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.