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.