A Meeting of Minds

Mind Association

A Meeting of MindsAuthor(s): Anthony PalmerSource: Mind, New Series, Vol. 93, No. 371 (Jul., 1984), pp. 398-409Published by: Oxford University Press on behalf of the Mind AssociationStable URL: http://www.jstor.org/stable/2254418 .

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Mind (I984) Vol. XCIII, 398-409

A Meeting of Minds

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 grammatical constructions so that all you would need to do would be to 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 Writings, p. 27I).

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

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remarks like those made by Anthony Kenny in his book on Wittgenstein where he writes:

Towards the end of his life, while staying with Norman Malcolm 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 I969 under the tital of On Certainty. In this work though Descartes is never mentioned by name, Wittgenstein conducts a three-cornered argument with Moore and the Cartesian sceptic (Anthony Kenny, Wittgenstein, p. 204).

What, then, was the problem which led Frege to speak in the way in which he did of a meeting of minds? The 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 'function' as it occurs in mathematics. Frege has just said that 'in the formula language of mathematics an important distinction stands out that lies concealed in verbal language'. It is the distinction with which mathematicians become familiar when they grasp, as they need to, the idea of a function. They need to come to terms with this idea, and they do so, but not as a result of any definition that is given to them by their teachers, for it is not susceptible of any definition at all. The reason for this is that the form of a definition requires that what is defined is not a function. To give a definition of a particular function, e.g. a sin function, you would need to produce an expression of the form 'The function "sin( )" .. .' and yet the one thing that an expression of that

form 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 writes:

It is here that the tendency of language by its use of the definite article to stamp as an object what is a function and hence a non- object proves itself to be the source of inaccurate and mislead- ing expressions, and so also of errors of thought. Probably most of the impurites that contaminate the logical source of knowledge have their origins in this (Posthumous Writings p. 273).

Time and time again in his later work Frege returns to this point. The mathematical notion of a function brings to the surface a



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distinction which he thought essential to grasp before any progress could be made in logic, viz. the distinction between concepts and objects, a distinction itself incapable of definition. We need to get clear about this distinction and yet how can we do so if what we say about it is always wrong? It is this problem which accounts for the seemingly despairing remarks in his article 'On Concept and Object' where he writes:

I admit there is a quite peculiar obstacle in the way of understanding with my reader. By a kind of necessity of language, my expressions taken literally, sometimes miss my thought. I mention an object when what I intend is a concept. I fully realise that in such cases I was relying upon a reader who would be ready to meet me halfway, who does not begrudge a pinch of salt (Posthumous Writings, p. i i 6).

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 is essential, and founded on the nature of language; that we cannot avoid a certain inappropriateness of linguistic expression; and that there is nothing for it but to realise this and always take it into account (Posthumous Writings, p. I I7).

One of the things which characterises Wittgenstein's later work is that he takes this problem seriously. Moreover, as I shall try to show, he also takes seriously the suggestion which Frege himself makes about the direction in which a solution is to b-e sought, viz. the suggestion that we must be able to count on a meeting of minds. 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 introduced in the Philosophical Investigations in the following way:

If language is to be a means of communication there must be agreement not only in definition but also, queer as this may sound, in judgements. This seems to abolish logic but does not do so. It is one thing to describe the methods of measurement, and another to obtain and state the results of measurement. But what we call 'measuring' is partly determined by a constancy in the results of measurements.




Now I think that Wittgenstein's thought at this point is that if we conceive of logical investigations as an attempt to describe the rules by logic, the rules by virtue of which what we say makes sense, we can remain quite clear about what we are doing so long as we suppose that the only agreement needed is agreement in 4efinition. On that supposition we could proceed with a clear conscience to chart the relationships between our definitions, i.e. the relationships between the ways in which we choose to use words. But if we were to suppose that agreement in judgement is also needed our conscience becomes clouded for it then becomes difficult to see how the statement of a rule would differ from a description of what as a matter of fact people say and do. The difficulty would then be to see how such a description could present us with the rules by virtue of which what we say makes sense. If describing the rules of logic involves describing what as a matter of fact people say and do it seems that the difference between empirical and logical propositions has been obliterated. And so if we hold that agreement in judgements is needed for language to be a means of communication this seems to abolish logic (see my Critical Notice of On Certainty in Mind 1972).

Central to the conception of logic that Frege was working through was the idea of extensionality, or if you like, the idea of logic as being truth functional. Frege himself remarked that the only objects with which logic deals are truth values. When this idea is thought through it has an effect upon the way in which we think of the so called logical constants. The effect it has, as Wittgenstein noticed in the Tractatus, is that of preventing us from construing them as genuine constituents of propositions. In the case of propositions which contain other propositions the role of the logical constants is exhibited by means of truth tables in which the constants themselves do not appear. In the case of propositions that do not contain other propositions the truth functional approach to their analysis is maintained by the application of the notion of generality; that is to say, the analysis of such propositions is the theory of quantification. We do not get at their structure by being, so to speak, more microscopical but by being more general. (This point is developed in my 'Ryle Cogitans', in Philosophy, I984.) What enables the theory of quantification to get off the ground is the application of the originally mathematical notion of function and argument to sentences. We form the expression for a function by extracting from a proper name a proper name. If we regard a



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sentence as a proper name for a truth value, then, if we consider the sentence, 'Socrates is wise' and subtract 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 propositions as having such constituents that we can introduce the idea of second level functions, namely the quantifiers. As Wittgenstein had it in the Tractatus, a function expression gives us the prototype of a proposition. 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 true. If we use Fx to symbolise a function then we have .(x)Fx, (x) -Fx, and 3xFx. However, it is when we have got this far that we meet the objection which leads Frege to talk about a meeting of minds and the inevitability of having to be met half-way. We have shown how we arrive at expressions for functions but 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 other 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 argument places of other functions without changing level we end up with an incomplete expression and therefore one which could not possibly be the name of a truth value, i.e. could not possibly be something which was true or false. The idea which enables 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 propositions which are symbolised by expressions for functions, i.e. we will not be able to say true or false things about concepts. Logic requires that we distinguish between concepts and objects but the very distinction itself prevents u-s from saying what the distinction is. It is at this point that Frege invokes his idea of a meeting of minds.

Others from the same starting point have gone in different directions. For example, I do not think that there is any doubt that it is this distinction that so much impressed Ryle. In 'Letters 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 that it expresses is not an assemblage of detachable sense atoms, that is, of parts enjoying separate existence and separate thinkability, and yet that one




truth or falsehood may have discernible, countable and classifiable similarities to and dissimilarities from other truths and falsehoods. Word meanings or concepts are not proposition components but propositional differences (Collected Papers, vol. I, p. 58).

And again in a later paper, ('Phenomenology Versus "The Concept of Mind",' Collected Papers, vol. i, p. I 87), he tells us that

the philosopher has apparently to try not just to deploy but to describe the concepts with which he is concerned. He has to say what pleasure and existence are. He has to try, necessarily in vain, to attach object characterising predicates to non-object mentioning expressions. But by no prestidigitation can the live verb 'enjoys' or the live verb 'exists' be made the grammatical subjects to live verbs. The philosophers description of a concept is bound to terminate in a stammer.

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 not true 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 sentences in which they are expressed. We achieve by moving into a semantic idiom what we could not have achieved without doing so. It is not only, as he somtimes put it, prudent to philosophise in a semantic idiom, on this account 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 'linguistic analysis' which was 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 the possibility of theorising.

It should be noticed that what is at stake here is not the reference of incomplete expressions. That they have a reference is something 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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reference to what they refer to in such a way that after having made such a reference we can then go on to say something true or false about what it is that we have made a reference to. The only way of referring to what incomplete expressions refer to is by completing the expression. But when we have done that we have not succeeded in saying anything true or false about the reference of the incomplete expression. ... is wise' says nothing true or false because it says nothing. If we complete the expression by inserting 'Socrates' in the argument place then we do say something true i.e., Socrates is wise. But in saying that we have not said anything about what the expression'.. . is wise' refers to. It follows, from this alone, that Michael Dummett's arguments in his first book on Frege do not extricate Frege from the problem to which his talk about a meeting of minds is directed. Here is what Dummett has to say about Frege's worries about the concept horse.

We can, therefore, truly say of what the expression 'the concept horse' stands for that it is not a concept, but an object; and, since we speak of that for which an expression stands simply by using that expression this means that we can truly say, 'The concept horse is not a concept but 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 particular concept it stands for, or to state for any relational or functional expression, which relation or function it stands for. Any attempt to say this must, it appears, lead to the formation of an expression which, by Frege's criteria, is a singular term, and by means which we have not therefore succeeded in referring to a concept (or relation or function) at all, but instead to an object.... Clearly if there were no escape from this dilemma-brought to light by Frege himself-this would be a reductio ad absurdum of Frege's logical doctrines

(pp. 2II-I2).

Dummett sees the problem here as merely one of the reference of incomplete expressions and proceeds using a suggestion of Frege's to show how we can sensibly talk about what an incomplete expression stands for. His central point is that we should not take the expression 'what "x is a horse" stands for' as a singular term and therefore we should not allow it to be inserted in the argument place of a predicate expression. Just as the singular term 'Mount Everest'




should be and indeed is substitutable for the singular term 'What "Mount Everest" stands for' so 'What "x is a horse" stands for' should be substitutable for 'x is a horse'. Since the latter is not a singular term it follows that the former cannot be construed as a singular term either but has to be itself construed as a pfedicate or an incomplete expression, i.e: it has to be construed 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 maintaining the idea that incomplete expressions have a reference. However, if what worries Frege is not the question of the reference of 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 Frege's remarks about a meeting of minds etc., are resolved once we have seen that we can construe the reference of incomplete expressions in a non-paradoxical way. The point is that when we do so construe them we can see why those remarks become so pertinent, and why Frege in his unpublished writings comes back to them time and time again. They do not constitute 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 between concept and object is of prime importance then what is required for communication is, queer as this may sound, not only agreement in definition but a meeting of minds or agreement in judgements. It is noticeable that Dummett makes no attempt whatsoever 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 that work in the context of Frege's problem it looks very different indeed from the way it looks if viewed from the background of general sceptical worries. I do not think that Wittgenstein ever was interested in epistemological worries as such. 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 knowledge is out of place. He asks, for example, what sense it makes



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to say that I know I am in pain, and he criticises Moore for replying to the sceptic who asks how he knows the propositions listed in 'A Defence of Common Sense' and 'Proof of an External World' by saying that he does know them. The question of knowledge is only to the point in situations where there is some doubt, whereas it would be difficult to know what doubting such propositions would amount to. Now we might ask why he should so urge that the concept of knowledge is only appropriate in situations of doubt and certainty. It is surely not, as some have thought, a question of usage. What is at stake is the relation of the concept of knowledge to truth and falsity. If I know that p then p is true. However, if we are operating in the area of agreement in judgements, if we have gone beyond agreement in definition, then whatever we say in that area will, as it were by definition, not belong in the area of saying true or false things, and will consequently not belong to the realm of things that I can be said to know or not know. It is the connection of the concept of knowledge with truth which locates it in the same dimension as that of doubt and certainty. When I am in doubt I am in doubt as to whether something is so or not, and when I am certain I am certain that something is so. When truth is excluded so are questions of doubt and certainty. Hence, if I am right in maintaining that Wittgenstein's notion of agreement in judgements, like Frege's idea of a meeting of minds, is only introduced at the point where saying true or false things is out of place, it follows that where such talk is inappropriate there talk of knowledge is inappropriate also.

The point can be illustrated by applying it to discussions of pain. If I say that I am in pain and someone asks me how I know, what is it that he wants to know about? The situation would have to be extraordinary if what he wanted to know was whether I am in pain, for I have told him that I am. Let us assume that it is not a question of him doubting my word.- The question is, of course, asked by the sceptical philosopher and what he wants to know about is the concept of pain. If I try to tell him about that by telling him what I know then all of the problems which beset Frege come flooding in. In this sense the sceptic's problems are not problems of knowledge at all. 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.

Finally, I think Frege's problem can help us with another much discussed term of Wittgensteinian art. When concepts prove




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 for saying of someone that he is in pain. Notice once more that what gives trouble is the concept of pain. Apart from special circumstances 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 than himself) is in pain. He is worried about the grounds for thinking so. It is therefore with regard to the concept that criteria are invoked. It is at this point that what we have learned 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 particular S that it is P we can do so after having measured it against 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 doubt just what 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 about the concept we are merely worried about whether a certain case falls under it or not. These are the kinds of cases in which Austin used to invoke criteria. How do you know that it is a Bullfinch? List the characteristics of Bullfinches. If it has those characteristics then it is one, no question. The person puzzled about Bullfinches 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 someone is puzzled about concept then any appeal to criteria has, of necessity to be different. If our worries are about P in the sense that it is the concept that we are worried about we shall be unable to move 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 proposition, we would have turned the concept into something 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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concepts to concepts, and this relating has to be a quite different enterprise.

Stanley Cavell in his recent book The Claim of Reason has his finger on this point. He does in fact say that for Wittgenstein criteria 'do not relate a name to an object but various concepts to the concept of that object'. The trouble is that in other place'she distorts this point by resorting, not without certain qualms which become altogether understandable 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 criteria he distinguishes between specific objects and generic objects. Specific objects he describes as such that the problem of knowledge they present is one of 'correct description, identification or recognition', whereas generic objects, the standard examples in traditional epistemology, '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 there'. He argues that Austin provides criteria when the knowledge in 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 Wittgensteinian objects then you lack, as it were, not only a piece of information or knowledge, but the possibility of acquiring information about such objects uiberhaupt. You cannot be told the name of that object because there is as yet no object of that kind for you to attach a forthcoming name to. The possibility of finding out what it is oficially called is not yet open to you (The Claim of Reason, p. 77).

This sort of talk can make it look as though Wittgenstein 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 entirely. With Frege in mind we can see how the sorts of distinction drawn in this passage reflect not a concern




for different sorts of objects but the crucial distinction between concepts and objects.

The passage which I have quoted which introduces the notion of agreement in judgement makes no reference to the term 'criterion' at all but it should be clear that the notion is playing a role there. When Wittgenstein says that 'it, is one thing to describe the methods of measurement, and another to obtain and state the results of measurement. But what we call "measuring" is partly determined by a constancy in the results of measurements' he is in fact making a point similar to the point about pain that I have just been making. What in effect he is saying is that amongst the criteria for the concept of measurement is a certain constancy in the results of measurement. Without such constancy in results there would be no such concept as what we call measuring.

When we correctly understand the difference between concepts and objects we see that concepts cannot, unlike objects, be made 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 problems then no accumulation of information is going to be of help with them. When criteria are evoked in cases where concepts prove troublesome they are not evoked as presenting the truth that will settle the issue.

The conceptual confusion of which Wittgenstein speaks is not just muddled thinking, due perhaps to ignorance or misinformation 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 we need to understand is agreement in judgements; seek for theory when what is in question is grammar.

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A Meeting of Minds