Sunday, 15 December 2013

Understanding: Discussion Summary

§§138-184 form a complex, interlocking series of remarks. Sometimes they seem to repeat themselves and and sometimes they go off on curious tangents. Wittgenstein wrote in his preface that “The same or almost the same points were always being approached afresh from different directions” and this is certainly a prime example.

It would be a mistake, however, to think that the discussion is presented this way simply because Wittgenstein wasn't up to the task of moulding it into a more conventional form. Rather, the presentation is bound up with the idea of philosophy as therapy. It attempts to reflect the experience of being in the grip of a particular way of looking at things. Our thoughts keep coming back to the same familiar notions – or, rather, those same notions keep reappearing in subtly altered forms. They cannot be despatched at a stroke; it requires patient work on the part of both the author and the reader.

At the same time, there's no doubt that it's easy to get lost in the maze of remarks that Wittgenstein presents us with. So I thought it might be helpful to provide a rough overview (which I actually wrote for my own benefit) to act as a guide when things get difficult. Obviously these notes aren't intended as a substitute for the text itself. They do not stand alone. Although here and there I offer some supporting arguments (usually in square brackets), my main aim is to highlight the flow of Wittgenstein's discussion and the connections between the various parts. Hopefully more detailed posts will follow in due course.

I have tried to keep things brief but I must admit it's turned into a bit of a monster. So in case reading it on the blog itself is tiresome I've prepared a PDF version without all this introductory waffle.

The discussion can be divided into four parts:

  1. §§138-150. This starts with the seeming clash between understanding as something grasped in an instant and meaning as something explained through use. It considers (and rejects) the claim that understanding amounts to having an “inner Something”. The following candidates are rejected: a mental picture; a mental state; a disposition. It concludes that “meaning” (and hence “understanding”) is more akin to having an ability.
  2. §§151-155. This considers a concrete case of “grasping in an instant” (“now I know”) which seems to go against the link to ability in §150. Again, it considers and rejects the claim that understanding consists of an inner Something. Specifically, it argues against understanding as a characteristic experience or an inner (mental or physical) mechanism. It concludes that understanding is logically (grammatically) bound up with the circumstances in which it takes place.
  3. §§156-178. To clarify this point, the case of “reading” is considered. As with understanding, the notion of reading as an inner experience or process is rejected. This time, however, the process is seen from the point of view of “deriving” or “being guided”, and the experience of reading is considered as an experience of this process taking place. But it is suggested that the pertinent difference between reading and (eg) pretending lies in the different circumstances of the two cases.
  4. §§179-184. The way in which circumstances enter into the concept of understanding is clarified. The nature of “now I know” is identified as a kind of signal rather than a report or description of an inner experience or state.

Now let's attempt a more detailed summary.

1. §§138-150. First Run-Through

§138 points out that when we hear a familiar word we understand it in an instant. This seems to clash with idea of meaning as something established by use, which is spread out over time. A number of questions are generated as a result:
  • What exactly is grasped when we understand a word in an instant?
  • How does what is grasped relate to use? How can it fit or fail to fit with use?
  • How can we grasp the whole use of a word in an instant?
  • How can observed use help us in novel situations – ie, how is it that we understand a word even when it's used in a sentence we've never encountered before?

Note how the mere idea of “grasping in an instant” suggests that what we need to understand is something “inner”. Again and again during the discussion observations about the public criteria for using the word “understanding” will be countered by objections relating to the first-person experience of understanding. One of Wittgenstein's main concerns is to clarify the place of such experiences in relation to the concept of understanding. He will not claim that they're of no importance (much less that they don't exist), but that we tend to misunderstand their role. Achieving a proper understanding, however, doesn't involve discovering a correct theory; what we need is to remind ourselves of the complex role understanding plays in our lives.

§§139-142: Pictures

What is grasped when we understand a word in an instant? The first theory considered is that we get a mental picture. If we have a picture of a cube and we pick out an actual cube then what is grasped fits the use. If we pick out (eg) a triangular prism then it doesn't.

But who is to say that picking out a triangular prism isn't a correct application of the picture? A picture by itself cannot provide a standard for its correct use. The same picture might be applied in two different ways, and we would say that it had a different meaning on each occasion. So the criterion for understanding is still the use rather than the picture itself.

[Note the link between this point, the discussion of ostensive definition (§§28-36), the discussion of deriving (§§163-164), and the discussion of “+2” in the rule-following argument (§§185-190). In fact, the discussion of ostensive definition foreshadows many of the points Wittgenstein makes about understanding. I'll group them together as the “anything goes” argument. I'm not saying they're the same argument each time, but they do seem connected. Further consideration might be rewarding.]

We're tempted to say that the picture forces an application upon us, but what this boils down to is that when confronted with a picture we often expect it to be used in a certain way – other possible applications do not occur to us. So “the picture fits the use” means “the use was the one we expected”.

Does all this mean there's no such thing as an application occurring to someone in an instant? No. It will often make sense to say such a thing. But we need to clarify the role of a statement such as “the application came before my mind”. This will happen shortly.

§§143-150: States, Dispositions, Abilities

As a prelude, however, Wittgenstein switches to a description of teaching someone the decimal series of numbers. It outlines certain broad, public criteria for saying that the pupil understands. It also emphasises (a) that at any stage the pupil's ability to learn may break down, and (b) that the type of instruction given will depend on the type of mistake the pupil makes. The point of this is to undermine the idea that getting the pupil to understand involves giving her a specific inner Something (a picture or formula, etc) the possession of which will be the source of correct performance. Rather, what the pupil is “given” depends on what she needs in order to perform correctly – and it's possible that there is nothing we can give her (ie, no course of instruction) that will achieve this.

Note also that the pupil's coming to understand is drawn out over time and there is no precise moment when we might say “now she knows”. There is no such thing here as “grasping in an instant”.

At §146 we get an important objection: applying understanding is not understanding itself. Understanding is the source of correct performance. Or, to put it another way, correct performance is derived from the source.

This is a variation on the “inner Something” idea; behind it lurks the notion that the “source” is a mental state – one in which a formula (or other method of application) occurs to the person who understands.

Wittgenstein makes two objections:

  1. A formula has the same problem as a picture. It does not come with its method of application built-in.
  2. Understanding a word is not best categorised as a mental state. Mental states (such as feeling anxious or euphoric) have specific duration and varying degrees of intensity. But I understand a word whether or not I'm thinking about it. My understanding isn't interrupted when I'm distracted by something, and so on.

Objection (b) prompts a revised version of the claim (§149): understanding is a state of an apparatus of the mind (or brain). (Wittgenstein sometimes calls this a disposition.) So, just as a pocket calculator can give us the answer to a sum because of its structure (ie, independent of this or that instance of calculating the answer), so I can be said to know a word because the structure for correct performance is in place even if I'm not currently using it.

Wittgenstein counters by pointing out that this gives us two separate criteria for saying someone understands: (i) ascertaining the structure, and (ii) observing performance. He doesn't here elaborate on the implications of this situation; they will emerge as the discussion continues (I'll call this the “two criteria” objection).

Instead (§150), we get a summary of sorts: the grammar of the word “know” is related to “able to”, but also to “understand”. I think this is emphasising a logical (grammatical) connection between meaning/understanding and performance. I also think it needs considering in conjunction with §155. But it all needs careful unpacking.

2. §§151-155: “Now I know!”

Wittgenstein now switches back to instantaneous grasping when he considers the significance of phrases such as “now I know” or “now I understand”. And this marks the start of his attempt to clarify the idea of an application coming before one's mind, which he mentioned in §141.

[Why did he first discuss learning the series of decimal numbers (§§143-150)? I think because that process is part of the general scene-setting (the circumstances) without which “Eureka moments” don't make sense. (Before you can even try to continue a number series you have to learn to count.) Compare this with ostensive definition. Viewed in isolation ostensive definition seemed to do something both fundamental and mysterious: provide an unmistakable super-bond between word and object. But its function was only seen aright when we reminded ourselves that actually it took place within a broader linguistic context. I think Wittgenstein is saying something similar about instantaneous grasping: if you overlook the broad context in which it actually takes place then it can seem to provide the essence of understanding and perform a truly mysterious function. The mystery is dissolved precisely by reminding ourselves of that broader context.]

Wittgenstein first points out that there are various things that might go on in someone who suddenly understands. This mitigates against the idea that understanding is a characteristic experience. But worse still, any of those experiences might occur and the pupil might still be unable to continue the series. So the experiences are not the “essence” of understanding; they are concomitant processes.

And now, just as when the notion of understanding as a mental state fell to pieces, we're tempted to posit a hidden process that lies behind what we actually experience. (Note how we've moved here from description to theory.) But if the process is hidden then how do I know that I actually understand? “How can the process of understanding have been hidden, given that I said 'Now I understand' because I did understand?” (§153). [This links back to the “two criteria” situation in §149.] If understanding is a state of an apparatus then how can I say I understand when (a) I don't know what that state actually is, and (b) whatever it is, I don't know whether it obtains?

Against this it is objected (§154) that there must be a state (or process). For if (eg) a formula occurring to me is not enough to provide understanding then something else must be necessary, and what could that something else be if not a hidden process or state?

Here we have reached an impasse. We seem forced to accept a theory despite the fact that it makes things worse (cf §112). This is a radical breakdown, and Wittgenstein's response amounts to a rejection of the whole approach that brought it about. Certainly something else is needed, he says, but not a state or process or disposition or structure or any type of inner thing. Instead we need to remind ourselves of the circumstances that warrant someone's saying “now I know” when the formula occurs to her.

3. §§156-178: Reading

To make this clearer, he introduces the analogous topic of reading. As with understanding, reading is a concept that tempts us to think its essential characteristic must be something inner. On the one hand, there is surely something computational about reading – we derive our words from the text – and this derivation is a process that takes place in the mind, or perhaps in the brain. On the other hand, reading is surely also a distinctive experience; just compare actual reading with pretending to read! These two characteristics might seem at odds with one another, but aren't they really different aspects of the same phenomenon? That is to say, isn't the experience of reading precisely the experience of the computational process taking place?

Here, then, we're once again confronted by the two notions that have dogged us throughout our investigation: process and first-person experience. And in the context of reading they seem to stand out even more compellingly than before. Accordingly, Wittgenstein's treatment of them is both richer and more probing in this part of the discussion.

§§156-158: Experiences and Mechanisms

As with §§143-145, we start with a (brief) description of the circumstances surrounding reading: learning to read, various criteria for saying someone is reading, the difference between a beginner and a fluent reader, etc.

This quickly prompts both the idea that reading “is a distinctive conscious activity” (§156e) and that some kind of mechanism must be at work (§156g). Against both, Wittgenstein observes that it makes no sense to talk about the first word a beginner reads (note the connection with §145b). The point here is that if reading is either a particular experience or the state of a mechanism then it ought to make sense to ask “what was the first word he read?” Concentrating on the notion of mechanism, Wittgenstein draws a highly significant distinction between our concepts in relation to machines and the way we apply them to living beings – even where the living being is used as a “reading machine”.

Against this it is objected (§158) that the different treatment merely stems from our comparative ignorance of the workings of the brain. Wittgenstein's response is to underline the claim's theoretical nature (a point already made at §146g), and to further suggest that it is a priori: whatever the evidence (or lack of it), things must come down to a mechanistic explanation.

[What is he getting at here? I think §158 is an enigmatic, troubling section. It seems to come alarmingly close to suggesting that our belief in causality as a universal principle is a kind of metaphysical superstition (cf Zettel, §609). It certainly requires careful, detailed analysis. For the moment, however, I'll offer a provisional, “middle of the road” gloss: “Why do you say things must come down to a mechanistic explanation? What evidence do you have for this? What we know is that 'understanding' is not used like a name for a mechanistic process – and certainly not a hypothetical one.” That's by no means the last word on the subject, but it'll have to do for now.]

§§159-161: The Conscious Act of Reading

The discussion now switches back to the first-person experience of reading. Isn't that the essential thing which distinguishes actual reading from merely pretending or the free-association of sounds with marks on a page?

Wittgenstein counters with the imaginary case where a drug produces a feeling of reciting from memory in someone who is in fact reading a passage he's never seen before. A variation is offered in which the person feels he is reading when he is actually associating words with signs in a completely unfamiliar alphabet. In the first case we would say he was reading despite his feelings to the contrary. In the second case, classification would depend on his reaction to the signs. If his words bore no clear relation to them (eg, he read “^#*” as “blue” on one occasion but as “left” on another) we'd say he wasn't reading. But if the same words were always associated with the same signs then we'd perhaps be more inclined to say he was. That is, it wouldn't be clear whether he was reading or not – it would be up to us.

[The point, of course, is that his experiences are not the decisive factor in either case. But nor is it exclusively down to what he does (for he might speak exactly the same words both times). Rather, it is down to what he does given the particular circumstances in each case. Wittgenstein underlines this with the experiment in §161. What is the difference between counting to twelve and reading the numbers from a watch dial? Again (I think) the implied answer is: the circumstances.]

§§162-164: Derivation

Here we switch back to understanding as a process – specifically the process of deriving. It's an idea that has sort of been “in the air”, but not directly confronted, ever since §146b (the same is true, by the way, of rule-following, which is closely connected to derivation; see §143a, §147 and §162).

Wittgenstein describes a particular case in which we'd be inclined to class reading as an example of deriving sounds from a text. But immediately comes the objection that we don't have enough here to be sure this is derivation; we taught him the alphabet, he read the words – what right have we to say that the link between the two was deriving?

[Note: (a) this already treats derivation as an “inner” or “hidden” thing; and (b) we're at once tempted to look inside ourselves and search for it there. This goes some way towards explaining why the discussion constantly switches between third- and first-person perspectives.]

So Wittgenstein alters his description to make it an even clearer case of deriving – that is, he changes the circumstances. But here it's objected (§163) that even if this is derivation, we can't assert it simply because the pupil looks at the chart and writes the “correct” letters. For whatever he writes might be classed as derivation according to some rule or other, and thus be “correct” (the “anything goes” argument – cf, §139). And now the very concept of derivation starts to look empty.

In §164 Wittgenstein offers the moral of the story: our search for the essence of deriving has led us into darkness, for there is no such thing. Instead, we have a complex family of circumstances in which the word “deriving” is warranted.

[A brief elaboration: when we treated deriving as a hidden essence it became logically distinct from its consequences. As a result, the very essence we thought we needed to find became empty. Compare this to the case of mental pictures (§139) and the “two criteria” objection to dispositions in §149. Also compare it to the famous “beetle in a box” example in §293. But our grammar doesn't treat deriving as if it was a thing in a box; instead it conceptually links it to various performances in various circumstances. These circumstances sometimes include what went through someone's mind (“I recited to myself 'Richard of York gave battle in vain' and derived the answer from that”). But sometimes they don't.]

§§165-178: “Experiencing the Because”

Yet again we revert back to a first-person argument. The discussion considers a cluster of related claims:
  • we know from our own experience that reading is a particular process (§165);
  • the words come in a distinctive way (§165);
  • they somehow cause our utterance (§169);
  • we feel the connecting mechanism between the word and our utterance (§169).

So finally the third- and first-person arguments come together. Reading is both a mechanism and a characteristic experience; it is a characteristic experience of a mechanism at work .

At each stage, however, Wittgenstein (a) exposes this account as a picture that we adopt rather than a straightforward description of the the facts, and (b) undermines the temptation to adopt this picture.

  • §165. If reading is a characteristic experience then it doesn't matter what sounds result as they can all be linked to the text according to some rule or other. [This brings together the “two criteria” argument (§149, §153, §§163-164), and the “anything goes” argument (§139, §§163-164).]
  • §165. Moreover, it's not enough that the written words makes the spoken ones “occur” to me, or “remind” me of it. That could happen yet what I utter might still be incorrect. Mere association is not enough.
  • §166. The claim that the words come in a distinctive way is a fiction. Consider normal cases of reading: we don't even think about how the words come or if there's something distinctive about it. We see the words and we make the sounds. What else do we know? Of course, we notice a difference when we (eg) associate sounds with squiggles but it mis-describes reading to therefore conclude that the words come in a special way. With reading it's automatic, with squiggles it isn't. That's the difference. And it's not an experiential difference; it's a circumstantial one.
  • §167. There is no single characteristic experience of reading. This undermines the idea that reading is a particular process that we experience. [To put it another way: even if there is a particular process, we cannot infer its existence from the experience of reading, for that experience is extremely varied.]
  • §169. It makes no sense to say that we experience the causing. Causation is established by experiment, tests, etc; it is not something that can be felt. [That would be like saying “I'm feeling inflation” when I'm shocked by how much the price of bread has risen.] This is a categorical (grammatical) distinction. Indeed, we do not say that the text is the cause of our reading – rather, it is the reason we utter the words that we do. That is, we appeal to a standard of correctness, not to causation.

§§170-178 provide a kind of summary. We assume that the difference between reading letters and associating sounds with squiggles represents (respectively) the presence and absence of influence. But being influenced (or guided) is no more a particular experience than reading is. It forms a wide family of cases, and the important factor is not the presence of a particular experience but the circumstances pertaining to any given case.

None of this bothers us during actual use, but when we reflect on these things mere circumstances can seem insufficient. We're tempted to posit a particular source of influence (in other words, we've started theorising). Maybe it's a strange feature of the words themselves – as if they exercised a kind of “thought control” – or a process (perhaps physical) operating behind the scenes. And now we take our varied experiences to be experiences of this elusive form of influence. We look at them “through the medium of the concept 'because'” (§177). Of course, it is right to say that we're influenced, but not because of any particular experience or process. Rather, it is correct to apply the word “influenced” in all these varied circumstances. [We have supposed an essence, but what we needed was to recognise a family resemblance concept.]

4. §§179-184. Back to Understanding

Wittgenstein now applies to understanding the insights gained from considering the case of reading. Not surprisingly, this involves reiterating the point made in §§154-155: “The words 'Now I know how to go on' were correctly used when the formula occurred to him: namely under certain circumstances. For example, if he had learnt algebra, had used such formulae before” (§179).

At the same time, he's aware of the temptation to take this point the wrong way. We might, for example, suppose that “now I know” (or “I understand”) is a kind of shorthand description of the circumstances – as if we somehow deduced that we understood from the fact that the situation was one in which “now I know” would make sense. This harks back to the interlocutor's point at §147: “When I say I understand the rule of the series, I'm surely not saying so on the basis of the experience of having applied the algebraic formula in such-and-such a way!” This is correct, but the interlocutor's mistake is to assume it shows that the circumstances are irrelevant. Rather, it shows that they do not connect with the language-game in the way he supposes. We do not appeal to them as a criterion of application; they are the context within which our criteria make sense. They “set the stage for our language-game” (§179).

A second temptation is to think that the circumstances form part of a causal explanation. Here the supposition is that if the right circumstances are in place (general education and other background features + the formula occurring to the pupil + a characteristic experience of understanding) then the pupil must continue the series correctly (§183). That this is mistaken can be shown from the fact that even where the phrase “now I know” is warranted it is still defeasible – the pupil might still be unable to continue the series correctly. In such a case we would normally say that the pupil's statement was wrong: he didn't in fact know. But it was still understandable. [Compare this to a case where you show a formula to someone with no mathematical training whatsoever and he says “now I know how to go on”. In those circumstances his claim is not so much wrong as completely bizarre.]

These considerations throw light on the role of “now I know”. It is best not thought of as a description of a mental state at all (§180). Rather it is a signal that the pupil is confident (perhaps certain) that he can go on correctly. But, of course, being certain you can give the right answer and actually doing it are not the same thing. We frequently find ourselves ruefully saying “I was so sure that answer was right!”

Next Steps: Rule-Following

I started this summary with a list of questions, but there's one I've not really considered so far: how can we grasp the whole use of a word in an instant? This is raised right back in §139 and is occasionally glanced at during the discussion (eg, §147: “I surely know that I mean such-and-such a series, no matter how far I've actually developed it”). Knowing the whole use of a word seems a criterion of understanding, just as knowing what a chess pawn is means knowing how it can move in any given position. But how can we know the whole use of a word? For however we've used a word up till now, what happens when we come to apply it in a completely new situation? How is our past experience supposed to help us?

Surely when I grasped the rule for using the word “cat” I didn't know that it could be used in the sentence “The cat sat on Jupiter's second-largest moon”? And yet in some sense I clearly did know that, for I was able to form the sentence without any trouble at all. It didn't come as a surprise to me that “cat” could be used in that context. The rule, it seems, guides us effortlessly through countless permutations that weren't envisaged when we learnt it.

How does it achieve this? Or, to put it more generally, what is the connection between the rule and its application? What keeps them in sync? That is the issue which forms the heart of the discussion in §§185-242.

Monday, 9 December 2013

Another Update

First, I've added a topic list, as you can see from the bar below the blog header. Hopefully that'll make the site a bit easier to navigate - I've found it pretty cumbersome recently when I've been looking to provide links to old posts.

Actually, that reminds me: I must get round to testing/updating the links in the right-hand column. Oh, and while I'm on the subject, don't bother with the Wittgenstein discussion forum that's listed there. It's run by a Quinean naturalist who only thinks he's a Wittgensteinian and can't understand why linking meaning to brain-states isn't something Wittgenstein would've advocated. Seriously! [Actually, turns out this was untrue - see comments below.] Maybe he's Dan Dennett in disguise. Needless to say, I was barred from the forum after a few posts. And, yes, alcohol was probably a factor.

Finally, the next proper post should be up in a few days. It's an overview of the entire discussion of understanding. Hopefully there'll also be a link to a PDF version, as it's a bit long.

Wednesday, 16 October 2013

Understanding Part 1: Pictures §138-142

1. The mythology of understanding as something “inner”

As I discussed in my previous post, a rapid series of modulations brings us to the topic of understanding when, at the end of §138, the interlocutor says:

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!

This is probably the strongest objection so far to Wittgenstein's account of meaning. Its power stems from the way it ties into various extremely tempting ideas about the process of communication. Above all, it suggests that understanding is some kind of thing that we acquire when we learn the meaning of a word, and which is subsequently represented to us whenever we hear that word.

The appeal of this idea is bolstered by various simple reflections. When we come to know the meaning of a word we gain understanding – so we must've gained something! Likewise, if we don't know the meaning of a word then we lack understanding – so “understanding” must be whatever it is we lack. And although we might exhibit understanding in performance (eg, by using a word correctly), that is not understanding itself; it is merely evidence from which others can infer that we do indeed possess understanding.

Moreover, when we hear words we are immediately aware of our understanding. The words strike us in a quite vivid and particular way. We don't simply hear sounds or see ink-marks on a page (or shapes on a computer screen) – we hear (or read) language. We experience the meanings that it conveys. To see that this is so, just compare the case of reciting a passage we don't understand (having learnt it parrot-fashion, perhaps) with that of reciting one whose words are familiar to us. Surely it is undeniable that what happens inside us in the two cases is completely different?

Such considerations present a challenge for Wittgenstein. When we understand a word we understand its meaning. But what we grasp in the instant of understanding doesn't seem to be anything like a use. (And, in any case, is use something that could be grasped in an instant?) But if what we grasp isn't use then meaning can't be use.

2. Pictures and their application

Wittgenstein begins his assault on this appealing conception by considering the notion that understanding is a picture that comes before our mind when we hear a word (§139). It's a natural enough place to start given that his early philosophy propounded what's called “the picture theory of language”. Moreover, that theory was itself a refinement of a venerable philosophical position dating back at least as far as Locke's Essay Concerning Human Understanding. In my last post I gave a rough sketch of the account of communication that the picture theory tends to suggest. It might be helpful to repeat that here:

Person A has the thought, in the form of a picture, that things are thus-and-so. She wants to communicate her thought to B so she “converts” it into a proposition: she speaks, writes, uses sign-language or Morse code, etc. The words she uses relate to the elements of her picture and are arranged in a similar fashion. Next, B perceives A's proposition and he re-converts it into a thought. That is to say, the words he hears (reads, etc) produce a picture in his mind. That picture is his understanding of what A said. If he has the same picture he has understood correctly; if he has a different picture then he has misunderstood (and if he has no picture at all then he has not understood at all). The correctness of his picture can be inferred from his behaviour. Of course, we can't be sure B's picture matches A's but so long as he fetches the right object (etc) then it is reasonable to assume that it does.
In attacking the idea of understanding as a picture, it is this last part of the account that Wittgenstein focuses upon: the link between the picture and subsequent behaviour. He points out (§139) that, whatever might happen in our minds, our behaviour is still a criterion for understanding. If someone consistently uses a word incorrectly then we say that he or she doesn't understand its meaning. So understanding is clearly bound up with use in some sense. But if understanding is a mental picture then what is the link between that picture and use? “Can what we grasp at a stroke agree with a use, fit or fail to fit it?” (§139.) Wittgenstein suggests an answer to his own question: let's assume that when I hear the word “cube” I get a picture of a cube in my mind. If I point to a cube my use fits the picture, but if I point to a triangular prism instead then my use has failed to fit the picture.
At first blush this seems straightforward, but Wittgenstein argues that it will not do. The problem is: who is to say that pointing to the triangular prism actually is an incorrect use of the picture?
His objection is couched in terms of the picture's “method of projection”. I assume that's a glance back to Wittgenstein's time as an engineering student and refers to techniques used in technical drawing. I'm afraid I have roughly zero understanding of such things (I looked up geometric projection on Wikipedia and it didn't help) but there are other ways of making the same point. Basically it comes to this: a picture by itself stands in need of a method of application. If no method is stipulated then it's impossible to say whether a picture has been used rightly or wrongly.
So, returning to the example of “cube”, the word presents me with a picture:

I then look about me and spot a triangular prism. I realise that in both cases they have equal ends and parallel rectilinear figures and that their sides are parallelograms. I therefore point to the triangular prism because, in that sense, it is the same as my picture. In other words, I have used my picture as an example of a prism (for a cube is a prism too). That might seem an unusual way of applying the picture, but who is to say that it's wrong?
To see how far use can deviate from expectation, consider the following example: I present someone with a dog and an iPhone. I then give him a photo of the dog and ask him to choose which of the two items it most resembles. He chooses the iPhone because, like the photo, you can hold it in your hand, put it in your pocket, etc. Of course most of us would automatically choose the dog, but that is only because we are already familiar with the activity of picking things out from photos. It is something we’ve done countless times and so it probably wouldn’t even occur to us to use the photo in a different way. But there is nothing that says choosing the dog must be the correct response in all circumstances. Indeed to someone with a different upbringing from ours the dog might seem an absurd choice.
The picture, don't forget, is not being cast as an aid to understanding; it is supposed to be the thing itself. But it's hard to see how it can play that role when it provides no standard of correctness. If this observation seems familiar, that's because it is closely analogous to the point made about ostensive definition in relation to meaning. There, it was supposed that the sample by itself could establish a link between word and object, that it was completely unambiguous and therefore unmistakable. But it turned out that it only functioned as part of an established practice of describing the rule for the use of a word. And it's a very similar story in the case of the picture (which is, after all, a kind of mental sample). We have the sample, but what we lack is the application. (I should also mention that as well as looking back to ostensive definition this point also anticipates aspects of the discussion of rule-following. See, for example, §201: “if every course of action can be brought into accord with the rule, then it can also be brought into conflict with it. And so there would be neither accord nor conflict here”. This overlap should not be surprising; the concept of understanding is internally connected to the concept of meaning. Each helps define the other. And they are both closely bound up with the concept of rule-following.)
3. Compulsion
The reminder that a picture can be used in various different ways also serves to highlight (and undermine) another temptation regarding understanding as an “inner” phenomenon: the assumption that the relation between representation and what is represented somehow takes care of itself. We don't need to stipulate a method of application because the picture does it for us. It's especially easy to think like this when we focus on the immediacy and fluency with which we usually understand language. We don't have to struggle to grasp the meaning – in fact, it's impossible for us not to understand. It's as if the picture somehow carries its meaning within it, like a kind of spirit, and exposure to the picture transfers this spirit to us, so that we cannot help but see the picture as an image of this object. The words (or rather the images they produce) force an application on us (§140).
In the Tractatus this seems to be regarded as a kind of logical compulsion. So long as picture and fact share the same logical structure there cannot be doubt about what's represented. Of course, this idea is exploded by the simple observations in §139 (it is, in fact, another example of a rule misrepresented as a necessary feature of the world). But there are other ways of presenting the idea of compulsion. As Wittgenstein says in §140, “we might also be inclined to express ourselves like this: we're at most under a psychological, not a logical, compulsion”. He then adds a typically cryptic coda: “And now, indeed, it looks as if we knew of two kinds of case.” What's he getting at here?
I think this is a warning against defending a preconception by taking refuge in theoretical explanations. We assumed we were under compulsion; the idea that it was a logical one has proved empty, so now we say it must be “some other kind”. And, happily, we hit upon the notion of “psychological compulsion” as a plausible-sounding alternative. (Already we can see the bewitching idea of a mental mechanism looming on the horizon.) But notice how vague all this is! How much do we actually know about psychological compulsion? Is it clear that this is an example of it? And how do we propose to find out? Will we be conducting field experiments or can we decide things from our armchairs? Isn't the idea of psychological compulsion just a guess – and a guess that invokes a mysterious realm of mental structures, subconscious computation, and so forth?
There's a second, perhaps more fundamental, issue. We've been attempting to clarify the concept of understanding, but now it looks as if we're sliding into a quasi-causal explanation. But that's like trying to find out what a watch is by examining the structure of its cogs and springs. Such an investigation may be useful in various ways, but it won't tell you anything about the role watches play in people's lives. For that you need to describe their use, not their internal mechanisms. The notion of compulsion tempts us away from a conceptual investigation towards an ersatz scientific one which is doomed to failure from the outset.
Well, Wittgenstein may be alluding to such thoughts in §140, but he doesn't elaborate on them at this point. Instead, he sidesteps the quagmire of compulsion and brings things down to earth: “our 'belief that the picture forced a particular application upon us' consisted in the fact that only the one case and no other occurred to us.” This, of course, is a move from the theoretical back to the descriptive. Why no other case occurred to us is not Wittgenstein's concern. But the fact that they didn't made it seem like the picture could only be applied in one way even though (as we now see) that's not true at all.
It is this observation that subsequently allows him to answer the question in §139: how can what's grasped in an instant fit or fail to fit a use? “[T]hey can clash in so far as the picture makes us expect a different use; because people in general apply this picture like this” (§141). What seemed to be a mysterious (perhaps impossible) relation between two entirely different phenomena turns out to be remarkably simple and ordinary.
4. Building in the application
Maybe, however, compulsion isn't the only answer. Perhaps we could build the application into the picture itself, thereby allowing it to perform its allotted function. Wittgenstein considers this in §141. “How,” he asks, “am I to imagine this?” The answer he suggests is a picture of two cubes with lines of projection between them. Something a bit like this perhaps:

Actually, I don't think that quite works. The cube on the left presumably represents the mental image and the one on the right represents actual cubes in the world (and the lines attempt to show the relation between the two). But we no longer have the mental image that the left-cube pictures! So we're going to need two separate images: first, the picture of the cube by itself and, second, the picture of the two cubes showing how the cube in the first picture is to be applied. But this raises a further problem: how do we know the relationship between these two images? How do we know that the left-cube in the second image represents the cube in the first image? Aren't we going to need a third image depicting the relation between the two we already have? And won't that in turn require a fourth and fifth image linking the third image to the first and second ones? And so on.
In a roundabout way this comes to the same objection that Wittgenstein makes about his own proposed image: whatever its content it will still just be another picture, and will therefore stand in need of an application. It's not simply that the initial picture did not provide its application (as if that were a kind of oversight); it could not do so. Application cannot be provided in that way.
Is Wittgenstein claiming, then, that there's no such thing as an application coming before one's mind? Of course not, but (he reminds us in §141) understanding what that amounts to involves looking at the use of the phrase “the application came before his mind”. It does not involve a doomed attempt to posit a hypothetical picture with miraculous powers. Instead of analysing the phrase himself, however, Wittgenstein leaves it up to us investigate. I think it's worth having a go because the conclusions it suggests (to me, at any rate) tie in with many of the points he will shortly be making about other accounts of understanding. Here's what I came up with:
a. Suppose I've been teaching someone to use mathematical formulae. Now I show her the series 0, 1, 1, 2, 3, 5, 8 and ask her to continue it. She ponders for a while and then cries “I've got it!” I ask her what's occurred to her and she writes down the formula “Fn = Fn-1 + Fn-2”. Then she correctly continues the series. That would count, I think, as an example of the application coming before her mind. Something occurred to her and it helped her continue the series.
b. However, it would also count if, instead of the formula, she writes down “Each new number is the sum of the previous two”. So what comes before her mind needn't be one specific thing.
c. But suppose instead when I show her the series she simply says “Oh, that's easy!” and correctly continues it: “...13, 21, 34, 55...”. And when I ask what occurred to her she says “Nothing – it was obvious.” (Perhaps she's worked through the series numerous times before.) Here no application came before her mind; she just knew what to do. In other words, correct performance by itself is not a sufficient criterion. Did she understand my order to continue the series? Yes, but that shows you can understand something without an application coming before your mind.
d. Finally, suppose that she writes down the formula as in the first example, but then has no idea how to continue the series. It later transpires that she'd previously seen the formula written below the series and that's why it occurred to her. Here again the application has not come before her mind even though what occurs to her – the formula – is exactly the same as in the first example. So correct performance might not be sufficient, but it's clearly important.
But what, then, is the difference between (a) and (d)? From the point of view of the criteria for the phrase “the application came before her mind”, the difference is not what's in her mind but her past experiences: her education, training and so on. The formula only counts as the application in the right circumstances. We might sum up all these reflections in the following way: however you slice it, understanding involves more (and sometimes less) than an application coming before one's mind.
5. Conclusion
A picture cannot fulfil the role of understanding by itself. This is not to deny that at least sometimes a word can bring an image before our minds, nor that the image might help us to use the word correctly. But it cannot show that we have used the word correctly; it supplies no method of application and hence no standard of correctness – and the criteria for applying the term “understanding” are closely bound up with correct usage.
However, the appeal of supposing understanding to be an inner “Something” is not so easily dispelled. Thus, for example, we might think that (questions of application aside) the pictorial account of understanding is implausible simply because it doesn't seem to match what actually happens. When we hear someone speak we don't get a torrent of pictures running through our minds one after the other. Yet instead of making us abandon the idea, this objection typically leads to attempts at refining it. We might wonder, for example, if the pictures are somehow unnoticed. Do they go by too fast? Are they perhaps unconscious? And need they be conventional images at all? Mightn't they take a form that we wouldn't easily recognise as pictures – formulae, for example? Now comes the thought that what we're really talking about is something that allows us to compute the correct output for a given input. And if that's the case, then isn't “understanding” a question of having the right mental structure – one that facilitates correct responses? And need this structure actually be mental? Couldn't it be a state of the brain? And so on.
It is these types of “refinement” that Wittgenstein considers in the remaining sections on understanding. They all, I think, flounder on the point already made: “understanding” is bound up with application, and correctness of application can only be given by an established practice. Nevertheless, it is important for Wittgenstein to deal with these new variations because otherwise the suspicion will remain that he has been over-hasty. The prejudice in favour of the inner “Something” is deep-rooted; digging it out requires tracing it through all its manifestations. So that's the next post.

Thursday, 10 October 2013

From Logical Form to Understanding: the Transition from §137 to §138

§138 begins a sustained investigation into the concept of understanding. I'll begin unpicking its various strands (which is a daunting prospect) in my next post, but here I want to examine the way Wittgenstein introduces the topic. Basically §138 perplexed me when I re-read it recently and it took a fair amount of effort to tease out the trajectory of its thought. That might just have been dimness on my part (in which case I apologise in advance for what's to follow), but I suspect that for many readers of the Investigations – especially those unfamiliar with the Tractatus – it can be easy to miss what Wittgenstein is doing in this section.
Typically, the shift between propositional form (§§134-137) and understanding (§§138-184) is treated as one of those abrupt changes of subject the author warns us about in his preface. Fogelin, for example, states that in §138 “Wittgenstein turns from his attack upon Tractarian themes” (Fogelin, Wittgenstein, second edition, p144 – I like the word “Tractarian”, by the way, and intend to make full use of it from now on). Hacker and Baker, by contrast, are a bit more nuanced. In Wittgenstein: Understanding and Meaning we are told that “§§1-142 of the Investigations are Janus-faced, looking back to the errors of the Tractatus […] and forward to the very different account now being unfolded” (Volume I, p357). And then, a little later, “§§138–142 mark a change” (ibid). So, it would seem, the breach-proper comes at §143 and §§138-142 form a sort of pivot or gateway into the full expression of Wittgenstein's new philosophical approach. Nonetheless, even here there's little or no sense that the discussion of understanding arises out of what comes before it, nor are we offered an account of how or why the one leads to the other. (Hacker and Baker might cover this in the exegesis, but – forgive me – I've never read it. There are limits, you know.)
But that's curious, because when you actually read the text the transition feels pretty seamless. Usually when Wittgenstein makes a jump it's not too hard to spot (eg, §134 or §243), but in this case §138 is clearly presented as a continuation of the discussion in §137. Indeed, the topic of understanding is raised before we've hardly realised it. At the same time, however, it must be admitted that there's something a bit odd about the transition. It reads like a continuation and yet, upon closer inspection, it's not at all clear how it fits with what's gone before. Is Wittgenstein resorting to a kind of authorial sleight-of-hand? Why would he bother – especially given his near-pathological aversion to fudging things? Why not just make the jump and have done with it? Time for a closer look.
§§136-137 consider the claim that the concept of truth and falsity (truth-functionality) fits the concept “proposition”. That is to say, the two concepts necessarily go together. Wittgenstein exposes this idea as a grammatical remark misleadingly disguised as a description (see Propositional Form). At first blush, the start of §138 merely seems part of this debate; with typical doggedness the interlocutor suggests a further example of “fitting” in order to shore up his position:
But can’t the meaning of a word that I understand fit the sense of a sentence that I understand? Or the meaning of one word fit the meaning of another?”
When you think about it, though, this is strange. What does the idea of a word “fitting” the sense of a sentence have to do with truth-functionality “fitting” propositions? How does the one support the other? It seems a glaring non sequitur. Of course, they both use the notion of “fitting” in relation to language – but, frankly, so what? If that’s all it amounts to then the interlocutor might just as well have said “But surely there’s such a thing as words fitting (or failing to fit) on a page?” We need something stronger than that.
To make matters worse, Wittgenstein's response is in some ways just as puzzling: “Of course, if the meaning is the use we make of the word, it makes no sense to speak of such fitting” (§138). This seems to suggest that if meaning is use then there's no such thing as a word fitting the sense of a sentence or of one word fitting the meaning of another. But this is surely wrong! Not only do we often talk about words fitting in this way, but when we do we are usually concerned precisely with the question of use.
So, for example, someone with little English who wanted a drink might wonder whether it was correct to say “Pass me the jug” or “Pass me the water”. In such a case we would tell them that it didn't really matter; in this context the words “jug” and “water” both fitted the sense of the sentence. The two expressions achieve the same thing; they are used in the same way. (Imagine a culture where, instead of “jug” or “water”, they had a word meaning “water-in-jug” that was always used on such occasions. So if you said “Pass me the jug” they'd empty out the water before handing it over, and if you said “Pass me the water” they'd pour the water into your hands. In such a situation neither “jug” nor “water” would fit the sense of the sentence – and again that is entirely due to the conventions governing use.) Here “fitting” is akin to aptness; it's a question of which words are effective, which words get the job done.
The final puzzle in this puzzling section comes with the interlocutor's response to Wittgenstein's criticism, which suddenly shifts the focus away from “sense” and on to “understanding”. With palpable exasperation the interlocutor says:
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!
This is a pivotal moment in the Investigations and I'll be discussing it in detail in my next post. But for our present purposes the important issue is the connection between sense and understanding. It may or may not be true to say that the phenomenon of grasping meaning “at a stroke” sits uneasily with the claim that meaning is use, but how on earth is this bound up with the idea of a word fitting the sense of a sentence?
So now we have three questions:
  1. How does the idea of a word fitting the sense of a sentence support the idea of truth-functionality fitting the concept of a proposition?
  2. Why does Wittgenstein respond by seemingly ruling out the idea of such fitting on the grounds that meaning is use?
  3. What is the connection between the sense of a sentence and understanding?
The answer to all three, I think, lies in what the interlocutor means by “the sense of a sentence”. In common usage, explaining the sense of a sentence typically involves paraphrasing it into a form that's easier to understand. In such a context, therefore, “sense” is roughly synonymous with “meaning”. But it shouldn't be forgotten that §§134-137 deal explicitly with the Tractarian notion of propositional form, so when the interlocutor raises the subject of “sense” in §138 he is still looking at things from the point of view of the Tractatus. That is, he is using “sense” according to the definition given at TLP 2.221: “What a picture represents is its sense”.
This brings us up against the picture theory of language. According to the Tractatus, the essential thing about language is that it pictures logically possible states of affairs. And it does this by mirroring the logical structure of what it represents. So “The cat is on the mat” presents us with objects arranged in a particular way, just like a drawing might. The assertion it makes may or may not be true – to find out we’d have to compare the sentence-picture with reality. But even if it’s false it still has a sense because what it pictures is possible: cats can be on mats. Compare this, however, to “The cat is on selfishness”. That proposition is nonsense precisely because it attempts to combine phenomena in an illicit way; selfishness can’t be sat on any more than it can be eaten or set on fire. So what the proposition attempts to represent cannot even be pictured and therefore lacks sense.
Now, how can we tell which words can legitimately be combined with which? That is down to the a priori structure of the world, for it is this structure which determines the combinational possibilities of objects. And these combinational possibilities must, in turn, be reflected in the logical syntax governing language. It is as if a sentence beginning “The cat is on…” leaves a gap which can only be filled by words of the right type. Or, to put it another way, only the right type of word will fit. This, I think, is the type of “fitting” that the interlocutor has in mind at the start of §138. It belongs to a conception of language as a structure made up of different shaped holes into which only the right kind of “word-peg” can be slotted. And this type of “fitting” has nothing to do with aptness or use; it is modelled on the physical sense of the word, as when a plug fits into a socket or a hand fits into a glove. Its ultimate legitimacy comes from the world rather than linguistic convention.
Now consider the very next line of the Tractatus, TLP 2.222:
The agreement or disagreement of its sense with reality constitutes its truth or falsity.
A proposition with a sense must be a picture of a possible state of affairs. As such, that possible state of affairs must either obtain or fail to obtain. In other words, a proposition must be either true or false. So, according to the Tractatus, the very notion of sense necessarily brings with it the notion of truth and falsity. You cannot have one without the other.
Now I think we can begin to see the connection between §137 and §138. So far as the interlocutor is concerned, the requirement for propositions to be true or false arises out of the definition of “sense”. Criticism of the former inevitably implies criticism of the latter. It is as if the interlocutor – worried by the attack on truth-functionality – moves back a step to protect the prior link in the chain of reasoning. For if that holds good then (it seems) the subsequent links must also be preserved.
To put it more generally, both claims are part of the same broad conception of language, ie: language as a kind of calculus whose rules reflect the necessary structure of existence and rigidly determine the way words operate. The various elements of the conception are closely interwoven (that is part of the beauty of the Tractatus); they hold each other in place and, consequently, if any one element is attacked the others automatically rise up in its defence (this, I think, sheds light on Wittgenstein's remark in the Blue Book (p44) that “no philosophical problem can be solved until all philosophical problems are solved”).
The answer to question (2) is also now clear. It is not “fitting” per se that Wittgenstein objects to so much as the interlocutor's specific interpretation of the term and the philosophical theory that lies behind it. (We might say that the interlocutor's remark at the beginning of §138 is somewhat duplicitous – he is trading on the ordinary meaning of “fitting” and “sense” to make his claim seem straightforward and uncontroversial.) The Tractarian account of “fitting” does indeed make no sense if meaning is use. For as we have seen, from the viewpoint of use, “fitting” is a matter of the role the word plays rather than its ability to mirror a supposed a priori world-structure. There is such a thing as a word fitting the sense of a sentence, only not in the way the interlocutor claims.
Are we any closer to answering question (3)? I think we are, but only if we read between the lines. The interlocutor's exclamation at the end of §138 (quoted above) marks the point where we move from discussing ideas explicitly set out in the Tractatus and on to what we might call the “uncredited assumptions” that lurk behind those ideas and help make them seem plausible. And one of those assumptions concerns the link between sense and understanding.
To clarify this we need to return to the picture theory of language. As we've seen, according to that theory a proposition pictures a possible state of affairs which is its sense. But, of course, a proposition doesn't just come out of nowhere – it expresses a thought, and a thought is itself a picture (TLP 3: “A logical picture of facts is a thought”). Therefore “In a proposition a thought finds an expression that can be perceived by the senses” (TLP 3.1). Now, what is it to understand a proposition? 4.024 tells us: “To understand a proposition means to know what is the case if it is true”.
From these brief remarks it is possible to construct an account of communication that goes like this: A has the thought that things are thus-and-so. And this thought is in some sense a picture – that is, whatever form it takes it must combine objects in a way that mirrors a possible state of affairs. A wants to communicate her thought to B so she “converts” it into a proposition. She speaks, writes, draws, uses sign-language or Morse code, etc. The elements of the proposition are arranged in a way that mirrors their combination in A's thought (and thus also mirror a possible state of affairs in the world). Now B perceives A's proposition and he (so to speak) re-converts it into a thought in his mind. And that thought is, of course, a picture. The sense of the picture is what it represents, and it is precisely this that B needs to grasp in order to understand the proposition. Grasping the sense of the picture (seeing that it represents this possible state of affairs) and understanding the proposition are one and the same thing.
This account will be familiar to anyone who's studied Empirical philosophy (especially Locke). The connection it makes between sense and understanding couldn't be more direct: grasping the sense is understanding the proposition. Understanding, therefore, is a thing (specifically, a picture) that we acquire instantaneously when we perceive the proposition. And that is surely right, isn't it? For when we hear or read words we understand them at once; we don't have to wait until we've studied their use before we know what they mean. So if the sense of a sentence isn't to be cashed-out along Tractarian lines how do we account for instantaneous understanding?

That thought, it seems to me, completes the chain of argument that leads from the discussion of propositional form in §137 to the topic of understanding at the end of §138. Wittgenstein's criticism of “fitting” in relation to truth-functionality causes the interlocutor to defend the notion of sense from whence the necessity of truth-functionality originated. And criticism of the notion of sense in turn provokes an appeal to the nature of understanding, because the immediacy of understanding can only be understood (it seems) if something like the Tractarian account of sense holds good. By now we have indeed moved away from the explicit theories of the Tractatus (which is notoriously silent about how thought, understanding etc actually work), and so in a way Fogelin, Hacker et al are right: §138 represents a break. But it shouldn't be thought that we've moved on to completely unrelated issues. We have moved from the explicit theories of the Tractatus to the implicit assumptions that lay behind them.

Sunday, 2 June 2013

Propositional Form

I suggested in Wittgenstein's Toolkit that one way to view the Philosophical Investigations is to see sections 1-133 as demolishing the “traditional” approach to philosophy (exemplified by the Tractatus) in order to establish a radically new method, which the rest of the book then puts into practice. But this is just a rough guide, and of course things are not quite as clear-cut as the distinction suggests.
For a start, §134 does not confront some big, sexy philosophical issue like free will or the nature of consciousness. Instead it begins a brief, curious discussion of the sentence “This is how things are”. Readers unfamiliar with the Tractatus are likely to be completely baffled. Of all the possible topics, why pick on this banal, inoffensive little statement? Actually, however, although the transition is rather abrupt there has already been a certain amount of (easy to miss) stage-setting. First, the topic is glanced upon in §65 when Wittgenstein’s interlocutor accuses him of taking the easy way out:
“You talk about all sorts of language-games, but have nowhere said what is essential to language-games, and so to language [….] So you let yourself off the very part of the investigation that once gave you the most headache, the part about the general form of the proposition and of language.”
Mention of propositional from leads to Wittgenstein’s account of family resemblance concepts (and that account will be highly relevant here).
Then, at §114 Wittgenstein quotes directly from 4.5 of the TLP: “The general form of propositions is: This is how things are.” His subsequent comment is typically cryptic: “That is the kind of proposition one repeats to oneself countless times. One thinks that one is tracing nature over and over again, and one is merely tracing round the frame through which we look at it.”
That remark is also relevant to the discussion in §134, but for present purposes the thing to remember is that the idea of propositional form was of central importance to the Tractatus. There Wittgenstein had attempted to sum it up in the phrase “This is how things are” (in German, “Es verhält sich so und so” – see the postscript below for a discussion of the translation).
Why was this idea so important? Well, it was an attempt to capture the very essence of language itself – to reveal at a stroke its necessary structure, the one thing common to all forms of linguistic communication, and which distinguishes them from mere arbitrary sounds or scratches on a page. Moreover, according to the Tractatus propositions work by mirroring (on the one hand) the thoughts they express and (on the other hand) the states of affairs they represent. So by revealing the essential structure of the proposition you at the same time reveal the essential structure of both thought and the world. In his notebook of 1915 Wittgenstein wrote that it would provide “the nature of all facts […] the nature of all being”.
That’s an astoundingly ambitious claim, and it’s perhaps hard to see how so much metaphysical weight could be supported by a phrase as unremarkable as “This is how things are”. But for Wittgenstein (in the Tractatus) it captured the proposition’s essential features in a pure and condensed form: it showed that a proposition was a picture of a possible state of affairs (ie, it asserted that something was the case); that it was a complex in which simple names were linked in accordance with logical syntax (and this logical syntax in turn mirrored the logical structure of the world); and that it was an essential feature of a proposition that it could be assigned a truth-value – it was true if it pictured a possible state of affairs which obtained and false if it pictured a possible state of affairs which didn’t obtain.
So although at first blush “This is how things are” seems a trivial, empty formulation, the more you unpack its implications the more it seems to take on an emblematic, almost mystical, status. As §114 mentions, you can find yourself repeating it over and over while straining to see with absolute clarity the relationship between language and the world: “This is how things stand, this is how things stand, this is how things stand….”
And it is to this totemic sentence that Wittgenstein turns in §134. So just when we seemed set to move into new territory we get one of the most backward-focused discussions in the whole of the Investigations. On the plus side, however, at least it seems we’re in for something momentous; having already attacked the TLP’s general approach, Wittgenstein is now going to strike at its very heart. Isn’t he? On the contrary! Rather than some “clash of the Titans”, §134 provides one of the most striking examples of bathos to be found in philosophy.
He starts by asking why he was tempted to see “This is how things are” as the general form of the proposition. Two reasons are offered: 1) it is itself a sentence and therefore an example of the phenomenon he was seeking to explain; and 2) it is commonly used as a kind of “schema” – a variable which stands in for a set of specific sentences. These two aspects would seem to leave it well placed to carry out its required role. But against this he makes two observations. First, there is nothing compellingly precise about the form of words chosen in the Tractatus. Any number of alternatives might’ve done just as well (eg, “such and such is the case” or “things are thus and so”) – indeed, even a single letter (“p”) could be used, as happens in formal logic. Of course, it would be ridiculous to call “p” the general form of the proposition, but this just goes to show how the schematic aspect of “This is how things are” fails to justify the metaphysical status allotted to it in the Tractatus. Indeed, its very role as a variable makes it atypical.
This atypical quality is brought home by Wittgenstein’s second observation: there is no such thing as comparing “This is how things are” with reality in order to see if it is accurate. And yet functioning as an object of comparison is supposedly an essential aspect of propositions (TLP 4.05)! Without the possibility of comparison a proposition cannot be assigned a truth-value (TLP 4.06). So the phrase chosen to represent general propositional form fails to exhibit one of its (alleged) primary characteristics. And if that’s so, how can “This is how things are” be called a proposition at all? Now, the Wittgenstein of the Tractatus might’ve agreed with this point and replied that “This is how things are” was a meaningless form of words which attempted to say what could only be shown (and here an obscure metaphysical theory is being defended by an even more baffling one). In the Investigations, however, Wittgenstein sees no need for such obscurities; unlike “p”, “This is how things are” is a well-known phrase with an uncontroversial use in our language. He concludes with withering irony: “so it illustrates the fact that one feature of our concept of a proposition is sounding like one”.
So the sound (or look) of a proposition is part of our concept of what a proposition is. That’s why we’re not troubled by calling (eg) “I sing the body electric” a proposition even though its meaning is obscure at best. (But what about “Joob wa stu”? Or “Gdk rrrx pypy”?) And the “conventional” or “familiar” form of “This is how things are” was one of the (unacknowledged) factors behind claiming it as the general form of the proposition. But of course this familiarity is a contingent feature of our particular language. In terms of the role the sentence plays it’s possible to imagine it being replaced by “p”, or an underscore, or even a hand gesture. But would we even have been tempted to take Wittgenstein seriously if TLP 4.5 had stated “The general form of the proposition is: ___”? Thus the grand metaphysical pronouncement which was to lay bare “the nature of all being” turns out to be (at least in part) almost comically human.
But if we’re going to reject the idea of propositional form, how can we account for the fact that we can and do recognise propositions and distinguish them from other sounds or marks on the page? This, of course, brings us back to the notion of family resemblance concepts, as §135 makes clear. It links not just to §65 but also to §23, where Wittgenstein stresses the endless variety of kinds of sentence. There is no one thing common to all propositions. Instead, there are an overlapping series of similarities that for us mean it makes sense to group them all under the same concept-word. If you have doubts about this, it’s relatively simple (yet instructive) to produce a list of propositions which vary in terms of their form and function. Here’s mine:
  •          The pen is on the table.
  •          All men are mortal.
  •          I am in pain.
  •          Every rod has a length.
  •          King Lear is more profound than Hamlet.
  •          Heroin is better than sex.
  •          Stately, plump Buck Mulligan came from the stairhead, bearing a bowl of lather on which a mirror and a razor lay crossed.
  •          A fool and his money are soon parted.
  •          2x2=4.
  •          E=MC²
  •          a=a

Confronted with the facts, the metaphysical theory looks to be in trouble. But §136 considers an alternative attempt to validate it by focussing on the concept of truth-functionality. To be honest, I find it a tricky, frustratingly cursory section, but my reading of it is as follows.
First, we’re reminded that truth-functionality as a necessary feature of propositions was one of the things Wittgenstein tried to capture in “This is how things are”, and in doing this he was (he felt) describing a necessary truth about language and its connection to the world. So “Such and such is true (or false)” would’ve been another way of expressing general form. But if language is conceived of as a rigid calculus (as was the case in the Tractatus) then this new formulation becomes problematic because “’p’ is true = p”. The “is true” part adds nothing; it is a redundant clause. Of course, in language as it is actually used (ie, not as a rigid calculus) “’p’ is true” is not a pointless elaboration of p. “It’s true that I lied to you” doesn’t have the same use as “I lied to you”. In fact, it doesn’t even always have the same use as “I lied to you. It’s true.” So either way “Such and such is true” fails to capture essence. From the point of view of language as a calculus the “is true” part is redundant, and from the point of view of use it is just another tool in the box rather than an expression of necessary structure.
That’s not to say, however, that we can’t decide to adopt a definition such as “A proposition is whatever can be true or false”. We might do so when we wished to use “proposition” in a technical sense as something distinct from other types of sentences. So (on this basis) “Give me a dollar” is not a proposition but “I gave you a dollar” is. The technique of asking “can it be called true (or false)?” might be useful here in telling one from the other, rather like the trick used to see if a large number is divisible by 3 (see §137). It should be noted, however, that since “proposition” is a family resemblance concept the meaning of assigning a truth-value will vary from case to case. Consider, for example, the varying significance of replying “that’s true” or “that’s false” to the following:
  •          Paris is the capital of France.
  •          2+2=4.
  •          Virtue is its own reward.
  •          A thing is identical to itself.

One might say “the kind of truth is the kind of language-game” (cf PI Part II, §332).
But the temptation here is to assume that the phrase “A proposition is whatever can be true or false” discovers something about the world. Wittgenstein’s discussion of this temptation focusses on the notion of truth and falsity fitting the concept of the proposition – presumably because that was the form the temptation had taken in his particular case. It is, so to speak, a suggestive form of words, conjuring up the notion of “true” and “false” as jigsaw pieces which only and always lock into another piece labelled “proposition”.
One can see how this way of looking at things might lead to puzzlement. For example, it suggests that truth and falsity exist independently of propositions, even though they can interact with nothing else. What sort of thing, then, is truth? In what sense does it exist? Are we talking about a Platonic Form here? Or something akin to a soul? Or should we say that truth and falsity do not exist independently of propositions but that the expression of a proposition necessarily calls them into being? But how might that happen? How can it be that truth and falsity must come into being with the proposition even though they are distinct from it? – For it cannot be an accident that the two are connected in the way they are, as if it might just as easily have been otherwise. But what is the nature of this necessary connection? Are we talking about a pre-established harmony here? And what does that even mean? And so on. The whole thing is starting to look thoroughly mysterious.
At this point Wittgenstein brings things down to earth by pointing out that the phrase “only a proposition can be true” is merely a potentially misleading way of saying “we predicate ‘true’ and ‘false’ only of what we call a proposition” (§136). In other words, it is the expression of a rule – a grammatical remark disguised as a description. (Re-read §114 now and you will see the relevance of the comment there about TLP 4.5. In fact, §114 is an aphoristic version of the point made in §50. See also "The Death of Metaphysics" for more on this.) What we thought was a startling, almost mystical, discovery – a truth about the world that could not logically be false – turns out to be nothing more than a definition enshrined in a typically idiomatic form of expression.
And now we can see where the puzzling sense of necessity came from: it was linked to the categorical nature of rules. They say “You must do things this way if you want to play the game. If you don’t then you’re playing the game wrong – or else you’re playing a different game altogether”. The hardness of the metaphysical “must” is a misunderstanding, a shadow cast by grammar.
Ultimately, then, Wittgenstein attacks the notion of propositional form as a typical example of the “sublimation” of our language (cf "Logic and Magic"). The formula presented in the Tractatus failed to do its job not because it was poorly constructed but because there was no such job to do. The problem, therefore, lay not so much with theory expressed as with the background assumptions which committed the young Wittgenstein to a particular way of seeing things. The Tractatus was merely an attempt to systematically work through the implications of those assumptions. They themselves went unquestioned – indeed, it never even occurred to him that they might be problematic (cf §308: “The decisive movement in the conjuring trick has been made, and it was the very one that seemed to us quite innocent”). This attempt to dig beneath the surface of an argument and locate the crucial difficulty at deeper level is entirely characteristic of the Philosophical Investigations. I mentioned at the start that Wittgenstein doesn’t tackle a big “sexy” issue in §134. In fact, he never directly does. For him, the problem lies not so much with what (eg) Empiricists and Rationalists argue about as with the assumptions that neither side question. Those assumptions are his real target. But so far he has barely scratched the surface.
Postscript: translating “Es verhält sich so und so”
I think there are problems with the translation of “Es verhält sich so und so”. For one thing, it’s irritating that the Investigations and the two major English translations of the Tractatus each offer a different version. Ogden’s 1922 translation of the Tractatus gives us “Such and such is the case”; then Anscombe’s 1953 translation of the Investigations gives us “This is how things are” (retained in all subsequent editions); and then the 1961 Pears/McGuiness Tractatus gives us “This is how things stand”. (Duncan Richter’s 2009 student edition provides a fourth variation: “Things are thus and so”.)
I’m not saying that any one of those is wrong, but at the very least the diversity creates issues for English-language readers which don’t exist in the original German. For one thing it means that if you come to the Investigations already familiar with the Tractatus you’ll be wrong-footed by the new rendering. I imagine that it’s easy for someone used to Ogden’s Tractatus to completely miss the reference in §134. On the other hand, those who’ve read Pears/McGuiness will get the reference but be irritated by the (frankly) pointless switch from “stand” to “are”. (Though of course Anscombe’s “are” came before Pears/McGuiness’ “stand” – was the change due to a copyright issue? It would be a shame to think so.) Either way, it dilutes the Investigations on an aesthetic level. For when Wittgenstein opened §134 with “Betrachten wir den Satz: “Es verhält sich so und so” he surely assumed that his readers would be familiar with the Tractatus and that their ears would prick up at the mention of this famous phrase. But if there’s no agreement as to what that “famous phrase” actually was then everyone’s ears are going to remain firmly in the “down” position.
It’s also important to realise that the different translations have philosophical implications. For example, it puzzled me for a long time that (in Anscombe’s translation) §134 claims “This is how things are” is used as a schema. You can just about see what this is getting at, but really that’s not the most obvious use suggested by the phrase. It more commonly functions as a prefix to a statement, and implies that the speaker is cutting to the heart of the issue. So someone might say “This is how things are: unless we can raise £5,000 by midnight we’ll lose the house”. For the phrase to work as a schema you have to imagine a strong emphasis on “this”, together (perhaps) with a hand-gesture suggesting the various things to which “this” refers. So it would be “This […] is how things are” with the gesture providing the “[…]”. That’s a bit of a stretch and, in any case, it seems to me that it’s now the gesture which is doing the schematic work rather than the actual words.
Of course, if you substitute (eg) “Things are thus and so” then the schematic aspect becomes much more obvious. (Mind you, I can’t help reflecting that English already has a well-established verbal schematic, namely: “blah, blah, blah”. I suppose it might’ve caused uproar if TLP 4.5 had stated “The general form of the proposition is: Blah, blah, blah”.) The problem with the “thus and so” version (so far as I can see) is that it doesn’t capture the declarative nature of propositions as strongly as “This is how things are”. This is an important element because it stresses the truth-functional nature of propositions. If I utter the words “the cat sat on the mat” merely because I like their sound then there’s no question of me being right or wrong. But if I assert that the cat sat on the mat then that’s either true or false. For this reason, I find it more useful to bear in mind Anscombe’s version when considering §136, which discusses the link between propositions and truth-functionality.

Having said that, it’s not as if the assertive element is absent from “Things are thus and so”; it’s merely less emphatic (because the “are” comes in the middle of the sentence rather than at the end). All in all I find “Things are thus and so” to be closer to the original (I also prefer it to Ogden’s “Such and such is the case”). I wonder why Anscombe changed Ogden’s version, why Pears/McGuiness pointlessly varied Anscombe’s version and why the Hacker/Schulte 4th Edition of the Investigations stuck to Anscombe’s version even though Hacker clearly has issues with the wording and suggests “Things are thus and so” as a more helpful alternative (see Wittgenstein: Understanding and Meaning, chapter XVI). I’d be interested to hear any views on the subject.