Monday, 10 December 2018

§§136-142: Meaning, Understanding and Rules


Annoyingly, this post turns back to reconsider §§136-142. I've written about these sections before (see here and here), but I don't think those posts grasped their full significance. For it seems to me that §§136-142 anticipate, or at least link up with, virtually all the main themes and arguments found in the rest of the book.

What I want to do in this post, therefore, is show how they relate to what comes after, with particular emphasis on the positive account of rule-following. So it's more of a springboard into the later sections than a simple exegesis of the material at hand.


Propositional form and bipolarity

In §136 Wittgenstein considers the connection between propositions and truth. The underlying target here is the Tractarian doctrine of bipolarity, which provides a fundamental element of propositional form. It is intrinsic to the concept of propositions that they can be true or false, and this reflects something deep about the nature of language (which in turn reflects something deep about the nature of the world). Importantly, it doesn't just mean that all propositions are either true or false; it further stipulates that that if a proposition is true then it must be possible for it to have been false, and vice versa.

This claim is bound up with the notion of sense. For a series of words to be a proposition at all it must picture a logically possible state of affairs. The pictured state is the sense of the proposition. But there is no such thing as a logically impossible state of affairs; beyond the logically possible there is only nonsense. So “The red door is two meters high” might well be false but it pictures a logical possibility and, as such, has a sense. By contrast, “Red is two meters high” doesn't picture a logical impossibility because it doesn't picture anything at all; it's nonsense. Likewise, “The door is the same as itself” doesn't picture a logical necessity; again, it's nonsense. We might put it like this: “Red is two meters high” cannot be true, and “The door is the same as itself” cannot be false – and that's why they lack sense. They fail to meet the requirement of propositional bipolarity.

Bipolarity and the rules of language

Thinking along these lines presents us with a distinctive conception of the rules of language. On the surface things are governed by more or less arbitrary conventions: we say “The door is red” rather than “Is red the door”, but this is just grammar. If we chose, we could alter it in various ways without changing the underlying meaning of our statements. But the surface conventions of grammar are constrained by the deeper rules of logical syntax. These rules govern the basic requirements of meaning itself – what can and cannot be said. As such, they set out the preconditions for any possible language. And these rules are not down to us; they come, as it were, from without.

More specifically, they mirror the a priori order of the world. The world is composed of facts – objects combined in a certain way. It is essential to objects that they can combine with each other, and the ways in which they can and can't combine are given with the objects themselves. Hence given the simple objects which form the foundation of the world we already have all their possible combinations into more complex states of affairs. Of these possibilities, some will obtain at any given moment while others will not. But it is clear from this that whatever obtains might not have, and whatever doesn't obtain might have. So states of affairs are intrinsically bipolar, and this is reflected in language, whose job it is to describe possible or actual states of affairs. Language too is intrinsically bipolar.

This amounts to a kind of hyper-realism regarding concepts. A proposition has a sense because it pictures a possible state of affairs. It is true if that state obtains and false if it doesn't. The names it combines to form its picture pick out discrete types of objects. If a word names a complex object (eg “horse”) then it picks out a possible object, since that combination of simpler elements might or might not exist. Even so, the possibility of the complex is given with the world itself. In other words, our concepts are given with the world. We say that both Red Rum and Mr Ed are horses (as opposed to, say, zebras or mules) and this simply reflects how things stand. The world draws boundaries: it groups these things together as the same and separates those things as different. “Sameness” is a feature of the world. Hence our concepts are correct or incorrect insofar as they match, or go against, these distinctions. If my language doesn't distinguish between horses and zebras then it is mistaken because it doesn't accurately reflect the structure of the world.

Bad pictures: “fitting”

It is this grand metaphysical vision that Wittgenstein is attacking in §136, but he doesn't confront the Tractarian doctrines head-on. Why not? Because the Tractatus is just an example of a broader way of thinking; it is the sort of thing we tend to produce when we think philosophically about meaning, knowledge, existence, etc. As such, the real problem lies not with specific doctrines, but with a whole tendency of philosophical thought. For Wittgenstein, the roots of confusion to lie further back in our ordinary forms of expression. One way or another these can produce a misleading impression, so that when we come to philosophise about something we start out facing the wrong way and go on from there. In §1, for example, Augustine's unduly narrow account of learning to talk gives us “a particular picture of the essence of human language”, namely that “the words in our language name objects – sentences are combinations of such names” (ibid). Such a thought fixes the framework of our enquiry and makes it a natural step to conclude that “Every word has a meaning. The meaning is correlated with the word. It is the object for which the word stands” (ibid). And we've just seen above an example of what that idea can lead to.

Wittgenstein calls these impressions “pictures” – meaning something like “conceptions” or a general way of looking at things (they are not to be confused with the mental images he discusses in relation to meaning and understanding). And the picture he takes exception to in the case of propositional form centres around the notion of fitting. He sets this out in §136b: “what fits the concept 'true', or what the concept 'true' fits, is a proposition. [...] What engages with the concept of truth (as with a cog-wheel) is a proposition”. Wittgenstein calls this a “bad picture” (§136c), but what's wrong with it? Well, it's not simply that it's incorrect; there is something undeniably apt about this way of putting things – and that's what makes the picture so hard to get away from. But as a straightforward account of the relation between propositions and the concepts “true” and “false” it is deeply misleading. Specifically, it tempts us to view that relation as a kind of pre-ordained structure written into the nature of the concepts themselves. And this “pre-ordained structure” is the logical form of the proposition.

What we are losing sight of here is that the statement “propositions fit the concepts of truth and falsehood” gives a figurative account of their relation. Propositions don't literally fit with anything, since they are not physical objects. Taken figuratively, the statement is harmless enough – indeed, it could be helpful in impressing upon someone the depth of connection involved (and therein lies its aptness). But, dazzled by the relentless consistency with which propositions can be designated as “true” or “false”, we can easily move from saying it's as if these concepts fitted to saying that they do fit – only “in a strange way” (cf §195). And this seemingly innocuous shift of emphasis sows the seeds of a full-blown metaphysical ontology, for it draws us into considering propositions as a ghostly kind of pseudo-object. They are “akin to” physical objects, with a range of analogous attributes (including the attribute of fitting), yet they are not physical. And it follows from this that they must operate within a realm which is “akin to” the physical realm only, once again, not physical.

Here we can either take the Platonist line and construe this realm as a kind of “alternative dimension” – a non-spatial space (!) in which the pseudo-objects (or “forms”) do their thing – or else we can see it in more Cartesian terms as the inner realm of the mind where propositions exist as thoughts. (In the Tractatus, Wittgenstein has it both ways: propositions are thoughts in the mind, but they reflect possible states of affairs, which exist in logical space.)

Fitting and rules

So Wittgenstein's objection in §136 to the notion of “fitting” can be seen as the first move against the philosophical conception of “the inner” (which is, of course, itself a misleading picture). This will reach its culmination in the private language argument, but throughout his strategy is the same: to show how the bewitching metaphysical vision is a misconceived reaction to the grammar of our language (cf Zettel, §55). Hence he points out that casting the relation between “proposition” and “true” in terms of “fitting” is like saying that “check” fits the king in chess (the king can always be checked, and only the king can be checked). But of course no-one is going to say that being checked is a mysterious attribute of the king; rather, it is simply a matter of the rules of the game. And in the same way, the rules of grammar always allow us to label a proposition “true” or “false”, and forbid us from doing so in the case of, say, questions or exclamations. As such, the connection between propositions and truth-functionality is definitional: it is part of the definition of “proposition” that they can be called “true” or “false”. So the metaphysical vision, spurred on by a bad picture, sublimates a grammatical rule and turns it into a law – not a physical or scientific law, but a logical one. In particular, it mistakes the timeless, imperative form of the rule (“You must always do this”) for an expression of a timeless, imperative truth written into the very possibility of existence.

Grammar vs logical syntax

Of course, such an assessment only works if you concede that grammar is not itself a reflection of the form of the world. Otherwise you will simply say that the reason grammar treats propositions as it does is because of the formal attributes they possess. This brings us back to the distinction suggested above between grammar (a matter of convention) and logical syntax (a reflection of a priori necessity). For we might argue that there's something crass about the comparison between chess and language in §136. The rules of chess are obviously mere conventions, whereas the rules of language have depth. Is it merely a matter of convention that “the red door is two meters high” makes sense but “red is two meters high” does not? Could we change that on a whim? The answer is surely no.

There are at least four areas where rules seem to run deeper than conventions ever could: logic, language, mathematics and ethics. Here our rules seem to come to us from without, as if they were discovered rather than invented. Wittgenstein's task in the Investigations is to expose the incoherence of this picture, while at the same time doing justice to the important truth which it reflects – albeit in a confused, distorted manner. The crucial step in this regard is to uncouple meaning from objects. The meaning of a word is not the object it signifies (§40), but its use in the language (§43). Hence the rules of language (its grammar) are not tied to the combinational possibilities of objects but rather express a way of living. They do not reflect the a priori form of the world (for there is no such thing); insofar as they reflect anything it is our contingent form of life.


Understanding and fitting

The interlocutor now shifts the focus from “fitting” in relation to propositions to a word's meaning fitting the sense of a sentence, or fitting the meaning of another word. This is an indirect attempt to defend the notion of propositional form, since if we allow that word-meanings fit each other (like jigsaw pieces) then, as before, we are presenting them as pseudo-objects – and in that case, the sentence we get by slotting them together will obviously be a more complex pseudo-object.

Note how the interlocutor's objection equivocates between two slightly different positions. On the one hand we have the notion of a word's meaning fitting the sense of a sentence, but on the other hand we have the notion of word-meanings fitting each other. This seems to cast meaning itself as an inner object which goes proxy for its physical counterpart. But it's the physical counterpart that's supposed to be the meaning! And if meaning is an inner object, what work is left over for the “outer” object to perform? For if I have the picture then I already have the meaning! But in that case, what's the difference between the correct and incorrect use of words? How can I tell the right picture from a wrong one? How can there so much as be a “wrong” picture?

Here we see how easily a hyper-realist account of meaning can slide into something like Idealism once we focus on the actual process of meaning something by a word. And the nub of the problem seems to reside in our account of the workings of the mind. This part of the puzzle is almost entirely ignored in the Tractatus, but it lurks behind the scenes, and is about to be dragged centre stage.

Leaving aside the Idealist implications, however, isn't this talk of meanings “fitting” each other open to exactly the same objection as before? Can't we write it off as another bad picture which mistakes grammatical rules for a description of metaphysical necessity? Wittgenstein more or less makes the same point: “if the meaning is the use we make of the word, it makes no sense to speak of such fitting”. Now, however, the interlocutor plays his ace:
But we understand the meaning of a word when we hear or say it; we grasp the meaning at a stroke, and what we grasp in this way is surely something different from the 'use' which is extended in time! (§138)

The basic point here is relatively straightforward and appealing: when I understand a word – say, in a conversation – I grasp its meaning in an instant. The meaning is here with me now, whereas the use is out there in the world, scattered across diverse times and places. The word slots into its place like a jigsaw piece and that's that; I don't have to work out the meaning by recalling various examples of its use. So what I grasp – the meaning – isn't a use.

Note how our focus has now shifted from the logic of language to the psychological concept of understanding. As promised, theory of mind is taking centre-stage, and soon a host of interrelated phenomena will make their appearance: intending, believing, thinking, remembering, willing, etc. What this amounts to is a shift from considering meaning as a noun (“the meaning of a word is the object for which it stands”) to considering it as a verb. Meaning is something we do. This active quality is perhaps more obvious in the case of understanding; for to say “the understanding of a word is the object for which it stands” hardly makes sense, unless it's an odd way of saying something like “by a given word I understand the object it signifies”. And we might make the same point with regard to meaning; we can present it as a noun, but that's just another way of saying “by a given word I mean the object it signifies”. (This alone puts considerable strain on the claim that meanings are objects. For it is not like the case of “hammer” used as both a noun and a verb. I can have a hammer without ever hammering anything.)

A mythology of meaning and understanding

Very well, but what does this “doing” amount to? The obvious candidate is a mental act of some kind. That much is already implied in the interlocutor's remark when he speaks of understanding as grasping a word's meaning. (Notice, however, that “grasping” in this context is somewhat metaphorical. It is modelled on the physical act of taking hold of something. This ought to arouse our suspicions.) Likewise, it is at least tempting to suppose that meaning involves a similar mental act. This seems to be Wittgenstein's position in the Tractatus. For although he brushes aside questions about the mind as none of his business, he does offer up one hugely revealing comment:

We use the perceptible sign of a proposition (spoken or written, etc) as a projection of a possible situation.
The method of projection is to think out the sense of the proposition.
TLP 3.11

Here a proposition is connected to a possible situation by an act of thought; the proposition's sense is, as it were, calculated (or constructed) out of its constituent components. Hence meaning and understanding are inner processes. The exact nature of these processes is purportedly the business of psychology, not logic – and yet we are already committed to a general conception of meaning as a mental event (cf §308). This seemingly innocuous step brings in its wake a large array of interrelated themes and ideas:

  • Understanding – grasping a word's meaning – is an inner-process which stands behind speaking and hearing.
  • It is this inner-process that marks the difference between language as a meaningful activity and mere behaviour – the manipulation of dead signs.
  • Hence the inner-process adds value to our words. For only meaningful language can be correct or incorrect; the manipulation of dead signs, on the other hand, is a “blind” process. It simply does what it does.
  • The inner-process is one that I have direct access to. I experience it. So when I understand I know that I understand without further ado.
  • I don't have direct access to the understanding of others. Hence there is a radical asymmetry between first-person and third-person cases. In a third-person case I deduce that they understand based on their correct use of the word. Their performance is evidence of understanding.
  • If I understand a word's meaning I use it correctly. I use it correctly because I understand. So the inner-process of understanding produces correct usage, like the output of a machine.
  • The process, however, is clearly not a causal one, for a causal process can only produce the manipulation of dead signs – and the process of understanding is the difference between dead signs and meaningful language.
  • The process is logical, not causal. It represents the recognition of the possible legitimate combinations of a word with other words.
  • So the process contains within it all the possible applications of a word. New ones are not discovered later, as a kind of surprise – as if, having said “the cat is on the mat”, I was then surprised to find that I could also say “the cat is on the chair”. If I don't know in advance that “cat” can be used in both those sentences (and countless others) then I don't understand the word.
  • The process therefore acts as the rule for the use of a word – not in the sense of a “convention”, but as a deep rule: a recognition of underlying logical form.

And now we're back where we started.

We can see from this how the interlocutor's appeal to understanding and meaning as inner processes links directly to the defence of logical form, and as such represents a challenge to the idea that meaning is use. And it should also be clear that these concepts are further interwoven with rule-following. They go hand in hand. So clarifying the notion of meaning and understanding necessitates the clarification of rule-following as well (this task begins at §143, and not at §185, as is sometimes suggested). In some ways this is new territory – that is, it doesn't relate to explicit theories in the Tractatus. But it is still part of the same enquiry in that it investigates a tempting conceptual picture which the Tractatus simply takes for granted. Moreover, as already noted, the Tractatus is being used as a typical example of philosophical thought more generally. The idea that meaning and understanding are affected via some kind of inner process (usually involving mental representations) is a common assumption in both Rationalism and Empiricism. It's there in Descartes, Locke and Hume, Russell and Frege – and it's also there in Kant, Hegel and the post-Hegelians (at least up until Sartre). In current philosophy it is a central tenet of cognitive science. Wittgenstein is taking on a sacred cow.

Understanding and correctness

The boxed comment at the end of §138 provides one step towards undermining this bad picture. Must I always know whether I understand a word? Clearly the answer is no: it frequently happens that we suppose a word means one thing, whereas it actually means another. This in itself contradicts one element of the mythology: the suggestion that if I understand something then I cannot help but know it – I cannot be wrong about it. But of course I can be wrong about it, and this raises the issue of correctness. Up till now it's been assumed that the business of fitting more or less took care of itself – after all, a jigsaw piece can only fit with certain others. But if that's how it works, then how could we ever be wrong about the meaning of a word? It would be like trying to put a square peg in a round hole and somehow supposing it really did fit. Using words wrongly would be more like insanity than a simple mistake.

But the implications run deeper, for now we're forced to ask what shows whether or not I genuinely understand a word. And the answer seems to be: how I use it. I can be as sure as you like that I do understand, but if I don't use the word correctly then, for all that, I don't understand it (cf §202: “to think one is following a rule is not to follow a rule”). Therefore the criterion of understanding that applies to me in a first-person case is the same one that I apply to you in a third-person case. So, at the very least, the privileged status of the first-person case seems less straightforward than we supposed. (Note that we're not denying there's a difference between the two cases; but it doesn't seem to be the difference between knowing and guessing.)



§139 continues the interlocutor's objection to meaning as use: when I hear a word that I understand, its use doesn't come before my mind yet I know what it means. Wittgenstein grants this but reiterates the point that meaning is determined by use (note, however, that he doesn't grant that understanding is essentially a matter of something coming before the mind). How can meaning be both something that comes before our mind when we understand and the way a word is used? And how might these two aspects come into conflict? If “understanding” equates to grasping an inner Something (ie, meaning) which generates use, then once we have the meaning we have the use – so how can there be conflict between the two?

To examine the question more closely, Wittgenstein suggests a picture as an example of this “inner Something”. (Obviously this is a nod towards the Tractarian picture theory of language but, as we've already noted, its implications run far wider.) So if I have a picture of a cube in my mind, how can this fail to fit with the use of a word? The interlocutor's account is appealingly straightforward: if I use the word to signify (eg) a triangular prism (by pointing to the prism and saying “cube”) that use doesn't fit the picture, because the picture is of a cube, not a triangular prism. In this way the picture establishes correct use by acting as a sample – and therefore as a rule for the use of the word.

Wittgenstein, however, objects with a rather startling question: “But doesn't it fit?” He then elaborates: “I have purposely so chosen the example that it is quite easy to imagine a method of projection according to which the picture does fit after all” (“method of projection” here is a direct reference to TLP 3.11).

This is a crucial moment in the Investigations, so it's worth spelling things out. First, how might the picture and the use fit? Perhaps not too easily if the picture is like this:

picture a

But how about this:

picture b

This too is a picture of a cube seen from a certain angle – and it matches up with (can be projected onto) a triangular prism seen from a certain angle. On this interpretation the picture fits the use.

If that seems like a bit of a cheat it's only because we've been taught a typical way of picturing cubes (drawing them, etc) and applying such pictures in various situations. In other words, we've been taught to use a certain configuration of lines (as in picture (a)) to represent cuboid objects. So actually the “cheating” runs the other way. The inner picture is supposed to govern the use of a word by “exhibiting” a standard of correctness – as if the standard “radiated out” from it. That seemed to be the case with picture (a), but only because we already have an established standard (a typical use) for such pictures: the one we learnt as children. Hence “The picture of the cube did indeed suggest a certain use to us, but it was also possible for me to use it differently” (§139).

Pictures and “the same”

Here we should note how it's easy to think that pictures, unlike words, are inherently representational. The word “cube” is obviously nothing like an actual cube, whereas a picture (we suppose) unmistakably represents cuboid objects because they're the same. That is, their sameness is a fact – it's “out there in the world”, rather than a convention established through use (we've already noted this suggestion with regard to conceptual realism). And this is why we're tempted to latch words onto pictures as a theory of meaning; it seems to create an unbreakable bond between the word and what it signifies. But Wittgenstein's objection draws attention to the fact that “same” and “different” are reactions or judgements, not inherent qualities of objects. As such, they are an expression of our form of life (see also the boxed comments at the end of §139). I don't think it's too much of an exaggeration to say that this point about sameness lies at the very heart of the Philosophical Investigations. In various guises it crops up over and over again – as we shall see.

Let's return to the “cube” example. I said that picture (a) wouldn't easily fit with the triangular prism, but that doesn't mean it can't be done. Suppose, for example, I'm presented with a sphere and a triangular prism. I have picture (a) in my mind and I point to the prism and say “cube”, because if you cut a cube in half you can make two triangular prisms (which can't be done with a sphere). So, again, on this interpretation the picture matches the use. But! By the same token, it's not too hard to produce an interpretation according to which picture (a) would fit with pointing at the sphere, not the prism (think of their respective planes of symmetry). And you can take this process as far as you want; according to some interpretation anything can be made to fit with anything else.

What it comes down to is this. The picture is supposed to act as a sample, but without a pre-existing method of application (a use) to establish what the picture is a sample of, we're just plucking connections out of thin air. Anything, or nothing, will be correct – and “that only means that here we can't talk about 'correct'” (§258). At a foundational level, it is not the sample which establishes use, but the use which establishes the sample as a sample.

This is a crucial insight, though in fact we've met it before. It flows directly from the observation in §28 that “an ostensive definition can be variously interpreted in any case” – for an ostensive definition gives a rule for the use of a word by providing a sample (“This is 'red'”). It then re-emerges in §§86-87 where because a rule can be variously interpreted in any case it seems like we need an infinite chain of them, each one explaining its predecessor. And we meet it again in the “add 2” scenario in §§185-186. There the pupil reacts to the rule “add two” in a way the teacher doesn't intend. From the interlocutor's point of view, the intention (or meaning) is akin to a sample (or rule) in the teacher's mind, and the problem arises because the pupil has grasped an inner sample that doesn't fit. But again Wittgenstein responds by asking (in effect) “who says they don't fit?” He goes on in §198 to draw a conclusion analogous to the one mentioned above: “Interpretations by themselves do not determine meaning”. And then, in §201: “what we thereby show is that there is a way of grasping a rule which is not an interpretation, but which, from case to case of application, is exhibited in what we call 'following the rule' and 'going against it'”.

What, in general terms, is the difficulty we're up against? I think it can be put like this. It is tempting to suppose that both meaning and understanding are essentially a matter of calculating or interpreting or figuring out. So when I say a word I mentally stamp an interpretation on it; I calculate that this is the right word in this context. And when I hear a word I figure out or calculate its meaning through a complementary act of interpretation. But calculations and interpretations stand in need of justification. Suppose someone says “My mastiff has fleas”; I don't know the word “mastiff” but I guess from the context that it's a dog of some kind. I will now need to confirm my guess – by looking up the word in a dictionary, for example. But of course if I also have to interpret the dictionary definition then I'm no further forward; I now need to confirm my interpretation of the definition. If meaning is to be established then interpretation has to end in something which is not itself an interpretation. For the interlocutor, this can only be a sign (eg, a picture) which somehow contains its own definition (or method of application). This we might call the “magical sign” theory of meaning. And Wittgenstein's protest throughout is that there's no such thing; a sign is a sign is a sign. So what does bring interpretation to an end? We shall get to that in the discussion of §142, but actually there is a clue in the boxed remarks at the end of §139.

Natural reactions

Of these, (b) is the most directly relevant to the section, as it gives another example of a picture we're inclined to use one way but which might be used differently. Note how this puts the emphasis on our inclinations rather than anything inherent in the picture. We react to it in one way; a Martian might react in another. And, of course, we have been taught to react in this way – so it's a case of “second-nature”. But second-nature is built upon first-nature; it is a refinement.

Comment (a) is a more general remark about “fitting”, and makes a telling connection with the notion of aptness. A word can fit a sentence in the sense of being apt, just as we might consider a glass of cognac a fitting end to a sumptuous meal (but not to, say, beans on toast). Here it is obvious that we don't mean “fitting” in a literal or quasi-physical sense – like a plug fitting into a socket. As in (b), it is rather a matter of our natural reactions.


Logical compulsion

So in a normal case we tend to take a picture in a particular way without possible alternatives occurring to us. This can create the illusion that a picture forces a use upon us. In §140 Wittgenstein calls this the illusion of “logical compulsion”, but what does he mean by that term? Well, suppose we think along the following lines. A picture can represent an object, but the essence of this relationship does not really lie in their looking the same. After all, we wouldn't mistake a drawing of a face (☺) for an actual face. Rather, what they share is a configuration of elements. The basic components of the picture-face stand to each other in the same relation as the basic components of a human face. That is, they share the same logical form. So long as they both have this form in common, a sign can depict an object even though it looks nothing like it – hence ink on paper, for example, can depict snow falling on a mountain. The syntax of the sentence mirrors the form of the thought it expresses, and the form of the thought, in turn, mirrors the form of the state of affairs it depicts. And, importantly, what links sign and object on this account is not a similarity or resemblance; they literally have the same form. That's why the connection between them cannot be missed – it would be tantamount to supposing that an object wasn't identical with itself.

Something along these lines is as close as I can get to making sense of logical compulsion. And really it just seems to be an imposing statement of ideas we've already discussed: the picture is inherently the same as the object it signifies; it carries within it its method of application. In other words, it is a magical sign. But as we've seen, this sublime account is exploded by the simple observation that the same picture might represent different objects, and different pictures might represent the same object. The notion of inherent sameness is an illusion.

Psychological compulsion

But what's left to us if we reject this account? Well, we've said that the illusion of logical compulsion arises because it often only occurs to us to take a picture in one particular sense. Aren't we therefore dealing with a psychological process such as automatic association? Certainly it's tempting to cash things out in this way: I associate a word with a picture and a picture with an object, and that's why only one application of the picture tends to occur to me. So “we're at most under a psychological, not a logical, compulsion” (§140). Having raised this possibility, Wittgenstein doesn't directly endorse or reject it. Instead, he cryptically remarks that “now, indeed, it looks as if we knew of two kinds of case”. This at least seems to favour psychological compulsion, since the implication is that logical compulsion doesn't even amount to a genuine case; it's an illusion.

But we should be wary here. Just because psychological compulsion is an established phenomenon in our lives doesn't mean it must be the answer to our problem. Furthermore,
there are strong reasons for rejecting it as the foundation of meaning. For a start, the move from logical to psychological compulsion is roughly equivalent to the move from Rationalism to Empiricism – and that in itself should make us pause, since Wittgenstein wants to reject both of those positions. More explicitly, psychological compulsion is a causal phenomenon, covering features such as conditioned behaviour, phobias, habitual reactions, etc. As such, it cannot help us make sense of concepts such as “meaning”, “understanding”, “knowing” and “rule-following”. For these are intrinsically bound up with the notion of correctness, and correctness plays no part in causal accounts. When magnesium reacts with water, it isn't acting correctly (or incorrectly). It's simply doing what it does. Likewise, if a certain word always gives rise to a particular mental image (perhaps through conditioning) then so far there is nothing correct or incorrect about what happens. For the image to be the correct response to the word you need a pre-established standard against which to judge what happens. In other words, you need a use.

Wittgenstein wants to reject the notion of logical compulsion but retain the distinction between a logical account of language and a causal one (cf §220). We can present this as a distinction between reasons and causes. For when we use a picture as a sample (ie, as a rule) the sample is the reason for what we do, not its cause. It is what we point to when justifying our actions as correct (cf §§217, 230). But casting this legitimate distinction in terms of logical compulsion gives us a “bad picture”, just like the notion of of “fitting” with regard to propositions and words. And the picture is bad for pretty much the same reason: it invokes an inner realm modelled on an analogy with physical objects and their interaction. So the notion of “fitting” casts propositions and words as pseudo-objects, and “logical compulsion” presents us with a pseudo-process – something that's analogous to a physical process and yet (somehow) is not simply a matter of causation. The problem with logical compulsion, therefore, is that it's too close to its Empiricist counterpart – and that hardly suggests that Empiricism provides a better alternative.

At the same time, however, Wittgenstein is perfectly willing to admit that everything hinges upon our natural reactions. Indeed, he insists upon it (see §143, §185, §198 and §242). Doesn't this amount to an endorsement of psychological compulsion? No. It recognises that in the context of a human life an act can be unreflective – or even automatic – without therefore being mindless. We tend to assume that if our behaviour is not the result of explicit deliberation (figuring things out, interpretation) then it must be rigidly causal or machine-like. But this simply overlooks the fact that, when it comes to living beings (especially human beings), our concept of action is not so starkly dualistic. We shall return to this point when we discuss §142.


Picturing the method of application

We've seen that a picture cannot by itself provide a foundation for meaning since it lacks a method of application. But couldn't such a method come before our minds along with the picture? If we mean by this that we get the picture plus another picture showing how to apply it, then the answer is no. For we would then need to know how to apply this second picture. Would that require a third picture? And now, of course, we've reached a regress of interpretation.

But can't an application come before my mind? Faced with this question, Wittgenstein makes a characteristic move: he suggests we clarify the use of the phrase “the application came before my mind”. The point here is that a flat denial seems to deny that people ever suddenly understand something or grasp in an instant how they should continue. That would be a startling discovery. Yet affirming the phrase seems to entail something equally amazing: that an infinite number of pictures flash into our minds, or else there's a magical picture – a picture that tells us what to do like a voice from the Beyond. In this way, the phrase “the application came before my mind” presents us with another misleading picture; it easily prompts us into conjuring up occult processes that seem both impossible and inescapable. The way out of this quagmire is to set the picture in motion, because that's when we see what it actually amounts to – the role it plays in our lives. As Wittgenstein comments in §423: “The picture is there. And I am not disputing its validity in particular cases. – Only let me now understand its application”. Clarifying the function of this picture will be a central concern of the Investigations from §143 onwards. In §141, however, we're given a scenario and invited to work through its implications for ourselves. So let's do that.

Grasping in an instant

Suppose I have been teaching a pupil to produce a number series using two formulas: (a) “n+2”, and (b) “nx2”. Now I test the pupil by writing “2, 4, 6” and asking her to continue the series using the correct formula. (This scenario is close to the examples considered in §151 and §185.) Let's consider some of the various things that might happen.

i) She thinks for a few seconds and then, with a sense of relief or sudden confidence, the formula “n+2” occurs to her (either as a picture or spoken words). She cries “It's n+2!”, and writes “8, 10, 12”.

ii) She suddenly realises that the numbers in the sequence increase by two each time. She sees that the next number must be 8 and now the formula “n+2” occurs to her. She cries “It's n+2!” and writes “8, 10, 12”.

iii) She spots the pattern of increase, as in (ii), and writes “8, 10, 12” but the formula itself doesn't occur to her. We ask which formula she has demonstrated. Imagine: (a) she says “n+2” without hesitation; (b) she guesses “n+2”; (c) she says “nx2” without hesitation; and (d) she can't give an answer.

In which of these examples does the application came before the pupil's mind? The answer seems to depend on what exactly we're testing her for – that is, it depends on the circumstances of the case just as much as whatever images pass through her mind. If we merely want to see if she can continue the series then we might well allow all three cases – including (iiic). If we want to see if she can continue a series and match it up with a formula then (ii) and (iiia) are fine, but not (iiib-iiid). But if we want to see if she can derive a formula from an example and then use that formula to continue the series we might object to both (ii) and (iii) since in those cases she at most associated the formula with the continuation. In other cases we might object to (i) on the grounds that it was merely the formula, and not its application, that came before her mind. Yet in (i) the occurrence of the formula was clearly the key to her subsequent correct application. Isn't that enough? Again, the answer will depend on the circumstances of the case.

The point here is that the phrase “the application came before her mind” does not simply refer to a particular play of mental images. In many cases it's just another way of saying “she got the answer”, while in others her specific train of thought is more important. But throughout its meaning is conceptually (grammatically) bound up with what happens both before and after any mental images occur. It is when we take the phrase as a straightforward description that it becomes misleading, because then it suggests that “understanding” is a matter of mental objects parading themselves in the private theatre of the mind. Some further examples might make this clearer.

iv) The pupil pictures “n+2” as in (i), but then gets stuck when she tries to write the answer. Here the application hasn't come before her mind, even though her mental image matches a case in which it did. Indeed, we might even suppose she pictures “n+2” and “8, 10, 12” but still can't see the connection between those images and what she's supposed to write. Here again in some circumstances we would say the application hadn't come before her mind – but in others we might say it had. The mental picture is not in itself sufficient to warrant the use of the phrase. We might also say that thinking you understand is not the same as understanding (cf §202 for the connection between this, rule-following and private language).

v) Now let's imagine we've written the two formulas on cards, so the pupil has to choose the right card and then continue the series (this draws on the suggestion in §141b that a physical picture will do just as well as a mental one). She glances between the numbers and the cards for a few seconds and then says “that one!”, pointing at “n+2”. Then she continues correctly. Again, I think we'd say that the application had come before her mind – but are we really to suppose that this was a matter of her inwardly picturing the formula she was looking at? (Can you do that? Stare at something and picture it to yourself while staring at it.) So not only is a mental picture not sufficient; it doesn't seem to be necessary either.

But is there no connection between what goes on in her mind and giving the right answer? Is it just a matter of writing “8, 10, 12” when presented with “2, 4, 6”? Of course not. We wouldn't say the application had come before her mind if she'd cheated or guessed. We want the pupil to write “8, 10, 12” because “n+2” occurred to her – that is, we want her to think of the correct rule and then follow it, not just write something that's in accordance with it. But “thinking of the right rule” does not simply mean having this or that mental image. And that's because following the rule (as opposed to merely acting in accordance with it) is a criterion of having thought of the rule (as opposed to merely having pictured it). To see this, consider the following example.

vi) The pupil has the mental image “n+2” and continues “8, 10, 12”. But when we question her afterwards she cannot explain why “n+2” gives that continuation. It was just that the mental image produced in her the urge to go on as she did. Here we would not say that the application came before her mind, even though she pictured “n+2” and continued in accordance with the rule. And the reason is that she didn't follow the rule. Does this mean that in order to follow the rule she must use it to calculate her result? Not necessarily:

vii) Suppose the pupil can add fluently. So now when we instruct her to continue the series “2, 4, 6” she writes “8, 10, 12” without having to think about it (and this, by the way, is an example of an action which is automatic yet not mindless). But when we ask her to explain her answer she does so in the normal way: “each number is two higher than the previous one, so I went on adding two – six plus two is eight, and so on”. Did the application come before her mind? No – that is, the correct solution didn't suddenly occur to her, because she was never in any doubt. Did she calculate her result using the rule? No; she just wrote “8, 10, 12” as you or I would do. But did she follow the rule? Yes: the rule was her justification for her answer; it was her reason for continuing as she did. She was, we might say, committed to the rule – and in that sense the rule compelled her. But here “compulsion” is more like acting out of duty than being carried along by a mysterious force.

The clash between picture and application

Let's recap. In §139 we noted that a picture, of itself, does not fit or fail to fit a use. That is, any given picture can be brought into line with, or made to clash with, any given use via a suitable rule for its application (a method of projection). It seemed like a picture forced an application on us, but that was just because we overlooked the various ways in which it might be used. Then, prompted by Wittgenstein's invitation in §141, we considered in what sense a method of application might come before our minds. This too turned out not to be a simple matter of visualising something (eg, a rule) – indeed, the visualisation need not be mental at all. Rather, it is conceptually bound up with the circumstances within which the rule occurs to us.

In §141c, Wittgenstein swerves back to the question of the way in which a picture might clash with an application. “Well, they can clash in so far as the picture makes us expect a different use; because people in general apply this picture like this”. So a picture can only clash with (or fit) a use if there's an established practice of applying it. This foreshadows Wittgenstein's likening of rules to customs in §§198-199, and his claim that there could not be only one rule followed on only one occasion (§199).

And, of course, it relates to the issue of an application coming before one's mind. For to say that an application comes before my mind presupposes that the application has already been established as a practice. That is the context within which it makes sense to say that the application occurs to me. Otherwise whatever comes before my mind is meaningless (cf §6d). Meaning requires a practice (a use); it cannot be willed into being by a mysterious mental act (“a hocus-pocus that can be performed only by the mind” §454).


Normal cases

At the end of §141 Wittgenstein reiterates the importance of normal and abnormal cases – it is because there is a normal case that we can go awry in an abnormal one (and hence a picture can clash with its application). He expands on this at the start of §142: “It is only in normal cases that the use of a word is clearly laid out in advance for us”. If you're familiar with the discussion of rule-following (§§185-242) then the phrase “laid out in advance for us” ought to be striking. It echoes phrases that reoccur in that discussion as an articulation of logical compulsion: “The steps are determined by the formula” (§189); “The machine seems already to contain its own mode of operation” (§193); “the beginning of a series is a visible section of rails invisibly laid to infinity” (§218); and “All the steps are really already taken” (§219).

But in §142 it is not the formula (or rule) that lays things out; rather it is the custom of applying such rules in a particular way. We are taught to apply the rule “like this” and we practice the application until we become fluent. And now it's as if the steps are already taken – but that's just a figurative way of saying that as I go about my business I'm not at all puzzled by what to do next (cf §238). So what seemed like a ghostly logical force turns out to be a matter of my reactive capabilities (we've already seen an example of this in case (vii) above).

Abnormal cases and interpretation

In a normal case language runs on smoothly, but abnormal cases are likely to catch us out or give us pause for thought. So, for example, I tell someone to wear a black tie to a funeral and he turns up with it tied round his wrist, because that's the custom where he's from. For me, his custom is an abnormal case, but for him it's the other way round. And if he was familiar with both customs he might wonder whether I meant him to wear the tie on his wrist or round his neck – that is, he would try to interpret my instruction, or figure out what I meant. But if there was only one custom, and we were both familiar with it, then no such interpretation would be necessary; it simply wouldn't cross his mind that there were other ways in which a tie might be worn – and nor would I have to stipulate “wear a black tie round your neck”. In a normal case there is no gap between a picture and its application, a word and the understanding of the word. It is only in ambiguous cases that there's a need to interpret – to figure things out. And in such a case successfully figuring things out amounts to closing the gap. So if my friend is unsure whether I mean him to wear the tie round his head or round his neck he will ask me and I will tell him; he doesn't need me to further explain what I mean by “round the neck”, even though here too a doubt is possible. For both of us “wear the tie round your neck” is a normal case and so he can apply the phrase without having to think about it. The gap has been closed.

The same

It's worth noting that we can express this point in terms of doing the same. So, in a normal case we're untroubled by the question of what counts as “going on in the same way”; it's business as usual and we just get on with it. This not only applies to closed systems (eg, reciting the alphabet) where saying “b” after “a” today is the same as doing it yesterday, but also to open-ended systems (eg, the number series) where saying “8004” after “8003” is the same as saying “84” after “83”, even if we've never counted that high before. And it also applies to grasping new rules which are obvious variations on ones we've already mastered. So when I'm confronted by a new object (eg, a dongle) and told its name, I can at once use the new rule (“This → is called a 'dongle'”) in all sorts of normal ways without further ado (“pass me the dongle”, “put the dongle over there”, etc). This new rule is the same as, or a simple variation on, countless others that I've learnt; I can assimilate it into my repertoire without breaking stride. Not every new case is an abnormal case.

Natural reactions

What must be recognised here is that this is a matter of our natural reactions. There is nothing inherent in the rule (or the logic of the rule) that compels us to go on as we do. At each stage it is possible that we might not be able to grasp these regularities – to see them as “going on in the same way”. (If this seems strange, don't forget that many people simply cannot grasp quadratic equations no matter how hard they try. And for all of us there are areas where our abilities peter out while others march on untroubled.) It is a basic fact about human beings that given certain types of training we almost all react in more or less the same way. That is, various things which might have baffled us simply don't trouble us at all. This is the basis upon which language is built – not some compelling, ineffable reflection of the a priori order of the world. In other words, Lebensform, nicht logische Form.

And if our reactions were not what they are then different concepts – different ways of living – might seem entirely natural to us. The pupil in §185 is one such example; for him it is obvious that “1000, 1004, 1008” is the correct continuation of “+2”, and we cannot demonstrate or prove that he is wrong. The disagreement between the pupil and the teacher lies too deep for that; it is not at the level of interpretation, but of natural reaction. To misquote §241, “this is disagreement not in opinions, but rather in form of life”.

Of course given his take on addition the pupil will not be able to live as we do; all sorts of avenues will be closed to him. But what if he doesn't want to live like us? What if he regards our mathematical technique – and its various applications – as ridiculous or disgusting? Obviously we would be deeply baffled by such an attitude, and here you can see the depth of mathematical rules. For it is indeed true, as we mentioned earlier, that breaking the rules of arithmetic is not like breaking the speed limit. But the difference lies in what is fundamental in us, rather than our being attuned to an a priori order of the world (cf RFM I, §74: “to the depth that we see in the essence there corresponds the deep need for the convention”). Our commitment to mathematical rules runs far deeper than our (often somewhat grudging) commitment to the highway code. Indeed, in the former case we are not usually so much as tempted by alternatives – but this might not have been the case, as the pupil in §185 demonstrates. (I'm sometimes drawn to the idea that “3x0” is not the same as “0x3”, since if you have three cows and do nothing to them then you still have three cows, but three lots of nothing is obviously nothing.)

It is a similar (though not identical) story in other areas where our rules strike us as deep. For example, we noted earlier that “red is two meters high” made no sense. There is nothing we can do with such a sentence, and this seems to reveal something deep about the nature of colour – something that is written into the essence of the world. But suppose that whenever we made a two meter-high object (eg, a door) we felt an overriding need to colour it red. Any other colour appalled us, as did red when applied to objects of other heights. In such a case we might feel it was a property of redness to be used in that way, and we might express this through the phrase “red is two meters high”. Different natural reactions make possible concepts which, to us, seem barely intelligible. Of course, we could not decide on a whim to adopt such a practice; indeed it's doubtful whether even the strictest upbringing could lead us to see things in that way. We simply don't live like that. And that's why the rules of language are deep and the rules of chess are not. But it's a fact about us, not the essence of the world.

Correctness and customs

But doesn't this bring us back to psychological compulsion? Isn't Wittgenstein reducing language to a matter of instinct and conditioning? – automatic stimulus responses, association, etc? How does the concept of correctness get a foothold in such an account?

Here we must keep in mind that, as we've already noted, learning language takes place within the context of an established practice. As such, the standard of correctness is there waiting for us from the very beginning. We are being inculcated into a correct way of behaving. Certainly conditioning (or training) plays a part: through reward and punishment, positive and negative feedback, these reactions are encouraged while those are inhibited (cf Wittgenstein's remarks about teaching in §§5-7, §143 and §208c). But right from the start the punishments and rewards are accompanied by words which categorize behaviour in terms of right and wrong: “naughty”, “good”, “correct”, “incorrect”, and so on. The focus is not simply on learning to avoid punishment, but on learning to do what is right. And embracing this concept of correctness is part of what it means to learn language – so if a child is reciting the alphabet and makes a mistake she will react to it as such. That is, she will be annoyed or crestfallen, and not merely fearful of punishment. She will also correct herself on occasion, and those around her too. She will say “No! That's not right.” Someone who acts solely out of fear, rather than out of a sense of correctness, doesn't understand the game – for she is not following its rules, she has merely been bullied into acting in accordance with them. Following a rule entails a commitment to it as a standard of correctness.

And this holds good even when our reactions are automatic or unreflective. When counting up to ten, for example, we don't have to think about what we're doing – we don't have to figure out which number comes next (“I follow the rule blindly” §219). But if we're challenged then we will justify ourselves in terms of following the rule, doing the right thing, etc. We won't simply shrug and say “Don't ask me – the numbers just came out of their own accord”. In this type of case, “automatic” equates to “fluent”, not “involuntary”. We're tempted to say that because we don't think about what we're doing there can't be any question of right or wrong. But rather: we're trained to be fluent so that we can do the right thing without having to think about it. And it is another basic fact about human beings that we can be brought to do things in this way; our initial reactions can be modified and refined, and these modifications can become ingrained so that they amount to a second-nature.

Broadly speaking, what this comes down to is that learning rules and following them takes place within the context of a human life. Teaching a child is not like fine-tuning a mechanism; there is a categorical distinction between the two (you can program a laptop, but you cannot punish it, or encourage it, or expect it to act out of a sense of duty). And nor is it the same as house-training a puppy – though here the comparison is much closer.

Living beings

This intrinsic “humanness” of rule-following – its animality – is touched upon in the way Wittgenstein develops his remark in §142 about normal and abnormal cases. As we've seen, a normal case is part of an established regularity – a custom (cf §199).
And particular instances of language use get their meaning from the fact that they're embedded within such a regularity. (This, of course, is just another way of saying that “the meaning of a word is its use in the language” §43.) But our customs are themselves embedded within the broader regularities of our lives as human beings. This is what Wittgenstein alludes to in §142 when he suddenly jumps from language-use to characteristic expressions of feeling (and we should note that here Wittgenstein is moving from the circumstances within which particular words or phrases have their home to the circumstances within which language itself makes sense).

At this point in the Investigations it is difficult to see exactly what Wittgenstein is driving at (he admits as much in the section's final sentence, which glances forward to the private language discussion). What has the characteristic expression of feelings got to do with the correct use of words or following a rule? Well, for a start we might ask how we could teach rules without natural expressions of satisfaction and displeasure – both on the part of the teacher and the pupil. How would a pupil know what to do if she was oblivious to signs of anger, encouragement or frustration? Perhaps more fundamentally, what would be the difference in the pupil's behaviour between following a rule and merely doing as she pleased (which might happen to be in accordance with the rule)? And once that distinction has been obliterated what's left to the concept of rules at all?

The temptation here is to suppose that this wouldn't be a problem because we could still have all the relevant feelings, just as we have them now, only we wouldn't express them. So although the teacher wouldn't know whether the pupil was following the rule or doing as she pleased, she would know – and that would be enough to preserve the distinction. Exposing the incoherence of this suggestion is one of the central tasks of the private language discussion (§§243-315). That falls outside the remit of this current post, but two points are worth making. First, the supposition that feelings are conceptually distinct from their expression presents them as a kind of inner object. Like an apple in a box, a feeling is either there or it isn't – whether or not we let someone know about it is irrelevant. We've already seen propositions, word-meanings, understanding and rules presented as inner objects, and now we can add feelings to the list. The question is: does this last example make any more sense than the others? Wittgenstein's answer is no; it misdescribes the concept of feelings (sensations, etc) to present them in this way. In certain crucial respects having a pain is not like having an apple in a box, and construing sensations on the analogy of physical objects makes them completely mysterious – just as it does with the concepts of understanding and rules (cf §293). Secondly, if the difference between following a rule and doing as you pleased rested upon the presence or absence of an inner “feeling-object” then “thinking one was following a rule would be the same thing as following it” (§202) – and in that case there would be no question of correctly or incorrectly following a rule. Whatever felt right would be right.

Feelings and their characteristic expression are conceptually woven together, and this expressive regularity is a precondition of rule-following – and hence of language. That is not to say, however, that such expressiveness is part of the language-game itself. You do not use a word wrongly if you fail to pull certain faces when you say it. Rather, characteristic expressions form part of the general framework within which our language-games have their life. On this or that occasion we might speak without any particular expression, but “if rule became exception, and exception rule; or both became phenomena of roughly equal frequency – our normal language-games would thereby lose their point” (§142).

The world

Wittgenstein further underlines this comment with a rather different example: what would happen to the language-game of weighing objects (eg, lumps of cheese) and pricing them accordingly if they frequently and arbitrarily changed size? Clearly such a practice would become useless insofar as it was intended to ensure that everyone paid the same for the same amount of cheese. So on the one hand we have the expressive regularity of living beings, and on the other the regularity of the world in which they're situated. And these two features, taken together, form the broad context within which our language-games mean what they do – they are the “extremely general facts of nature” mentioned in the boxed remark at the end of §142.

It is significant, I think, that Wittgenstein's example impacts upon a mathematical practice. As such, it forms a counterpart to the pupil's natural reactions in §185. Different natural reactions could produce a different mathematics, and different regularities in the world could render our mathematics pointless. In both cases the aim is to loosen the grip of the idea that mathematical rules express a metaphysical essence. And in both cases the point holds more generally. We have already seen this with regard to natural reactions and the rules of language; we can now make a similar move with regard to the world. Suppose, for example, that whenever any object reached two meters high it became red – and only two meter-high objects were red. So as a tree grew it turned red when it reached two meters and changed back when it grew taller. Here again we might find it natural to say “red is two meters high”, and here again what seemed like a necessary truth is revealed as contingent.

But this emphasis on the regularity of the world can easily seem as if it undermines Wittgenstein's commitment to the autonomy of grammar. Doesn't it bring us back to a Tractarian position whereby language simply reflects the behaviour of objects? But this thought misses the subtlety of the situation sketched out in §142. For Wittgenstein does not say that our language-games would become impossible if nature changed its ways; rather, they would lose their point. And, of course, the point of a language-game is something supplied by us, not the behaviour of objects. Going back to the cheese example, there would be nothing to stop us continuing with the game, just so long as we weren't bothered by the fact that it no longer resulted in the same amount of cheese for the same amount of money. Instead, we might see it as a kind of lottery, and look forward to finding out if today we were going to be lucky or unlucky. (Wittgenstein's example of the wood sellers in RFM I, §§148-150 makes a similar point.)

Language is not simply an inert mirror of the world; it is part of what we do (cf §25). Our various activities – building things, mucking about, grieving, making love, etc – are soaked through with it. But, of course, these activities take place in the world – and the world as it is, not as we might want it to be. We cannot change the world on a whim, and nor can we recreate it by dreaming up new concepts. Indeed, the world's independence forms part of the scaffolding within which our language and our concepts make sense. If the world is an illusion – a kind of conceptual mirage – then I am not now really thinking or writing (cf On Certainty, §676).

The essence of language

With this observation we have, in a sense, come full-circle. We began in §136 with the Tractarian notion of propositional form, which sought to present the essence of language as something sublime – a deified phenomenon whose crystalline logic reflects the a priori order of the world. But now we have a very different conception – not a rival account of the essence of language, but perhaps a description of the most general circumstances within which language finds a home: living beings in the natural world.

Within this description, language is contingent rather than a priori; pluralistic rather than reductive; active rather than reflective; and amorphous rather than sharply defined. It has an endless, unpredictable array of possible forms and functions, rather than one essential form, one essential function. Above all, it is a natural phenomenon – not an intrusion of divine purity into the sordid world of mud and phlegm. “This seems to abolish logic, but does not do so” (§242). That is, it does not turn philosophy into a form of Naturalism continuous with science. For, as we have noted, the logic of our language – its grammar – is not beholden to the world; it is an expression of the form of life in which it arises. To be sure, this form of life is a natural, physical creature – that is itself part of the logic of language. But here “natural” is being used in a sense that would not be recognised inside a laboratory. Language-using forms of life (paradigmatically human beings) are not ghosts in the machine. But neither are they machines simpliciter. They are: people.

This way of putting it can make it seem as if Wittgenstein is proposing a theory. And that's because it's likely to strike us as controversial rather than platitudinous. It's at odds with how we tend to think about these things, and with the educated chatter considered respectable in our culture (which gains its purist distillation in philosophy). But Wittgenstein is not putting forward a theory. He is drawing our attention to the way in which we do, in fact, live. It's a simple fact that, as alluded to above, when I talk with a friend I don't regard him as a biological machine – and nor as a spirit lodged within such a machine. My attitude is altogether different. And that's not because I subscribe to some grand theory about about the essence of humanity.

My attitude towards him is an attitude towards a soul. I am not of the opinion that he has a soul.
PPF iv, §22


  1. I enjoyed these reflections on Philosophical Investigations but I think they're not a general critique of the Tractatus, since parts of this is already conceived there. In my view, picturing is even for the early Wittgenstein something done with language rather than a (mental or otherwise) reflection of an independent, metaphysical notion of sameness. To see this, we have to reconsider to what extent logical picturing in the Tractatus can be considered a static relationship. The Tractarian view combines a notion of 'name' with the notions 'form of representation' and 'operation', and all of these have something to do with 'objects'. They don't mean the same thing, but they are in certain contexts importantly interchangeable.

    On the Tractarian conception, the 'rules of' (limits of construction in) logical syntax don't come from without like you assert, they come from within. When Wittgenstein says a name is ‘representative’ (3.22) of an object, he means that within the picture it has the role of that object, not that the name references it as it were statically. This can be compared to the way a point can have a position in geometric space so as to make up a part of a circle, line or other figure. Names do not merely externally refer to objects, but are combined directly with objects in order to form a picture.

    Thus Wittgenstein emphasises that the atomic proposition isn't an object, and can’t be written as a list of names, but is a fact in its own right (3.14). Also, it’s one reason why he stresses a name only has meaning in a proposition (3.3). Since objects in facts are co-determining links (2.03), this limits, not which combinations of names/objects are ‘allowed’, but which pictorial facts we are capable of producing. Names and objects are interchangeable. The name is configured in some way in the proposition, and its configuration is an object that in turn helps determine the meaning of the name. Understanding a proposition is a matter of replacing the signs with configurations/objects according to the configuration of those signs.

    (And this point is what separates a static picture hanging on a wall that depicts only indeterminately ("a picture is worth a thousand words") from a logical picture with sense (proposition). Here enters the significance of the function-argument form and composition in general (5.47). Consider a case like Fa and Gb, and whether, on Wittgenstein's conception, these two must consist of distinct names, differing in meaning. No, Fa and Gb can reduce to the same set of names/objects, sharing a place in logical space, but their senses differ; they are like arrows pointing in different directions from the same spot. The sense depends on which elements are signs and which are configurations thereof, on what is said and what is shown in the picture. Thinking the sense of the proposition is to think of the manner of translating into a situation, which differs in the two cases.)

    So the meaning of a name isn’t assigned arbitrarily as the second step in a two-step procedure, like e.g. Zalabardo and many others suggest, but derives from 1) the way the name is configured in the proposition and 2) the general interchangeability of the name with an object (a form of representation, a fundamental operation (5.474)). Because any configuration of names ipso facto is a picture, it’s not like there are some would-be atomic propositions that fail to make sense, but only that seemingly assertive sentences fail to express atomic propositions (5.4733). This disposes of the notion that Wittgenstein was committed to metaphysically independent isomorphism, picturing implying isomorphism rather than the other way around. And with that goes any notion of limits on sense deriving from outside language. Due to the interchangeability of names and objects, this distinction cannot be drawn: rather, "the limits of language mean the limits of my world".

    1. I don't see how your account makes linguistic rules something that come "from within" in the sense that I am using that term - ie, rules that are not beholden to the a priori form of the world, but which arise within - and are specific to - a particular form of life.

      In the Tractatus, logical syntax governs the possibility of any language whatsoever, whether it's human, Martian, or the language of angels. And it does this by mirroring the form common to any possible world. So, in a sense, the rules of logical syntax come from "without"; if language is to happen at all, it can only happen via *these* rules.

  2. Many thanks for the comment, mgs. V busy at the moment, but I'll try to give a more considered response in the new year.

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  4. Thank you so much... this was wonderful. Excellent analysis and a joy to read.

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