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 4^th 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.