11 Rule-following
By ‘rule’ Wittgenstein does not mean an abstract standard according to which some act may be judged right or wrong. Rather he means a concrete item, such as a noise, mark or gesture, which is presented to a person and by attending to which they direct their behaviour, the link between rule and response being learned and conventional. An enormous number of human activities can be seen as instances of rule-following. They include imitating the gestures and noises which others make, copying shapes, converting marks into noises as in reading music, chanting the number sounds in sequence, and so on. More generally, both nonverbal behaviour in response to verbal instruction (fetching a book when told to do so) and also producing linguistic reports (where the world itself is the guide and the utterance is the response) may be described as rule-following. Rule-following is thus at the heart of linguistic competence. If we further accept that coming to use a rich and expressive language is an indispensable part of coming to grasp complex concepts and to make reflective judgments, then rule- following is also at the heart of our lives as thinking creatures.
It is generally agreed that Wittgenstein has telling negative points to make about one attractive but misleading picture of rule-following. On this picture, to understand a rule, for example, to grasp what is meant by ‘Add two’, it is necessary and sufficient to have a certain sort of item, an image, feeling or formula, occur in the mind when the instruction is heard. For example, having a mental image of two blocks appearing at the end of a line of blocks is the sort of thing which might be imagined to constitute understanding ‘Add two’. This image is supposed to do two things. First, it helps bring about that the person goes on to produce a particular response, for example, saying ‘Eight’ if the previously given number was six; second, it sets a standard by which that response can be judged correct or incorrect.
But the picture will not do. A person might have such an image while responding to ‘Add two’ as if it meant ‘Multiply by two’. Moreover their behaviour (the regular patterns of action, what seems to be regarded as a mistake, and so on) could show that for them, ‘Add two’ actually means ‘Multiply by two’. So images guarantee neither subsequent behaviour nor the appropriateness of a particular standard of assessment.
What this case makes us see is that an image, feeling or formula is merely another rule- like object (that is, a potential vehicle of meaning) rather than the meaning itself. An item is not automatically a self-interpreting sign, that is, one which fixes and enforces a certain reading of itself, simply in virtue of existing in the mind rather than in the outer public world. So images and the like are not sufficient for understanding; but neither are they necessary, since in many cases they do not occur. Typically when someone responds to everyday and familiar language they just act unhesitatingly and spontaneously, without consulting any inner item.
To teach someone to follow a rule, for example, to understand ‘Add two’, we put them through a finite amount of training, primarily by working through examples of adding two. These examples may appear to be another resource for pinning down meaning. But being only finite in number, they are bound to have more than one feature in common. Thus they do not themselves determine a unique interpretation for the sign we associate with them. A learner might exhibit a future bizarre divergence from what is expected, for instance by saying that adding two to 1000 yields 1004. And if this occurred it would suggest that they had all along been struck by some feature other than the one intended.
The central point here is that, for there to be meaning, the rule-followers must have fixed on one rather than another of the various similarities between the teaching examples and have associated it with the rule, that is, with the mark or sign to which they respond. ‘The use of the word ”rule” and the use of the word ‘’same” are interwoven’ (1953: §224 ). But neither the examples nor the rule itself determine which similarity this is; and imagined inner surrogates, in which we would like to see the relevant resemblance encapsulated, turn out to be equally inefficacious.
These reflections do not just undermine one picture of the psychology of understanding. They are also relevant to the picture presented by the Tractatus. If there were a fixed structure for world and language as envisaged in the Tractatus, then there would exist items, namely the simple objects, which would fix the one and only absolute standard of similarity. If there is a simple which is a common element in two separate facts then there is a basic real resemblance between those facts; if not, not. Every other real resemblance which can be meaningfully labelled, for example, by the predicates of everyday language or science, must be founded in simples. A putative linguistic expression which is not tied to some definite combination of simples is, on the Tractatus view, an expression without meaning which is merely randomly applied. Further, as we saw earlier, a simple is the kind of thing which, when apprehended, must be apprehended as it is. So representing a simple, whether by a direct cognition of it or by having in mind something which encapsulates its nature, is to be aware of a self-interpreting item, something which dictates what is to count as ‘the same’. But this sort of confrontation is what the rule-following considerations suggest to be unintelligible.
Thus the discussions of §§143-242 can be seen as interweaving with and reinforcing those of §§1-88. The whole undermines not only the idea of closeness of fit between a Tractatus world and everyday language, but the underlying conception of that world itself, namely as already determinately articulated into facts by simples which we can apprehend (see Meaning and rule-following §§1-2).
12 The later picture of meaning
The Tractatus offers us a world articulated, independently of our detailed human concerns, into value-free facts which are the subject matter of the natural sciences together with a mind confronting that world and attempting to mirror it in its thoughts. It also tells us that there is (in some sense) only one subject and that it is an item at the limit of the world which cannot act responsibly in the world.
However attractive the first element here, everyone would agree that there is something seriously wrong with the solipsism of the second. So one essential move in amendment is to reintegrate the psychological and the metaphysical subjects of the Tractatus, by making the self responsibly active, bringing it in from the limit and locating it firmly in the world, together with other selves. We may do this while leaving in place the idea of the world as the totality of value-free facts. Then the existence of the self which is now located in the world must be some subset of such facts. This yields an extremely powerful and attractive overall picture, namely the picture of reductive naturalism. But it also generates many philosophical puzzles, those to do, for example, with giving naturalistic accounts of consciousness, free will, rationality and so on.
This overall picture cannot be Wittgenstein’s, however, if §11 is right in its reading of the rule-following considerations. The idea of an independently articulated world is not acceptable to him. We cannot understand our concepts by pointing to simples which reveal themselves as the ultimate constituents in any world and so make evident to us the necessity and defensibility of our way of thinking. To understand meaning we must look at use, at how our actions and concepts are interwoven. The fact that makes a sentence true is grasped through seeing when the sentence is correctly used, and that in turn is grasped only by seeing the full shape of the language games in which it is used. For a concept to be truly applicable to the world, and so for its corresponding property to have instances, is not for it to pick out some simple which is among the timelessly given building-blocks of all worlds. Rather it is for the life of which use of that concept is a part to be liveable in this world. Wittgenstein thus moves from a form of the correspondence theory of truth in the Tractatus to a redundancy theory in the Investigations (see Truth, correspondence theory of; Truth, deflationary theories of).
The self need not, on this view, be an assemblage of value-free facts. Neither need we conceive it as a unique metaphysical limit to the world. It is rather a living, human locus of abilities, a person who can be trained to follow rules, to use and respond to language, in the way normal humans can. And since concepts are aspects of our way of life rather than items built into the one conceptual scheme and underpinned by simple objects, understanding what it is to have a particular concept involves ‘assembling reminders’ about how it works for us and how our various activities and ways of talking build together into our way of life.
If it is correct to conceive of understanding as an ability, then the exercise of this ability in everyday situations will often be just some confident, spontaneous action or utterance, which the subject will not be able to justify by pointing to something, other than the situation or words responded to, which guided them.
‘How am I able to obey a rule?’ – if this is not a question about causes, then it is about the justification for my following the rule in the way I do. If I have exhausted the justification I have reached bedrock and my spade is turned. Then I am inclined to say: ‘This is simply what I do’.
(1953: §217)
But this need not worry us. ‘To use a word without justification does not mean to use it without right’ (1953: §289 ). The fact is that we do find such confident and unhesitating responses in ourselves. Also we (usually) agree with others; and where we do not we (usually) agree on how to settle the dispute. So we have no reason to doubt that in general we do indeed mean what we take ourselves to mean.
Indeed we can put things more strongly than this. It is not just that it is sensible, practically speaking, for me to make a leap of faith and decide to carry on as if I and others mean what it seems we mean. We have no more choice about this than we do about taking ‘Eight’ to be the right response to ‘Add two to six’. The language game of ascribing meanings to the remarks of ourselves and others is as central and indispensable to a recognizably human life as anything in our linguistic repertoire. Moreover the rich and complex social world in which we find ourselves sustains our practice of so doing. So we and our meanings are just as much part of the world as the stars, rocks and trees around us. And since we are no longer committed to the idea of one totality of facts, those of value-free natural science, this recognition does not now produce cramps or pressures to reductive manoeuvres (see Private states and language §4 ).
13 Alternative readings
The account of §§10-12 presents Wittgenstein as inviting us to abandon the idea of our meanings and judgments being securely moored to something given to us and for which we have no responsibility. We see that there is no guarantee of any unique conceptual scheme to be revealed by analysis, or of a world articulated once and for all in terms of its categories. We are instead to become aware of our involvement in and responsibility for our own judgments and the way of life of which they are part. We are also to acknowledge that we cannot prove the unique correctness of our way of life and its associated concepts. (The arguments of the Investigations against the position of the Tractatus thus have much in common with themes explored by other late-nineteenth-century and twentieth-century thinkers, such as Nietzsche, William James, Heidegger, Quine and Derrida (see Nietzsche, F. §6; Heidegger, M. §§2-4; Quine, W.V. §5 ).) But, the reading given in §12 implicitly suggests, this need not lead us to scepticism about the notions of meaning, fact, objectivity or truth.
This interpretation, although not idiosyncratic, is by no means generally accepted. There are a large number of differing construals of Wittgenstein’s overall intention, many of which have in common that they present the consequences of abandoning the Tractatus view as more radical and/or more deflationary, than is suggested in §12.
One interpretation stresses a contrast between the Tractatus and the later writings which is different from any highlighted earlier. It takes the rule-following considerations to show that we cannot make sense of grasp of meaning which fixes truth conditions independent of our ability to verify that they obtain. The later Wittgenstein is thought to insist (as against his earlier self) that all meaning be explicated by appeal to assertibility conditions rather than such possibly verification- transcendent truth conditions and he is recruited onto the antirealist side of the debate in the dispute between realism and antirealism.
Another much discussed view is presented by Saul Kripke . If there were facts about meaning, he argues, they would have to be constituted by something about past behaviour or present occurrences in the mind. So §§143-242 can be read as showing that there are no facts about meaning. Our practice of labelling remarks ‘correct’ or ‘incorrect’ and ascribing ‘meanings’ to them has a role in our social life. But such linguistic moves do not have truth conditions. Instead they have only appropriateness conditions. We are licensed to make them when others in our community keep in step with us in certain ways in their patterns of utterance.
Yet a third interpretation takes it that Wittgenstein espouses relativism. One response to the idea that there are no simples is to take it that the world is a featureless mush or unknowable something. Any apparent structure in it is then imposed by us. Hence the familiar physical and social world we experience is a creation of ours. But there are several possible but incompatible ways of imposing structure, one of which we are physiologically and/or socially caused to adopt. So no judgment can claim to be ‘true’ in a non-relative sense; at best it can be ‘true for us’.
An important issue in assessing this third view is what status Wittgenstein intended for the sketched alternative ways of responding to language teaching. Certainly they need enough feasibility to dislodge the conviction that there is one and only one possible way of dividing up the world. On the other hand it is not clear that he takes us to be entitled to assert that there are conceptual schemes which are both incompatible with ours and also fully possible.
Many other readings are also possible, detecting in his writings elements of pragmatism, behaviourism and even deconstructionism (see Behaviourism, analytic ; Deconstruction; Pragmatism §2; Realism and antirealism §4; Relativism ).
A general question is whether Wittgenstein should be read as a philosophical theorist or as a therapist offering to relieve us of the impulse to construct philosophical theories. To take him to be offering anti-realist, sceptical or relativist views is to see him as a theorist. Those who read him as a theorist in his later work are also likely to favour a metaphysical reading of the Tractatus, seeing it too as expressing a philosophical theory, for example some version of realism. Other commentators (representing a mainstream view) see him as shifting from a theoretical stance in the Tractatus to a therapeutic one in the later work. Yet a third group favours a therapeutic reading of his intentions throughout and believes that the ideas offered in the Tractatus are much more similar to those of the later work than is often supposed.
This entry assumes that the second approach is right, at least in that the Tractatus embodies commitments which are, in effect, theoretical and which Wittgenstein later recognized and criticized as such. But it allows also that the third group may well be correct in thinking that Wittgenstein’s overt intentions always had a therapeutic aspect. (It may also be that the distinction between theory and therapy is less clear-cut than previously assumed.)
14 Philosophy of mind
The Tractatus picture of the relation of language to its subject matter is especially attractive in the case of some psychological notions. A sensation such as pain is easily conceived as a phenomenon which impresses its nature and identity conditions on one who has it, independent of external circumstances or bodily behaviour. The private language argument (§§243-71) examines this idea in the light of the earlier discussion of meaning. One aim is to show that our actual use of terms for sensations does not and could not conform to the pattern suggested.
The rule-following considerations suggest that no standard for what is to count as ‘the same’ can be fixed merely by uttering a word to oneself while being vividly aware of what one experiences. For one kind of item rather than another to come into focus out of the indefinite variety potentially presented in an experience, that experience must be embedded in one kind of life rather than another. Relatedly, for a word to have meaning there must be some extended practice in which its use has a point. This is as true of sensation words as of any others. We teach and use them in a complex setting of physical circumstances and expressive bodily behaviour. This setting, says Wittgenstein, is not externally and contingently linked to sensation but is an integral part of the sort of life in which the general category ’sensation’ makes sense and in which particular sensations can be individuated.
Wittgenstein considers many other topics in philosophical psychology, among them intention, expectation, calculating in the head, belief, dreaming and aspect perception. A constant theme is the need to counter the attraction of the model of name and object, which (together with such things as the special authority which each person has to pronounce on their own psychological states) leads us to conceive of the ‘inner’ as a special mysterious realm, distinct from the ‘outer’ or physical. He offers such general remarks as ‘An ”inner process” stands in need of outward criteria’ (1953: §580 ). He also returns repeatedly to the idea that authoritative first-person psychological claims should be seen as expressions or avowals of those states which we are inclined to insist that they describe. These sorts of moves have led to the idea that he denies the existence of the ‘inner’ and is really a behaviourist.
He was aware of the risk of this reading:
‘But you will surely admit that there is a difference between pain-behaviour accompanied by pain and pain-behaviour without any pain?’ – Admit it? What greater difference could there be? – ‘And yet you again and again reach the conclusion that the sensation itself is a nothing.’ Not at all. It is not a something, but not a nothing either!
(1953: §304)
Thoughts and experiences are, on his view, necessarily linked to expressive behaviour. ‘Only of a living human being and what resembles (behaves like) a living human being can one say: it has sensations; it sees; is blind; hears; is deaf; is conscious or unconscious’ (1953: §281). But this does not mean either that any reduction of the mental to the behavioural is possible or that the psychological is not real. To see Wittgenstein’s view sympathetically it is important to keep in mind the upshot of §§1-242. There is no a priori guarantee of some privileged set of classifications (for instance, those of natural science) in terms of which all others must be explained. To understand any phenomenon we must get a clear view of the language games in which terms for it are used; and the logical shapes of these may be very different from those which are initially suggested by the pictures which grip us (see Private language argument §§ 1-3 ).
15 Philosophy of mathematics
Platonism in mathematics involves two claims, that there is a realm of necessary facts independent of human thought and that these facts may outrun our ability to get access to them by proofs. Platonism is attractive because it accounts for several striking features of mathematical experience: first that proofs are compelling and yet may have conclusions which are surprising, and second that we seem to be able to understand some mathematical propositions without having any guarantee that proofs of them exist.
Wittgenstein never accepted Platonism because he always took the view that making substantive statements is one thing, while articulating the rules for making them is another. So-called necessary truths clearly do present rules of language, inasmuch as accepting them commits one to allowing and disallowing certain linguistic moves. Wittgenstein holds that it is therefore a muddle to think that such formulations describe some particularly hard and immovable states of affairs. Thus in the Tractatus mathematical propositions are treated together with tautologies as sets of signs which say nothing, but show the logic of the world.
Nevertheless the Tractatus view has some kind of affinity with at least the first claim in Platonism, inasmuch as the rules of our language, on which mathematics rest, are rules of the only logically possible language. But when Wittgenstein comes to see linguistic rules as features internal to our (possibly varying) practices, the resulting picture is unwelcoming even to this. We cannot now assume there to be such a thing as ‘the logic of the world’, whether to be shown or said. Instead, in Remarks on the Foundations of Mathematics , he explores ideas of the following kinds.
At a given time we have linguistic practices directed by certain rules. Someone may now produce a proof of a formula which if accepted would be a new rule – for example, ‘14+3=17‘. It is natural to think that to accept this is to unpack what we were already committed to by our understanding of ‘17′, ‘+’, and so on. But the rule- following considerations unsettle this assumption because they undermine the idea of an intellectual confrontation with an abstract item which forces awareness of its nature upon us and they also bring to our attention the element of spontaneity in any new application of a given term. Rather to accept the proof and its outcome is to change our practices of applying signs like ‘17′, because it is to adopt a new criterion for judging that seventeen things are present, namely that there are two groups of fourteen and three. Hence to accept the proof is to alter our concepts. What makes mathematics possible is that we nearly all agree in our reaction to proofs, and in finding them compelling. But to seek to explain this by pointing to Platonic structures is to fall back into incoherent mythology.
The present author’s own view is that it is persistent uneasiness with the first claim in Platonism which primarily motivates Wittgenstein’s reflections on mathematics. But those who see him as an antirealist will put more stress on hostility to the second claim (the idea of verification transcendence) and certainly some of Wittgenstein’s remarks (for example, his suspicion of the application of the law of excluded middle to mathematical propositions) have affinities with ideas in intuitionistic logic. A third reading will bring out the conventionalist-sounding elements, on which we choose what linguistic rules to adopt on pragmatic grounds.
In addition to reflections on the nature and use of elementary arithmetical claims, Wittgenstein also applies his ideas to some more complex constructs in mathematical logic, such as the Frege-Russell project of deriving mathematics from logic, Cantor’s diagonal argument to the non-denumerability of the real numbers, consistency proofs and Gödel’s theorem. His general line here is not that there is anything wrong with the mathematics but that the results have been misconstrued, because they have been interpreted against a mistaken background Platonism. Some mathematical logicians claim that Wittgenstein has not understood properly what he is discussing. His views on consistency and Gödel in particular have aroused annoyance (see Antirealism in the philosophy of mathematics §2; Intuitionism; Realism in the philosophy of mathematics §2 ).
16 Ethics, aesthetics and philosophy of religion
In the Tractatus Wittgenstein consigns ethics to the realm of the unsayable, and he takes the same line in his ‘Lecture on Ethics’ ([1929] 1993 ). Here he says that ethics (which he links to aesthetics and religion) arises from a tendency in the human mind to try to express in words something – roughly the existence and nature of absolute value - which seems to manifest itself to us in certain experiences. (He gives as an instance the experience of finding the existence of the world miraculous.) It is essential to this impulse that it seeks to go beyond the world and significant language; so it is bound to issue in utterances which are nonsensical. Nevertheless, he says, he has the greatest respect for this impulse and would not for his life ridicule it.
This position resembles the emotivism associated with logical positivism in distinguishing ethical utterances sharply from those of science (that is, those which are capable of rational assessment, and can be true or false). But it also differs from it in being, in spirit, an ethical realism, albeit of a mystical kind.
In his later writing he rethought his views on meaning, mathematics and the mind but did not return to any sustained discussion of ethics or aesthetics (although there are scattered remarks, particularly on the aesthetics of music, in Culture and Value (1980)). One interpretation of the later outlook, however, provides a hospitable setting for an ethical realism of a less mysterious kind, one which allows for the statement and rational discussion of truth-evaluable ethical claims. Philosophers of meta-ethics taking themselves to be working within a Wittgensteinian outlook have urged that our inclination to insist on a dichotomy between fact and value, or between cognition and feeling, should be resisted, as the outcome of the grip on us of some misapplied picture. Moreover Wittgenstein’s emphasis on attention to the actual workings of language could encourage a distinctive approach to first order ethical questions (see Wittgensteinian ethics §2 ). But he himself never developed this, nor does he engage with issues in political philosophy.
The later outlook enjoins us to study each distinctive area of language as far as possible without preconceptions. If we do this for religious language, Wittgenstein holds, we shall see that religion is not a kind of science and hence is not open to criticism on the grounds that, as science, it is unconvincing (see, for example, ‘Remarks on Frazer’s Golden Bough‘ ([1931] 1993) ). Some take it that this implies that no religious utterance can be properly subject to any criticism other than that coming from inside the same religious community or tradition.
17 Epistemology
One familiar traditional philosophical problem is that of scepticism, that is, whether we can rightly claim to know such things as that physical objects exist independent of our perception, that the world was not created five minutes ago and so forth.
Wittgenstein’s most extended discussion of these issues is in On Certainty (1969). He starts from the kinds of examples invoked by G.E. Moore in his attempt to combat scepticism, such as ‘Here is a hand’ and ‘The Earth has existed for a long time before my birth’ (see Moore, G.E. §§3-4 ). Moore is wrong, Wittgenstein thinks, in taking it that we are plainly entitled to assert that we know these things. But Moore is right in thinking that the claims form an interesting class. It is impossible to conduct life and thought without taking some things entirely for granted, and the propositions Moore identifies are the articulated forms of things which play this role for us. They help to define our world picture and underpin the procedures by which other claims (ones that are in fact doubted and tested) can be assessed. But they cannot themselves be assessed because there is nothing relatively more certain by which we can get leverage on them. Someone who seems to doubt them is thought mad and, from a first-person point of view, when I imagine doubting such things I contemplate a situation in which I would no longer know how to reason about anything. There are close links between these themes and the idea that the workability of any language game presupposes certain very general facts of nature.
The relevance of this for the traditional question of scepticism is that it is, in its form, misconceived. The central use of ‘know’ is in connection with propositions where testing is possible. Hence one who uses it in connection with the propositions which help define our worldview (as is in fact done only in philosophy and not in ordinary life) has extended the word to a situation where procedures do not exist for assessing either the first-order claim or the claim to knowledge of it. This is not to say that the word ‘know’ is unintelligibly and wrongly used in the philosophical debate. We can sympathize with the sceptical impulse, which springs from awareness of the fact that our language games are not based on grounds which compel us to adopt them or guarantee their continued success. But we can also sympathize with the anti-sceptical position which insists that acceptance of these central propositions underpins our being able to do any thinking at all, so that claims to doubt them are empty (see Scepticism ).
18 Wittgenstein’s conception of philosophy
In two central respects Wittgenstein stands squarely within the main historical tradition of philosophy, first in the nature of the issues which excited and intrigued him intellectually – meaning, the self, consciousness, necessity – and second (going back to the roots of the tradition) in his being a ‘lover of wisdom’, that is, one who is seriously concerned about having a right stance to the world both intellectually and practically and who is committed to the use of the intellect (among other things) in helping to achieve this.
But he differs from many philosophers in his conviction that a great number of traditional philosophical problems are the result of some deep kind of muddle, and in his belief that the answers given and the way they are debated hinder rather than help us in achieving wisdom. This conviction gripped him from very early on and philosophical thought therefore presented itself to him as a tormentingly difficult struggle to be honest and to free himself from misleading preconceptions.
So the word ‘philosophy’ has, in all his writings, two uses. On one it describes a body of confused utterances and arguments, arising largely from misunderstanding of the workings of language, and on the other it describes an activity of helping people to get free of the muddles. Another important continuity is his insistence that there cannot be philosophical theories and that the helpful activity of philosophy ought only to consist of making uncontentious statements, of describing and assembling reminders. In the context of the picture theory of meaning, this is comprehensible (see §7). But it is less clear that it is required by the later view.
In part Wittgenstein is here stressing that we cannot have the kind of explanation of our concepts which the Tractatus picture seemed to promise. Our form of life cannot be grounded but only described and lived. In part he is questioning the impulse to look for quasi-scientific theories of the nature of philosophically puzzling phenomena. But these two interrelated points do not obviously add up to a complete embargo on anything which could be called ‘philosophical theory’. It is in the spirit of the later philosophy to point out that there are many different kinds of things which can be called ‘theories’. Everyone engaged in reflection on the topics Wittgenstein considers (including Wittgenstein himself) finds it natural to articulate in words the states they arrive at and to engage with these words and those of others in the mode of further comment and assessment.
We become aware here, and at many other places, of the open-ended and unfinished nature of Wittgenstein’s reflections. His writings have aroused great devotion because of the honesty and depth which many find in them. But it is important not to treat them with superstitious reverence. Rather they should be read in the spirit in which he intended, namely as an invitation to explore with as much integrity as possible one’s own perplexities and what would resolve them.
