGICAL

language were to be the rules that produced all and only the well-formed formulas of the system, The best contemporary example

1)

two trar. Hill For 9ar-

vorc Harr the i nte oyt

2)Th

Carr trar, love (Car esta t9. have subs Tear co^s work will 1 mD r that

3 ) So

Mill

waV ölff cate cbvl the> v

V surface structu And so t^at whe loQlcal form tpar, station, I exatrDleg laKolf cf consecuence Bar Hi I te I I? thought that co cal|«d "formatl

I shaI I argue« is concerned ar that ""any of wouIfl no rma I Iy Dart'c'Jiar logl

By that I Inten

fa^e on the bas «h i ch are not *ror0, For exn infer, as a chaIr Ir the or huffa-1; that I Tove dowrwards theje i nf arenc ▼aV also be fai all incuct've, content, howeve

res in a natural languaoe to have Inferential content, n Lakoff wrote of grammatical rules as "relating to -iur^ace form" he did not mean simply rules of shall have no difficulty In establishing this from the uses, hence GS Is a thesis that does trlng the notion Into linguistics, and in an even stronger form than oked for. For, in the oaoer I referred to, Bar Hll|e| nseouence would probably not be necessary for what he onal analysis",

then, that tne notions of Inference with which Lakoff e of no particular linguistic Interest. Moreoveri In the inferences with which he concerns himself are what be called inductive Inferences, they are üf no

cal interest either,

d to refer to the whole area of Inferen-es that humans Is of wnat they see, hear, know, and remember, but VALID inferences, in that they may w«. I I turn out to be np|e# If we hear someone say "Please sit clown", we may natter of social habit, such things as that there is a esence of the soeakeritnat whatever Is spoken to Is n obeying the reauest. If ne ooes so, the hearer will (though he may already be lying down), Any or all of es may be true, and may moreover be usually true, but se on any Particular occasion , These Inferences are

habltuali empirical, but have no interesting logical r, because they are not valid Inferences,

If, anci i shall show this below, the inferences Lakoff deals In are of tnis sort, tnen his system cannot be any sort of logic» other than a orooafci | istIc logic, which is not In question here. Howeveri It •seerrs to me tnat In bringing linguistic attention back to the subject of general Infarence(wnich I take to Include inductive infererce)Lakoff may be doing a service. For the enterprise that IS concerned with such inferences Is neltnar logic» nor linguistics as traoitionaIly understood, out artificial Inte | | IgenceCAI ] , AI Is much concemad with the construction of a human-like reasoning and uncerstand I ng systerr, and that Is no small or unworthy task,

M^ view is that such Inductive rules can on|y be a useful part of a mechanism which is able to FOLLOW UP xhese» oosslb.y mistaken, inffjrences to see whether or not they are Justified by the information reaching the system later, and hence Is able to abandon erroneous Inference where possible, NO such procedure Is rosslpi« within tne conventional Paradigms of logic or llngulstlcsj certainly not witMn inductive logic in the o robac I I I st I c form In which these woros are normally taken, On|y within some such context as artificial Intelligence» then, does It make much ser.se to discuss the sort of nuoious inference I am referring to, such as whether or not a chair wae cres«nt in tne "Ple&se sit down" example I gave earlier.

, i

my

No*«, there should be nothing astonishing In claiming that, If LaKoff's work has a oropep place It Is within AI, for most modern linguistics has been fundamentally concerned with the construction of a Possible mechanism, even If In a less clear way than Lakoffe work is. ano even though the linguists In question might utterly reject description of what they have been uo to all this time,

Choirsky's se | f-lmppsed task, It wj ij.be remembered, was the description of a Possible mechanism that would generate all and only the language strings satisfying some criterion of correctness. That regains the fundamental description of what Chomsky was a^Ing at, ever though It Is now called "weak ganepatlve capacity",and the criterion of correctness Itself 'las wobbled a bit over the year% and even though Chomsky has given other desiderata that the mechanism also haa to satisfy- such as being a scientific description of data, reducing them to order; describlng a possible mechanism by which humans IN FACT pfodyce language;formal I sing the structure that humans THINK thelr language has.- and go on,

There seems to tc a continuing confusion In current linguistics on this point, in that, In their eagernesss to dlsolalm any Intention to ffodel the mind or brain or other prn-essss of an actual speaker, some linguists have gone too far and disavowed the original gospel of sentence production as well. The task of the linguist is then thought to be to assign descriptions to Individual sentences, out by -rethods which must remain wholly mysterious If he has already rejecteo all specific analytic or productive ci 9] algorithms, A« I shall show, Lakoff himself Is In danger of falling Into this particular procedural limbo. Chomsky's original description C83of his own enterprise was undoubtedly productive, and even when he came later to clarify the notion of "generation" he continued to draw the analogy with Post derivations In logic C9; p, 93 which Daradlgrrs of olrected mechanical sentence production,

ape

Perhaps I have set rather a wide and extensive scene for the detailed discussion that follows, but then Lakoff himself does consider his own contributions to be fundamental, and not merely peripheral, to linguistics. i must now establish three points by detailed reference to Lakoff's text, In order to Justify the rather larg* genera' claims of this introduction. They are (Dthat the thesis of Gb^ uses conseauence to establish linguistic well formednessi(2)The nr'lon cf consequence used Is frequently Inductive consequencej(3)That the thesis of 5S , unless it Is merely a notatlorai variant of existing linguistic theory. Is false whether or not It rests on a notion of consequence.

In the two sections that follow I first examine the notion of a natural logic and then proceed to tho central thesis of GS,

- -—

II > THE NOTION Of A NATURAL LOGIC

It is Dropep to ask first what Lakoff means by a natural lofllc, Ha writes (16, P. 54):

"(iv) Me want a logic In which all the concepts «xoresslble In nat'.ral language can be expressed unambiguously, that Is. In which a|i non-synoryrrcus sentences have different logical forms.

(v) we want a IOQIC which is capable of accounting for all correct

inferences ^lade In natural language and which rules out Inoorrect fines,^ we wi;i call any logic meeting the goals (above) a "natural

Again ( |P|d, , p. 58):

Mlr raturäl Uglc .... logical equivalences could not Just be arbitrarily set oown; rather they would be Just those necessary to characterize the notion "valid Inference" for natural arSurrents",

Ana aga] r, (Ibid, , D, 126) :

anguaae

"Natural logic, taKen together with linguistics, is the ampirleal stuay of the nature of human language and human reasoning",

This aM sounds a very nice idea, and qe.ieraMy a good thing, but what does it really co^ie to? These Quotations, for example, taken tosetner, express a curjous ambivalence towards formal logic that runs right through Layoff's paper, Lakoff wrltes of a natural log!" In tern's of the general study of human reasoning, but the fact Is that most real human reasoning (s of a sort, that is of Interest to no one but psycho jog Ists.and sometimes psychiatrists, Real oeoole arQue rruch of the time along the linag of "That man has a sauint, therefore he probably -ants to mug me". And, of course, sometimes the> are right in such inferences, The notion of Inference, as such, «as no real logical content: Inferences are Just the inferences that

a| oecpie actually naka, Philosophers from Moore [20] to Lakoff Clbld 0, 9]have criticised the basic connective "3M, of materU, Implication, in the PropositIonaI Calculus, on the grounds that It in no (^ay expressed the natural usage of "If. . . . then" in ordinary la^suaoe, because it allows any statement to |mp|y any other, as long as the first is not true while the second is false, In the Propos tional Calculus one could Properly say that "The Aooilo space craft Is nearing the moon" Implies "I have a head-ache coming on" If Indeed I do, and that has always seemed to me quite a fair picture of how oeonle actually reason In real life. But mere seriously, Lakoff also refers, in the passages I Quoted, to "valid" and "correct" Inference when setting out what a natural logic Is to be "Valid" Is a reasonably well-understood term and covers such Inferences as "all f's are g and ail g's are I, therefore a|| f's are | , as well as those like "John is a younger son, therefore John

«

0

has a öpothÄr".

We can easily construct a sansa of "corraof Inference, too, dlffarant from that of "valid Inferenca" but still of Intaraat to loalc For exanpje, and to ua' an old logical favorlta, we can Infer fro* '"This Is a creatura with a heart" that "This s » o^»^;\J ^ a Mver» we can do this becauaa the missing premise Is unlvarially true, since all creatures with hearts do as a matter of fact have ivers, though 't does not depend on the meanings of words as does

»he "younger son" case. But such Inferences will be correct In some eiear sense In that they will (while the world stays roughly the same as now) always lead from true premises to true conclusions, and so a "natural logic" should probably be conoerned with them, But, and tMs Is mj point, wSat does Lakoff think loglolans, trad tlonal and modern, have baen up to. If not the discussion and Investigation of such valid, and sometimes, correct Inferences?

To be Precise, does Lakoff Present any valid or correct Inferences In

his oaoer, as oart of a proposed natural ioglc, that have not been extensively discussed by logicians In the normal course of their Job? I would think not, and this leaves me puzzled as to what Lakoff Intends the distinctive contribution of his natural logic to be,

paperi a considerable number of relationships

sort that have constituted one of Lakoff's There are, in establIshed of

his the

In a natural logic would went to call a valid '"^«"c«' " J*»* Inferring a trivial synonym from another is *..e sort of thing that logicians do, and Lakoff complains of, ,'ather than a real Ife natural inference. For who would actually say "Sam smoked oot last night, therefore last ntoht Sam smoked pot"?

Now there are indeed Inferences to be found In Lakoff's paper . that are real world Inferences, but would not be found in a logic book. However, they also hav« the drawback mentioned earlier» that they are rot valid, or oven correct. In the sense defined above.

Lakoff writes Clbld. , p, 423:

(34a) "(34)a. Nixon refused to try to shut Agnew UP. entails (3ba) {35)a. Nixon didn't try to shut Agnew UP".

If Lakoff is using "entail" I" Its normal sense to cover valid Inferences, those where the consequent must be true if the antecedent IS, then what he claims is Just not so, To refuse to do •of«^';; u to decline, to nrrfopm a verbal act, and is so described In both American and British c Ictlonarlee. It Is perfectly Poss.ble to refuse to do * and then to do It, even though as a matter of faot It

8

rrav be usual not to do x once you've refused to.

Again CibId , , po, 8-103 Lakoff "gne more beep, and I'll leave" I "If" such as "If I drink one more fore« of the example Is that between the two sentences In the In which c»^e he Is saying tha leave« entails "One more beer and not so, for I might neither h case "If I have another beer then "I'M have one more beer and I consequent) Is false, and so ther antecedent with "If" Is true, and

argues at length that the sentence s derived from a sentence contalhlng beer then I'M Isave", and the there is a relation of consequence

derivation (of one 'rom the other), t "If I have one more beer then I'll I'M leave", But that again Is

a^e another beer nor leave, in which I'M leave« Is still truei but

'II leave" (a natural meaning of the e can be no entallment, since the the consequent Is false,

Now, I trpy have Interpreted the whole notion of GS wrongly (see below Part IIP In that the derivation relation here Is not intended to be consequenlal, But IF IT IS then nera again Is a very shaky form of jiife- "^e at the heart of the system, and one which, as I argued In the first section, will Just not fit into the standard logical or linguist's derivational Daradigms, but only Into one that has the ceoeclty to find out that it has inferred wrongly and to try again,

WhMe pointing out that modern logic Is still concerned with valid

inferences. It must also be admitted that much of Lakoff's criticism of Its preoccupations Is true. His demonstrations of the ways in which logical caicui! faM to capture the awkward proliferations of language are famlMar to readers of Moore, Wittgenstein and Austin, but nevertheless valuable as reminders, in that the arroflanoe of logicians about language blossoms again In every generation as If It had never been trimmed, Again, much of the preoccupation of logicians with the ax lomat i sat i cri of logic is hard to understand for those concerned with the Problems of language, and indeed Kneale Ci5] has pointed out that there is something rather odd about wanting to axlomatlse logic Itself (which Is where much logical energy has Oone In this last fifty years): axlomatI sat Ions always used to be of some area of subject matter, such as geometry, using the techniques of logic.

But here again, things are not as bad as they might seem, and even the most foundational logicians are aware that their formal systems »ust respect the vaMd Inferences of some area of discourse. The trouble Is, from the point of view of those interested In language, that tne area of discourse that many or all foundational logicians are Interested In Is mathematics, not natural language,

But sorre of these foundational concerns should be of ultimate concern to Lakoff In the construction of a natural logic. Supposing he w.re eble to oo what appears to be his alms to out together an enormous number of postulates or rules of Inference for natural language argument, It would surely be Important to Know If they were consistent: for the fact that speakers felt sure about each of them

so of In of

Individual ly would not guarantee that consistency at all, At en« Dolnt, though, Clbld. » D, 94] Lakoff does refer In oasslno to one of h|s Dostulates as a theorem, and theorems are derived from axioms, Perhaps he does have In m|nd some ultimate axlomatIsatIon ind test consistency, However, thepe are other more Immediate burrlers the way of such an assemblage of postulates. When I wrote above Layoff's ambivalence towards loglci I had 'n mind his switch from, often justified, criticisms of formal logic to an extraordinary deflree of acceptance, One form of It In this paper Is an assumption that one can assemble an aggregate of postulates by picking and choosing from different areas of logic.

The overall format of Lakoff's paper Is In fact a gentle meander through dlffe-ent areas of logic; quantifiers, meaning postulates, modal logic» model theory. But there Is no system suggested at any Point, only an aspiration and a new notation with every subsection. It Is not at all self-evident that all these notions cm be usefully combined In one system, Meaning postulates and m de I theory» ^Or exair.Ple, represent very different ways of going about doing logic.

Another assuippti Job he h mlsunder clear, b fingers, "paradox view, Q dropped, oontInue Inferenc Presuppo because of enta valued" larguaOe fortral n But Uk aporeprI Harry I alright do we value? NOT TRUE he real! Presuppo

♦ orrn of on that as In m stands ut It c Some p es of e ulne though to d

es In sltlon, the usu I[ment: ental Is

axamp otlon o off us ate. s a f In an e real |y It see In tha

zes etc sltlon,

Lako a nu nd,

as we annot hl los ntal I 233 If o

escri natur

whl a| de

S' T les» f pre es | He t Ink" veryd want

ms to t cas

A but

ff's over

mber Of lo One such

saw, T be o esse

ephers wo ment" have has given ne did so be many o a| langua ch Is an f inltIon o C273 "S or hjs Is a v and most

suPposttlo t bllthel si Is us Ci presuppns

ay sense o to say

me much m e that Sam nd If It something

conf Id

Deal s en

he baa d too uld c this

much t It Is f what ge.

extr f It, esuppo ery dt of the n have y whe bid. , es tha f ores '.hat « ore st real '

s not more

ence I

ceneep tai I me lc not far

ertain effect Ime to not ea seem

erne | y such a ses S' ff Icul logic kept

re en o, 51

t "Har upposo Sam re ralght zes et true Ike an

n logic Is his ts offer firm too nt. which Lakoff ion of entalIment or It slips |y argue that »and,from another arguing that the

sy to see how to be perfectly cl Another ease Is difficult notion

apparent s for the somewhat

Is fatrlv through tne

the so-cal led point of notion be we would ear valId that of

. pertly s Strawson's» Is If and only If "S

t notion to apply lans who have made It safely within tal Iment would seem 3 that "Sam realizes

n terms Is truth to real use of a calcuj I.

more that

ry Is a fink"» which sounds but If Harry Is not a fink

a|izes etc. " has no truth forward to say that It Is c, , because he only thinks then we do not have a ental iment.

A footnote Clbld,, p, 133] suggests definitions of "presupposition" like the above, and that there Is some need to Moreover, he exolcres the notion j-esupPosl t io-i with some care, and contrasts

that Lakoff Is awars of one of strawson's quoted

beware of confusing the two. of the transitivity of

Its fa!lure In certain

10 4>

.,

eases too, foot" tf loht oresu

entgl that lofllc nelt^ loflte an t that

So th or«su Clbld Inclu Clbio r9lat • earino norira Thaor Incor thos« sens« Trare TALSE Stra*" that ciea'" loole notat for»ra f roir •tnbpa

with the 'rat Jtlvlty of antal l^tnttthough of oourse» but let us Ignor« that)» But than otas as Cl7i D,235n,5 wha^a ha says that

prefer to use "pragmatic Imol Icatlon'* DOosltlon| I think oarheps UtHoff Is right fflueh what wrote earlier when I aoeu Ifent with me j Inductive Infapenoe, And, a Is a very damaging criticism-of Lakof

••-even if it com«s cs an admission from h er linguistics nor logic oroper can really that may infer wrongly at any Dolnt,And,e^e

nductlve logic adequate to such a task,it w mastery of English also required mastery of

that come su 80M9

for wh i and th sad him s I ar f's whol Is own handle

n If the culd be that log

is ch oh at at of

d re lo h In eo

gued e cas hand

an In re oo an od le.

isoKted vealTng ■ODhers s ea|is deed Is nfusfng there,

e about , For duotlve uld be d claim

en, i do poosl tie i P. 521 de i»

ed

an P. 51 to th

, hoi t be J Ily unde y of D poratlng

cannot s of co e, then inot Jus son's n doctr In ,non-Rus ai forms ion for i izatlon the St

c« Ci.e,

not see why Lakoff cling n In his |inguistic da "An account of the log

account of the oresuop 3 "Then we win say t e logical form LI ONLY IF ds between LI and 12, , . ustifted in terms of rstood;sven though In cer efinlte Oesorlot ions, the certain existence assump be ca|led Presuppostt

urse, because for Hues the statement that the or t without truth value,And otion of PresuPDOSltlon w e of Russet I 'a. But se||tan,notation for |nc he does not really sot I

presuooositIons due to Ho of a notion of Austin's, rawsonlan definition th Ibid,,0,1313,

s so strong sor lotion a leal forw o osttions o hat tho su (my capita . . , ". F

the notion tain cases, re aru we I I tlons into ions in St ell, If th esent King ,a3 is w»t| as specific If Straws

oroorating t cut,What rnf.see 253 and Is in at Lakoff

ly to the notion jl nd to claims such as f a sentence must f that 8entenceMjand rface form SI can be Is) the relation, . or thesi claims Just of presupposition as such as Russell's known arguments for

a logical form,yet rawson's or Lakoff's ere is no King of of France Is bald Is

known of eou^se, aily directed agilst on has some ether presuppositions Into he gives us Is a which claims to be a any case different somettmes seems to

On Horn's vie' as foI lows;

presupposition and entallment are to be distinguished

If (S*S') and (-S-S') then S oresuppos«s 3",

If (S*S'j and l-S'* -s) then S entails S',

This Is different from Strawson's de'Mnltlon ---«•In that It is not a definition of presupposttlen in terms of entül |ment,and It does not make use of the notion of being trtth valued---'-bL)t like It »it is inconsistent with the Theory of DescrlotionsCsee ^53, However,Its weak Point Is the unexplained "

V

y

u

11

of presuppos I tton different from that of «ntallmtnt on th« basis of those two definitions, for If ,S' allows us to Infer ^S then the two notions,by the definition of entallment fllven aboveicannot be distinct, i would then argue thati If weaker than material IBID | Icat Ion, L?koff's and Horn's "*M can only be our old Inductive Inference a9fttn,Mlth all the troubles for a derivational linguistics that I have mentioned already,

As a general v.hei!s about »he translation of sentences Into logical 'orir Lakoff» c|a|m absut Dresupoos 111 on» Quoted above, Is surely ynaceep^abie, For example» t

h*re 's the Drob|en of ^he recesslon of presupposition? In aulte straightforward santenoesi should every sentence about a physical objeot , such as "The boy tnrew the stone" have & presupposition "something exists" embedded tn Its logical forir? (And the prefix 3x does not gulte do that), I dc, not see how Lakof can avoid dojng this without resort to an arbitrary cut-off of presupoosltlonaI |eve|,

But of course there Is no need for any such nonsense» for all that Layoff describes as presupposK.ons can be handled Jerf'ctly well by Inductive Inferences without any embeddlngs In LT's» and he admits as »uch In the footnote I quoted. The only trouble from his point of vie»« Is that the handling must be as part of an artificial IntsIlIgence system.

Note that I am not saying for a moment that I am shedding any light on these difficult notions, such as presupposition and entallment, bgt only pointing out that they are Cifflcuit and unclear, have vexed logicians and philosophers, and are net nice clean tools that Lakoff, or any other linguist, can Just pick UP and get to work with, They neeo a lot of conceptual cleaning UP themselves, and Lakoff shows no sign of being prepared to do that, Another term in this category is

oglcal form, Lakoff uses the term freely all p, 53] before he admits that "it makec sense forms of sentences only with respect to some

the central one of the way up to Clbid, , to soeak of logical system cf logic".

The logical form (LD of a sentence Is the form It requires to take Part In deductive relations. Some logicians would also hojd that the 17 is In addition the real meaning, or structure, of a sentenoe. This one could call the "backbone'« view of L^. Layoff Is tempted by both these points of view and, since he Is a linguist not a logiolan, this leaves an Important ambiguity In what GS means (See Section jn be Iow),

The very first example In .akoff's long oaper falls to notice the funoamental relation of L' to deduction He writes Clbid, , p, l]i

"(l)The -nembers of the royal family are v e ! ig dignitaries.

(2)Vlsltlng dignitaries can be boring,

12

, , . , corresDonding to each of these grammatical analyses (of 1) we fina a pattern of deduction".

But tha above (1), be soffe syffbo( I eons Ist Dr«d Ice ia^guaQ dr >e ca tne g dlsaope

LaKoff lofllc, Calcuiu arOu^en fortrat» exDress not exo wi shes: ot^er o structu con; I de has no adopted o * e x p to g«t

t Is Just not so. We cannot deduce two conclusions from the sentences, depandlng on the preferred grammatical analysis of cause we cannot deduce anything until the sentences are In recognizable if, f^nd that LF does not have to be C;Indeed» one could Say that the heart of Artstotelean logic s In trying to squeeze sentences Into Aristotle's rebarbatlve te form» ail of which was wholly expressed In the natural e of "terms". Only when something equivalent to that has bean n we begin to tall< of deduction. But» of course» |n doing It rammatlcai ambtgutty Layoff's example requires will have ared,

warns but

s for ts t when

ed I ress

al oints re t rabie t Pi R lOS

re&sl into

us t then expr

hat It I

n tr sredl I th [Ibt

r fcis, doub

nned e'y e ng th It,

hat If , wit essing can t s aopr ee f o cate f at ma d,

and t as t down

nough e ling

only make hout warnl sentence

hemsoIves oorlate to rm, Ther ormuias by kes this DO. 14, writes o

o what Lat< the Predlc for one to ulstlc var

s sen ng» s struc be or the

a is tree

odd i 15 fo f th off t ate C know lety

se with ettles f tures i edlcates system h no reaso s rather s that l r exampl em as LF h|nks a alculus whether

that he,

respect or a mod one with

He e Is d n y'v a

than akoff al • 2 of s 'si, whic logical format h or not esoeola

to a oar Ifled Pr oredlca then us

1scuss! n IIngulst strIngs so makes tandard h leaves form Is. e seems It Is I ly, wou

ttoular edtcate tea and as this g» but should If he use at phrase e-i In

He to have cao^.ble Id want

In the matter of quantifiers» too» one's faith in the cofrffonsenslca M ty of La^o"'* natural logic Is not increased by his Initial battery of examples which starts withjclbid, . p, 123

"(1) The archaeologist discovered n|ne tablets",

Thlsi La*off claims. Is ambiguous because " It can mean either that the archaeologist discovered a group of nine tablets or that the number of tablets he discovered altogether totalled nine, though they may not have been In a group",

But, one is tempted to reply» It might Just as usefully be argued that the sentence is ambiguous depending on whether or not the ■;chaeologlst Is an officially certificated one!What Lakoff has done here is to take a distinction fundamental In mathematics and logic, that between a set and Its members» and to claim that It has «molrleai significance In a natural language. But that Is an extraorqlnary procedure » and doubly so for an advocate of a NATURAL logic, one free from the oreoccupatlons of mathematically oriented log|c|ars----for wnat normal speaker could seriously consider the Quoted sentence ambiguous?

——^-— ■Ml.

13

It Is lirporttnt to be d|fftr»pt from a r«currl OrarriTat i ca I structures I t lu^i^ated by logical Qgln« assumes, In Ordsr distinctions to be I I

clear here that LaKoff's point Is oulte ng one of Quint's }that we understand certain an'J distinctions better by seeing them description Csee for example 23« o. 443 .

to make this point» Pre-existing grammatical tumlnated, and does not envisage a SEARCH for

mathematical distinctions In the operation of natural language,

But som« advances It Mat becoming could hot handle Dartlcujar» so as as "Everybody love this sentence can that could be a (3*) tyMLyx) and not normally expre sentence If they Dactlcutar example trees for the sent gives no bottom-le and derive two ease» and the trie discovering logic theoretic logic wi Sanoiwait [24J an Calculus notations determinate manner

are present In Lakoff's treatment of Quantifiers: wait known that standard transformational theory the notions of variable and Quantifier» In

to give two readings to sush old logical chestnuts s someone", Most people can be got to see that be Interpreted to mean two aulte different things, ssoclated with the Predicate Calculus formulas (x)(3y)(Lxy) respectively, even though they would

ss the two messages Involved by means of that one wanted to be understood. Now Lakoff discusses this » and displays two (conventional phrase«struoture ) ence» but (and this seems to ma the vital oolnt) he V9I rules that show how one could take the stitence readings for It, That Is the serious test In this k we all want to see done. while takoff is

Moravcslk and Gabbay have provided a strong set- th grammar- rulesC12&21]that does do Just that, d S'mmonsC263 have also provided modified Predicate that deal with such examples In a procedurally

layoff's failure to provide any sort of system of rules» however miniaturised in scope, Is an important one» as I argued earlier, for It leaves an important doubt as to Just what a natural logic» or indeed a generativa semantics, Is intended to aoo^mplish with regard to soire body of sentences in a naturel language. And» It is not Possible for ^akoff to take refuge here in some competence-performance distinction and to say that of course he is not attempting to model a speaker's performance etc. etc, » precisely because that Is not what he Is being accused of, The reauest for determlnateness and precision is in no way to be confused with a demand for psychological imitation.

It I Into reore hint the s taKe diffe logic struc the n vital

s pe their sent of a enten Shalt repce ian ! tures atura iv i

rfect I y work a certaln

determln ess to t er with

betwee s concer

ne der I langua moertant

true,

nd In natu

ate tr he str the lo n t^e ned ab ves :

ge th Rut

of c form ral la anslat uoture gleian

logi ova al the ex ey "h Lakoff

ourse.- that their reade nguage sente Ion procedur s, But I do s hare» fo -tans* ante I with the f act relation 00k onto" » on the oth

loglcia rs the noes, w e that not thl r ther ror1st ormal r betwee Is sec er hand

ns Impor t those thout e

would ta nk that e Is a and hi elatlons n the st ondary

descrI

t stru stru

ver gl ke us Lakoff n Imp s own, betwe ructur even bts hi

ctures ctures vlng a

from could

ortant The

en the es and though s task

14

in tenM of the proauctlon or ganeratlon of sentences along ilth their structures. So, for hin, the missing determlnateness Is» and ""ust be, centra I ,

1 rray veil not have done justice to the wealth of Lakoff's examples In this paper, But It should be said that there are certain oulte gratuitous difficulties In the way of dclng so.In particular Lakoff's curious treatment of the status of linguistic examples, It has baan reffarkeo In detail eisewhnre by UndsayCSS] how bizarre tha M» notation" Is «he-« used to mark SentenceS considered llnguistlcai|y I l iegltimate. Illustrate the addlt'onal Lakoff's under discussion,

Let me add twp glosses to t^os« Crlt'dspjs difficulties present In tha work

to of

In th that aster 0. 75 cone I in any sensg, unless load:

ie present taper he considers isk Is attached

to Inaicate a üons, Sut

,••,, to mark LOGICAL items

false. For example» the

Layoff also displays that is to the arbit aroltrary acceptance sney I d ; i ve :.TJ f I 4V

"The assigi'unt of a the author's soeech, exarro les can easl ly

Lakoff also U4es the

false, or logically to PERMIT(x» Y» Sl) = REQUIRECX. Y, S1) Clbld. ,

n Inference that d^es not in general lead to true the statement can hardly be called ungrammatleal that hard

worked word Is to carry an even haavler

an opposite techniaue In this paperJopposlte

rary exclusion of examples. Tor it amounts to the pf examples, T^o quotations from footnotes

•r of :ne lo^njj;

ster'sxs in ^hi foMnwIni examolns corresponds to

Readers whose idiolects disagree with these construct similar examples In their own soeech. "

It's ha that I reorodu i»hat n

exairo I e since the oth Engi ish st-r.^ar rrethod arbl tra author' an autn

e is at S in my < ha Is wr!

er hana, , then a Eng I i sr 93 the

ry exclu! s 0 i a I e( or cou I cl

ry

ly to this id on the sh» then

I myse moreover» ler and It ) les can n ir perver Jthor not acceptanc ') because s that th

)! trary po

» excep part Icu It thro If cann see no Is his

a repro slty, to do s e of e » i f on ere are "nt abo

t that he lar dlale ws consid ot Heasl I

reason Job to c

duced eas in a pap o, I r xamples ( e does no no holds

ut EnglIs

y" re

surel; d cann( e doubi product

I 5h< ee me, n star parent f ed to aous t( ersten? ed and this wi

•--■

w

15

Dhtiesoohy and orjlnary discourse that 98«m to elude eonventlo«.»

ti 3c«rl^ne ■COnSt:Uct,2n 0' d|s50^"s and Inferencer aoo oS litJ to certain forms of mental disorderiAndersor «DBropriaxe

HI GtNERATIVE SEMANTICS

Layoff's thesis of Cs can be discussed separately from natural looic

^kr^r'h^J' I09!C !8 Cltar,y about the exDHclt Inferences peoD|. »a^e, for better or worse, when tney reason, GS, on the other hand Is about the more standard linguistic ta^ of Jlnn^/dJin ^ oroduction of we | i form9d sentences . or, |f one Prefers to soeaktn •psychological mod., about Imp | Idt InferenceJ mid« " the

^ration process for sentences. l

D a gen

y«

K

c

16

sentsncB» containing "Dosslbly" e»n reouire a rul« ralatlno that word to so»« orlmltlve symbol axprasslm the concept of certainty, Yat translation of such sente.icea Into modal logic will reaulre somt such rule — — or the comolement of It, where "certain" raplaoas "posalbla" mutatis mutandis, Sur«|y Lakoff's conjacture-assartlon about rule Identity excludes this possibility?

Again, Lakoff's defense of GS at this point Involves some very odd forrrs of argument Indeed. The fol lowing seems to be essential to his Justification.Clbld. , p, 11]

"It should be noted that the above conclusions [that Is, GS3 depend upon a form of argumentation upon which Just about all of the linguistics of the oist decade and a half depends, namely, that If a given theory necessarily requires that the same rule be stated twice then that theory Is wpong. Not Just Inelegant, but ampirloally Incorrect. "

Well« 'f that Is true, then perhaps so much the worse for recent Mngul Jcs, For that form of argument. If correct, would out l|nguh Ics In a unjaue theoretical oosltlon among the sciences and humane disciplines. There are very complex discussions In the contemporary philosophy of science about what exactly It means to say that ore theory Is more economical than another. In terms of excluding more alternative possibilities and so being more testable In some defined sense, Paratlgms of such argument concern, for exairPle. whether the hypothesis that the planets have circular orbits Is fore or less economical than the alternative In terms of eillotlcal orbits. But no one, to my knowledge, has suggestec1 the emoioymont of the principle referred to by Lakoff I that a less economic theory, in any sense, Is not Just less economic (with respect to the same data) ^ut Is ergo EMPIRICALLV WRONG;

with GS, as with aM such theses, there ae therrs one Is to take the words as meaning wh the other Is to assum» th?.t they mean somethl first approach gives ui what 1 shall call the CONSEQUENCE view depending on how we take th last quotation. The second approach would g the RENAMING vie-. By that I mean tha lofllcal form he doesn't mean that In any stand linguistic structure, either familiar or of either case, on the renaming view, GS would no at s|l. and disputes about It would be wholly linguistics, When Chomsky C103 writes of GS of his own work he Is taking the renaming view

two ways o at they app ng quite dl TRANSLATION e word "reI Iva what I t when Lako ard sense, his own dev t real ly be an Interne

as "notatlo

f look ear to fferen view

ate" I could

ff ape but as Islng, ABOUT

I matt nil va

Ing at meant

t. The or the n that

cal I aks of

some In

ogle er for riant"

The consequence view Is the most obvious posslbl'lty, namely that the "relates" Is by inferenp , valid or otherwise, and that the well fc'tredness of sentences Is settled by whether or not they can bo Inferred from logical forms. My points In the Introduction about BarhlHel assumed that this was Lakoff's view, Much of the evidence

17

'U

for t

dlscu Intro

«of« sent« the "bac* trans one r real I no Dl co^se clear

his a sses ductl to r

no «9" trans bopa"

latlo effenb y ab ace a quenc and

ssumo

GS on of eores Clbl latio . of

n. ers h out t t al I e via s Imp I

tlo" I n g

rule entln d. , n vj sente The

ow mu rans | in a

w IPUS

e con

Is ci

ener« s of g mea D. 75 ew: noes trans ch of at Ion disc

t be sider

rcumsta"

I terns Inferenc nlngs th 3. Tha

that and can latlon v the pao Into io

usslon o Lakoff's atlons t

tla

8 an t |o be le er

91 f v

el

with s|m

quot Clca ral

w al Is

cal n«t tew i ag

ecaus

But "It

ply P atlon I fo ated so be about form ural If he alnst

e Lak It

Is cl rovt d seem

rms to th comes Infe

then logj has It«

off rare

Is relnf ear tha Ing log! s to me are the em by me less pi

rence I

Infereno c. So a fIrm v

|y actually

orced by his t there is cal forms cf to rule out meaning • or re rules of auslble when !♦ GS ware e would have

theni the tew, TWO

(1) There Is Just no clear not'on available of Inference going from

logical forms to sentences. Rules that cross the jnfllcal forrr-aertenoe boundary are rules of translation,

(2) There Is t^e problem of "reverse direction"» how could we analyse sentences with reverse Inference rules to Produce logical fortrs? Reversing Inference rules Is to oroduce false,hood, as In »If this is not colored then It Is net red," What possible interpretation could we attach to such a procedure In the context of GS?

In addition there is the general ImplausibiI Ity of believing that the

forn- or meaning of what we say Is determined In any way by operations Involving the notion of truth, This is a separate and detailed philosophical matter, of course, one Inappropriate for discussion here, but which should,! believe,by now be considered settled In favor of the common sense position,The questions Involved have been rruch d i scussed, but Strawson'sC28] i s an excellent recent restatement of that position.

The possible analyses of GS I have offered, and the knockdown

«rQu^ents I have produced against It when so Interpreted, may be criticised as cava|ler and inadequ j, That Is true, I am sure, but I oo rot s&e how Justice can be done until Lakoff produces considerable clarification of GS, at tne top level. If I may use that phrase. It should a|so be added, In fairness, that I have not (rentlon«d the many fundamental points, such as the pr jmacy of semantics and the Importance of what Is now called "laxleal decoirpos 11 Ion", on which I, lii

u

18

w

u

F'a8Snrore# j,, ?3)Gulne,H,V.O, 24)&andewalI,€,

REFERENCES

i Be|naPiN.D., Enthymemes» Jouma I of How to do things with Oxford,1962, Prjnclpla Metaphysica Logical Syntax and Se Remarks on Sptnoz '8 The Logical Syntt of Logical Syntax and Se Syntactic Structures, Aspects of the Theory Cambridge,Mess.il963, Qeeo Structure,Surfac nteroretatIon, n stelnoerg & Jakobo ambrIdge,l971 , rtlflclal Parcnota.A epresentatlon of the he Supoes semantics, n defining analogy,P n the rules of suppo n McCall(ed),PolIs* he Development of Lo Inguistlos and N*,tur tgdies In Generative ni v.of Ann Arbor,Mlc

ces here are to this vers avallab|a,I think.It als

Synthes«,197i, and In HintIkka.Moravcs Ik an Approaches to natural Davidson & Harman(eds

19

•

25)Schni tZtriH.f

26)S tmironsiR. »8

27)Strtv»son,P,F,, 2e)Str«K8on,P,F., 29)^1 |Kg,Y,.

30)U Iks.Y,,

3l)m|h8,YM

Presupposition.EntalIment and Russtll'a Thsory of DescrlPtlonsiFoundatlons of LanguagSf1971.

Bruc« B,i So^e relations between Predicate Calculus and semantic net rtoresantatlons of dlscoursOiPrwC. 2nd,internet,Conference on Artificial Intel IIgenca, Lendon»197l. An Introduction to Logical Thaoryil.ondon.1952, Meaning and Truth.Oxford,1970, One small head- —on models In Linguistics, ProcInternat.Conf,on Computational Linguistics, Debrecen,Hungary,1971, The Computer Analysis of PhMosophlcaj Arguments, (|n press) Deotdebltlty and natural language. Mind,1971.

t

I

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