Palmer a a Meeting of Minds Mind-1984-PALMER-398-409

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Vo l. XCIII, 3 98- 409

A M eeting of M in d s

ANTHONY PALMER

Shortly before he died Frege wrote the following.

How does a child learn to understand grown-ups? Not as if he

were already endowed with an understanding of a few gram-

matical constructions so that all you would need to do would beto explain what it did not understand by means of the linguistic

knowledge it already had. In reality of course children are only

endowed with a capacity to learn to speak. We must be able to

count on a meeting of minds with them just as in the case of

animals with whom men can arrive at a mutual understanding

{Posthumous W ritings, p. 271).

Shortly before he died Wittgenstein wrote the following.

I want to regard man here as an animal; as a primitive being to

which one grants instinct but not ratiocination. As a creature in

a primitive state. Any logic good enough for a primitive means

of communication needs no apology from us. Language did not

emerge from some kind of ratiocination On Certainty, para.

475)-

The views expressed here are strikingly similar. Wittgenstein,

however, is reminding us of views that he had developed in his later

work, while Frege, although he constantly in his later writings

adverts to the problem which had pushed him into this talk about a

meeting of minds and something animal, did not develop the idea.

Nevertheless, I think that Frege s characterisation of the problem

can help us to understand many of Wittgenstein s later views. In

particular I think it can help us to understand the use which

Wittgenstein makes of the notion of agreement in judgements,

together with his various comments, not obviously related to this,

on the circumstances in which it is appropriate to speak of

knowledge. The failure to see this relationship has seriously

distorted the interpretation of much of his later work. It has, for

example, led philosophers to think of On Certainty as a specimen of

belated concern with epistemological questions. I have in mind here

398

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A M EETING OF MIN DS 399

remarks like those made by Anthony Kenny in his book on

Wittgenstein where he wri tes:

Towards the end of his l ife, while staying with NormanMalcolm in Ithaca in 1949, he was stimulated by the study of

Malcolm's articles to begin to write on epistemology. His

notes , which were continued until two days before his death

and were of course never polished, were published posthum-

ously in 1969 under the tital of On Certainty. In this work

though Descar tes is never mentioned by name, Wit tgenstein

condu cts a three-cornered argum ent with Mo ore and the

Cartesian sceptic (Anthony Kenny, Wittgenstein, p. 204).

W ha t, then , was the problem wh ich led Freg e to speak in the way

in which he did of a m eeting of minds? T h e passage quoted occurs

in the course of a discussion of the nature of definition, which in

turn arises out of a characterisation of the difficulties that are

involved in giving a definition of the term 'fun ctio n' as it occ urs in

m athe m atics . Frege has jus t said that ' in the formula language of

m athe m atics an im por tant distinction stand s out that lies concealed

in verbal languag e' . I t is the distinction with which m athem aticiansbecome familiar when they grasp, as they need to, the idea of a

function. T he y need to come to terms w ith this idea, and they do so,

but not as a result of any definition that is given to them by their

teac her s, for it is not su scep tible of any definition at all. T h e reason

for this is tha t the form of a definition req uire s tha t wh at is defined is

not a functio n. T o give a definition of a pa rticu lar fu nction, e.g. a sin

function, you would need to prod uce an expression of the form 'T h e

function sin( ) . . . ' and yet the one thin g that an expression of thatform could not designate is a function. Expressions of that form

would be names of arguments or names of objects. However, a

function is precisely not an argument but what leaves a place open

for an argument . Consequently Frege wri tes:

It is here th at th e tend enc y of languag e by its use of the definite

article to stam p as an object wh at is a function and hence a no n-

object proves itself to be the source of inaccurate and mislead-ing expression s, and so also of errors of tho ug ht. Pro bab ly mo st

of the impurites that contaminate the logical source of knowl-

edge have their origins in this (Posthumous Writings p. 273).

T im e and time again in his later work F rege retu rns to this p oint.

The mathematical notion of a function brings to the surface a


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400 ANTHONY PALMER:

distinction which he thought essential to grasp before any progress

could be made in logic, viz. the distinction betw een con cep ts a nd

objects , a distinction itself incap able of definition. W e ne ed to get

clear ab ou t this distinc tion and yet how can we do so if what w e say

abou t it is always wro ng? It is this prob lem which acco unts for the

seemingly despair ing remarks in his article On Concep t and

Object ' where he writes :

I admit there is a qu ite pec uliar ob stacle in the way of

unders tand ing wi th my reader . By a kind of necessity of

language, my expressions taken l i teral ly, sometimes miss my

th o u g h t . I m entio n an object when w hat I intend is a concept. Ifully realise that in such cases I was relying upo n a reade r w ho

would be ready to meet me halfway, w ho does not beg rudg e a

pinch of salt (Posthumous Writings, p. 116).

Again at the end of the same article he writes:

Over the question of what it is that is called a function in

analysis we come up against the same obstacle; and on

thorough investigation it will be found that the obstacle isessential, and founded on the na tu re of language; that we

cannot avoid a certain inapp ropriateness of l inguist ic exp res-

sion; and that there is no th ing for it b u t to realise this an d

always take it into account (Posthumous Writings, p. 117).

O ne of the things whic h characterises W ittg en stei n's later work is

that he takes this proble m seriously. M oreove r, as I shall try to

show, he also takes seriously the suggestion wh ich Fre ge himselfmakes about the direction in which a solution is to be sought, viz.

the suggestion that w e m us t be able to count on a me eting of min ds .

It is this suggestion which becomes in Wittgenstein's later work the

notion which is on any account central there, viz. that of agreement

in judgements . The notion is in t roduced in the Philosophical

Investigations in the following way:

If language is to be a means of comm unicat ion there m us t be

agreement not only in definition bu t also, qu eer as this m ay

soun d, in jud ge m en ts . T hi s seems to abolish logic bu t does no t

do so. I t is one thing to describe the meth ods of m eas ure m ent,

and ano ther to obtain and s tate the results of m easu rem ent. Bu t

wh at we call 'me asu rin g ' is part ly determ ined by a constancy in

the resul ts of m easure me nts .



























402 ANTHONY PALMER:

senten ce as a pro per n am e for a tru th value, then , if we consider the

sentence, 'Socrates is wise' an d sub tract from it the proper name

'Socrates' we shall be left with an expression for a function, viz. . . .

is wise ' . It is because we can think of prop osition s as having such

const i tuents that we can introduce the idea of secon d level

functions, namely the quantif iers. As W ittgenstein had it in the

Tractatus, a function express ion gives us the pro to type of a

proposi t ion . We can then consider the case in which all of the

propositions which exemplify that proptotype are true, the case in

which none of them are true, and the case in which at least one of

them is t rue . If we use Fx to symbolise a function then we have

(x)Fx, (x) Fx, and 3xFx. However , it is w hen we have go t this farthat we m eet the objection w hich leads Frege to talk about a m eeting

of m ind s and the inevitabili ty of having to be m et half-way. W e have

show n how w e arrive at expressions for functions bu t our very way

of doing this prevents us from saying anything true or false about

them. The only way in which functions can appear in the argument

places of othe r functions is when we change level and quantify.

However , when we do so we are not saying anything true or false

about functions. If we try to place functions in the arg um en t placesof other functions without changing level we end up wi th an

incomplete expression and therefore one which could not possibly

be the name of a truth value, i .e. could not possibly be something

w hich w as true or false. Th e idea w hich ena bles us to proceed with

the notion of extensionality in logic seems to have the consequence

that we cannot say true or false things about those constituents of

pro pos itions w hich are sym bolised by expres sions for functions, i .e.

we will not be able to say true or false things about concepts. Logicrequires that we distinguish between concepts and objects but the

very distinction itself prevents us from saying what the distinction

is . It is at this poin t that Fre ge inv okes his idea of a m eeting of

m i n d s .

Others from the same starting poin t have g one in different

direc tions . Fo r exam ple, I do not think th at there is any do ub t that i t

is this distinction that so m uc h im presse d Ryle. In 'Le t te rs and

Syllables in Plato ' he talks about Frege's

difficult but crucial point that the unitary something said in a

sentence or the unitary sense th at it expresses is not an

assem blage of detacha ble sense atom s, that is, of parts enjoying

separate existence and separate thinkabili ty, and yet that one

























A MEE TING OF MIND S 403

truth or falsehood may have discernible, countable and

classifiable similarities to and dissimilarities from other truths

and falsehoods. Word meanings or concepts are not pro-

position components but propositional differences {Collected

Papers, vol. 1, p. 58).

And again in a la ter paper , ( 'Phenom enology V ersus T h e Con cept

o f Mind , ' Collected Papers, vol. 1, p. 187), he tells us that

the philosopher has apparently to try not just to deploy but to

describe the concep ts with w hich he is conc erned . H e has to say

what pleasure and existence are. He has to try, necessarily invain, to attach object characterising predicates to non-object

m entio ning ex pressio ns. But by no prestidigitation can the live

verb 'enjoys' or the live verb 'exists ' be made the grammatical

subjects to l ive verbs. The philosophers description of a

concept is bound to terminate in a s tammer.

It was precisely this difficulty which made Ryle shift into a

linguistic or semantic mode. He thought that while concepts could

not be made the subject of true or false propositions this was nottrue of the constituents of sentences. So, instead of talking about

functions and arguments, why not talk about sentence factors and

sentence frames? The idea was that while propositions are true or

false, unfortunately for conceptual investigations they do not have

extractable parts. Nevertheless we can get at their construction by

talking about the parts of sentenc es in wh ich they are expres sed. W e

achieve by moving into a semantic idiom what we could not have

achieved without doing so. I t is not only, as he somtimes put i t ,pru de nt to philosoph ise in a sem antic idiom , on this accoun t there is

not actually any other way of doing what we want to do. The only

way that we can talk about concepts is indirectly by talking about

the expressions which, so to speak, house them. Hence the label

' l inguistic analysis ' which w as used to characterise his work (a label

which he hated) and the subsequent developments which are so

familiar. It also accounts for an emphasis present in Ryle's work but

notably absent from Wittgenstein 's, viz. an emphasis on thepossibility of theorising.

It sho uld b e notic ed th at w hat is at stake here is not the reference

of incom plete expression s. Th a t they have a reference is som ethin g

that Frege never questioned. The trouble is not that they have a

reference but that we do not and cannot have a means of making


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404 ANTHONY PALMER:

reference to what they refer to in such a way that after having made

such a reference w e can the n go on to say something true or false

about what it is that we have m ade a reference to. Th e only way of

referring to what incomplete expressions refer to is by completing

the expression. Bu t when we have done th at we have not succeeded

in saying anything true or false ab ou t the reference of the

incomplete expression. . . . is w ise' says no thing true or false

because it says noth ing. If we com plete the expression by inserting

'So cra tes ' in the argum en t place then we do say som ethin g true i .e. ,

Socrates is wise. But in saying that we have not said anything about

wh at the expression ' . . is wise ' refers to. It follows, from this alon e,

that Michael Dummett ' s arguments in his first book on Fre ge donot extricate Frege from the problem to which his talk about a

meet ing of minds is directed. H ere is what D um m et t has to say

about Frege's worries about the concept horse.

W e can, therefore, truly say of wh at the expression ' th e con cept

horse' stand s for that it is no t a co nc ept , bu t an object; and , since

we speak of tha t for w hich an expre ssion stan ds simp ly by using

that expression this means that we can truly say, 'The concept

horse is not a concept bu t an object . ' . . . [T]he paradox is

intolerable because it leads to the conclusion that it is not

possible, by any means whatever, to state, for any predicate,

which part icular concept it s tands for, or to state for any

relational or functional expression, which relation or function

it stands for. Any attempt to say this must, it app ears, lead to

the formation of an expression which, by Frege's criteria, is a

s ingular term, and by mea ns which we have not thereforesuccee ded in referring to a co nc ep t (or relation or function) at

all, but instead to an object. . . . Clearly if there were no escape

from th is d i lemm a— brought to light by Fre ge himself—this

would be a reductio ad absurdum of Fre ge 's logical d octrine s

(pp . 211-12).

D u m m e tt sees the prob lem here as me rely one of the reference of

incomplete expressions and proceeds using a suggestion of Frege's

to show how we can sensibly talk ab out wh at an incomplete

expression stands for. His central point is that we should not take

the expression 'wha t x is a h or se stan ds for ' as a singular term a nd

therefore we should n ot allow it to be inserte d in the arg um en t place

of a predicate expression. Just as the s ingular term 'M ou nt Eve rest '

























A ME ETING OF MIND S 4°5

should be and indeed is substi tutable for the s ingular term 'What

M ou n t Eve res t s tands for ' so 'Wh at x is a ho rse s tands for'

should be substitutable for 'x is a horse'. Since the latter is not a

singular te rm it follows that the former can not be cons trued as a

singular term either but has to be itself construed as a predicate or

an incom plete ex pression, i .e. it has to be constru ed as leaving open

an argument place, i .e. as having the form 'y is what x is a horse

stands for ' . If we so construe it then Frege's paradox can never

arise, for it could never be intruded into the argument place of

another predicative expression. We avoid the paradox while

ma intaining the idea that incom plete expressions have a reference.

Ho we ver, if wha t worries Fre ge is no t the questio n of the referenceof incomplete expressions but the difficulty of saying something

true or false about the reference of such expressions we have not

advanced much with his problem. Dummett is inclined to think

that F rege 's rem arks about a m eeting of m ind s etc. , are resolved

once we have seen that we can con strue th e reference of inco mp lete

expressio ns in a non -parad oxica l w ay. T h e po int is that whe n we do

so construe them we can see why those remarks become so

pert in ent , and w hy Frege in his un pub lishe d writ ings comes back tothem time and t ime again. They do not consti tute the reductio ad

absurdum of Frege's logical doctrines but rather show you what is

involved in an acceptance of them. What they show is that if

language is as Frege thought it to be, i.e. if it is such that the

distinction b etween co ncep t and object is of prim e impo rtanc e th en

wh at is requ ired for com m unic ation is , que er as this ma y sound , not

only agreem ent in definition bu t a m eetin g of m ind s or agreem ent in

judg em ents . I t is noticeable that Du m m ett makes no a t temp twhatsoever to avail himself of this aspect of Frege's work or of the

development of it in the work of Wittgenstein.

Wittgenstein 's remark with which I began comes from On

Certainty. If we see tha t work in the contex t of Freg e's prob lem it

looks very different indee d from the way it looks if viewed from the

background of general sceptical worries. I do not think that

W ittgens tein ever was intereste d in epistemological wo rries as suc h.

To understand his later writings we need to ask ourselves what the

difficulties were that led to him to say the things about knowledge

that he did.

Both in the Philosophical Investigations and in On Certainty he

tells us that there are certain situations in which the concept of

know ledge is out of place. He asks, for exam ple, w hat sense it mak es

























406 ANTHONY PALMER:

to say tha t I know I am in pain, an d he crit icises M oore for replying

to the sceptic who asks how he knows the propositions listed in A

Defence of Com mon Sense ' and 'Proof of an Externa l W or ld ' by

saying that he does know them. The question of knowledge is only

to the point in si tuat ions where there is some dou bt , whe reas it

would be difficult to know what doubting such propositions would

amount to . Now we m ight ask why he should so urge that the

conc ept of know ledge is only app rop riate in situations of do ub t a nd

certain ty. I t is surely not, as som e have thou gh t, a question of usage.

W ha t is at stake is the relation of the concept of know ledge to tru th

and falsity. If I know that p then p is t rue . How ever , if we are

operat ing in the area of agreem ent in jud gem ents , if we have gonebeyond agreement in definition, then whatever we say in that area

will, as it we re by definition, no t belo ng in the area of saying tru e or

false thin gs, and will con seq uen tly n ot belong to the realm of thing s

tha t I can be said to know or not know. It is the co nne ction of the

concept of knowledge with tru th w hich locates it in the same

dimen sion as that of doubt and cer tainty . W hen I am in dou bt I am

in doub t as to w hethe r som eth ing is so or not, and wh en I am certain

I am certain that something is so . W hen t ru th is excluded so arequest ions of doubt and cer tainty . Hence, if I am right in m ain tain -

ing that Wit tgenstein 's not ion of agreement in judg em ents , like

Fr eg e's idea of a m eetin g of min ds , is only introd uce d at the poin t

w he re saying true or false thin gs is out of place, it follows tha t w he re

such talk is inappropriate there talk of knowledge is inappropriate

also.

T h e p oint can be il lustrated by applying it to discussions of pain.

If I say tha t I am in pain and som eon e asks m e how I kno w , wh at is it

tha t he wants to know about? The situation wo uld have to be

extraordinary if what he wanted to know was whether I am in pain ,

for I have told him that I am . Le t us assum e that i t is not a que stion

of him doubting my word. The question is, of course, asked by the

sceptical philosopher and w h a t he wan t s to know about is the

concept of pain. If I try to tell him abou t that by tell ing him w hat I

know then all of the p rob lem s wh ich beset Frege co me flooding in.

In this sense the sceptic 's problems are not problems of knowledgeat a l l . His problems are conceptual problems and about concepts

there is no question of saying true or false things and therefore no

question of knowledge and no problem of knowledge.

Final ly , I think Fre ge 's problem can help us with another m uch

discussed term of Wit tgenste in ian art. W hen concepts prove

























A ME ETING OF MINDS 4°7

troublesome, as the concept of pain was proving troublesome to the

sceptical philosopher, Wittgenstein will ask for the criteria of

whatever it is that is in question. If the concept of pain is giving the

sceptical philosopher trouble then he will ask about the criteria forsaying of someone that he is in pain. Notice once more that what

gives trouble is the concept of pa in. Ap art from special c ircu m -

stances we are not ordinarily troubled in the way in which the

sceptic is about whether people are in pain or not. It is the concept

of pain that gives the sceptic his worries in that he is bothered

about whether anyone (other tha n himself) is in pain. H e is worried

about the grounds for thinking so. It is therefore with regard to the

conc ept th at criteria are invoked . It is at this point th at wh at we havelearned from Frege about concepts affects the way in which we

think of criteria, for there is a use of the term criterion which is not

like this at all. If we restrict ourselves to the situations in which we

are genuinely worried about whether a person is in pain or not (we

need to know how to treat him for example) there are certain tests

that we shall make and if those tests turn out positive we shall not

doubt that the person in question is in pain. Generalising, when we

say of a pa rticu lar S tha t it is P we can do so after h av ing m eas ure d itagainst the criteria for a things being P. Naturally there will be

many areas in which we employ a term when we shall be in some

do ub t ju st wh at the criteria for its application are, and in many cases

we shall need to make a decision. Nevertheless the principle holds

that we can move directly from the fulfilment of the criteria to the

application of the term . In these cases we are not worried a bo ut the

concept we are merely worried about whether a certain case falls

un de r it or not. Th es e are the kinds of cases in which Au stin u sed toinvoke criteria. How do you know that it is a Bullfinch? List the

cha racte ristics of Bu llfinches. If it has tho se chara cter istics th en it is

one, no question. The person puzzled about Bullf inches just does

not know what those characteristics are and needs to be informed,

and he can be so informed by someone who knows. However, if

som eone is puzz led abo ut conce pt then any appeal to criteria has, of

nece ssity to be different. If ou r worrie s are ab ou t P in the sense tha t

it is the concept that we are worried about we shall be unable tomove directly from criteria to the concept. If we could so directly

move we would be involved in making that concept the subject of a

true proposit ion, we would have turn ed the concept into so me thing

which it precisely is not, namely, an object. Criteria in the one sense

relate concepts to objects whereas in the other sense they relate


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408 ANTHONY PALME R:

concepts to concepts, and this relating has to be a quite different

enterpr ise .

Stanley Cavell in his recent book The Claim of Reason has his

finger on th is po int. H e does in fact say tha t for W ittg en ste in criteria'do not relate a name to an object but various concepts to the

con cep t of tha t objec t ' . T h e troub le is that in oth er places he d istorts

this point by resort ing, not without certain qualms which become

altogether un ders tand able if you have been reading Wittgenstein in

the background of Frege, to the vocabulary of different kinds of

objects. In discussing the difference between Austin and

Wittgenstein in their use of the term cri ter ia he dis t inguishes

between specific objects and generic objects. Specific objects hedescrib es as such that the pro ble m of know ledge they pre sen t is one

of 'correct description, identification or recognition', whereas

generic objects , the s tan dard examples in tradit ional epis temology,

'are ones specifically about which there just is no problem of

recognition or identification or description, ones about which the

only problem, should it arise, would be not to say what they are but

to say whether we can know that they exist, are real, are actually

th er e ' . He argues that Austin provides cr iter ia whe n the know ledgein question is of a specific object, whereas Wittgenstein provides

criteria when the knowledge in question is of a generic object. And

so he writes:

The general relation between these notions of criteria is

roughly this: If you do not know the criteria of an Austinian

object (can't identify, name it) then you lack a piece of

information, a bit of knowledge, and you can be told its name,told what it is (officially) called. But if you do not know the

criteria of W ittgen steinia n objects then y ou lack, as it w ere, n ot

only a piece of information or know ledge, bu t th e possibility of

acquir ing information about such objects iiberhaupt. Y ou

ca nn ot be told the na m e of tha t object b ecause th ere is as yet n o

objec t of that k ind for you to attac h a for thcoming nam e to . Th e

possibility of finding out what it is oficially called is not yet

open to you (The Claim of Reason, p. 77).

T h is sort of talk can m ake it look as tho ug h W ittge nste in only raises

questions about criteria when the existence of some curious sort of

object is at stake, perhaps mental objects or physical objects, and

this mistakes the point en tirely. W ith F rege in mind we can see how

the sorts of distinction drawn in this passage reflect not a concern

























A ME ETING OF MIND S 4°9

for different sorts of objects but the crucial distinction between

concepts and objects .

T h e passage which I have quoted w hich introduce s the notion of

agreem ent in jud ge m en t makes no reference to the term 'cr i ter ion 'at all but it should be clear that the notion is playing a role there.

W hen W ittgenstein says that ' i t is one thing to describe the m eth od s

of measurement, and another to obtain and s tate the results of

me asurem ent . But what we call m ea sur ing is par t ly determined

by a constan cy in the resu lts of me asu rem en ts ' he is in fact ma king

a poin t similar to the point abo ut pain that I have jus t been m ak ing .

What in effect he is saying is that amongst the criteria for the

concept of measurement is a certain constancy in the results ofmeasurement. Without such constancy in results there would be no

such concept as what we call measuring.

When we correctly unders tand the difference between concepts

and objects we see tha t concep ts canno t, unlike objects , be m ade the

subjects of true or false propositions. It follows from this that the

upshot of conceptual investigations cannot be an accumulation of

true or false propositions. If the sceptics problems are conceptual

pro ble m s then no acc um ulation of information is going to be of helpwith the m . Wh en cri teria are evoked in cases wh ere concepts prove

troublesome they are not evoked as presenting the truth that wil l

settle the issue.

The conceptual confusion of which Wittgenstein speaks is not

just m ud dle d thinkin g, due perhap s to ignorance or misinform ation

or lack of logical expertise. It is, as Frege recognised, a confusion

founded on the nature of language. We mention an object when

what we intend is a concept; press for definitions when what weneed to und ers tan d is agreem ent in jud ge m en ts ; seek for theo ry

when what is in question is grammar.

D E P A R T M E N T O F P H I L O S O P H Y ,

U N I V E R S I T Y O F S O U T H A M P T O N ,

SOUTHAMPTON, SO9 5NH


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Palmer a a Meeting of Minds Mind-1984-PALMER-398-409