The Sense of a Proposition

One of the perennial problems of philosophy is the problem of the ‘aboutness’ of thought. When I was a child someone told me that the Andromeda Galaxy is the nearest galaxy to our own. Having read some science books I pictured a sort of vague fuzz of stars that was nearer to our little spiral fuzz than some other fuzzes farther away.  Being that sort of child, I would have confidently asserted that the Andromeda Galaxy was the nearest galaxy to the Milky Way to anyone who cared to quiz me on the matter.

The question is: what made my thoughts, my mental pictures, my words ‘about’ the Andromeda Galaxy? Gorgias, as paraphrased by Sextus Empiricus, puts the problem marvelously: “It is evident that objects of thought are not things with being. For if objects of thought were things with being, then everything that one thinks of, however one thinks of them, would have being. But this is nonsensical. For it is not the case that if one thinks of a man flying or a chariot being driven in the sea, there immediately is a man flying or a chariot being driven in the sea. And so it is not the case that objects of thought are things with being.” (R. G. Bury, trans.) 

So since the mental representation is not identical with the object it represents, in virtue of what does the representation represent?

The magnitude of the difficulty can be appreciated by opening Book III of Aristotle’s De Anima, in which one of the most sober-minded thinkers in the history of philosophy reads like Hegel. One way of parsing Aristotle’s theory, loosely, is as follows. The mind is a sort of infinitely plastic – something – that can take on any form at all, and what constitutes the aboutness-relation for our thoughts is that the infinitely plastic something that is your mind takes on the same form as the thing out there in the world that you are thinking of. Further, since form is abstract, and since your mind and the thing you are thinking of have the same form, there is a sense in which Gorgias was simply wrong: your thought is in fact the thing you are thinking of, at least when you think of something real – not materially, but formally, just as two matched silver cups share the same formal cause. Thus there is a sense in which, for Aristotle, when I think of the Andromeda Galaxy, my plastic mindstuff has taken on (vaguely?) the form of said galaxy, and because my thought and the galaxy share this form, I am thinking of the galaxy.

This sort of resemblance theory of mental representation got some additional support two thousand years later, when the author of La Géométrie pointed out that owing to the perfect clarity and distinctness with which we can form the idea of an infinitely good, powerful, and knowing being, such a being must exist, and that the existence of such a being is incompatible with wide-scale general failure of aboutness of thought.

These were extremely intelligent people. We are talking about the inventors of formal logic and analytic geometry here. Try to solve the problem on their terms for yourself and see if you do any better.

In the Tractatus Wittgenstein solves the problem essentially by rejecting its parameters. In order to serve as a picture, a thought or proposition does, as in Aristotle, ‘share a structure’ with the fact it represents if it is true. In fact, we can even go farther with the parallel: just as in Aristotle, the true proposition and the fact it speaks of share a common structure. 

But it’s not: the fact over there, the proposition which picks it out over here, and some common structure possessed by both which ‘makes it the case’ that the thing over here means the thing over there.

Rather, “The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs. The mutual spatial position of these things then expresses the sense of the proposition.” (3.1431)

That is, the way things actually are expresses the sense of what we say. This is an inversion of the usual formula, wherein the sense of what we say expresses the way things actually are, or tries to. The usual formula is also OK by W, I think, but the fact that it goes both ways is highly significant.

Even more clearly: “What the picture represents is its sense.” (2.221)

That is, whatever it is we do to understand “Winnie is on the Tunisian rug” is (one of) the same things we do when we look at the Tunisian rug and see whether Winnie is on it; and (one of) the same things we do when we look at a crayon drawing and see that it’s a picture of Winnie on the Tunisian rug; and so on. To understand the sentence or the drawing is to know how to apply it; to be able to look at the rug and see whether Winnie is on it is to be able to understand the proposition. Likewise if we say it in German, etc. (cf. 4.243).

This is the thing in Wittgenstein which gets turned into verificationism, but it’s not verificationism. Verificationism takes a similar insight and crossbreeds it with empiricism to arrive at the doctrine that (roughly) only operationally defined terms with a clear sensory interpretation are meaningful. I think that in the Tractatus W sometimes leans in a verificationist direction, but even then he can’t have been a verificationist, because this is in effect a doctrine of sense, which we can’t have: what it makes sense to say is primary. At the very most verificationism would be the sort of thing that ‘shows itself,’ not a doctrine that could be directly articulated.

It’s also not idealism. “From what you’re saying, Wittgenstein thinks that there’s nothing more to reality than our true thoughts of it!” In a way that’s true, but you could also just as well say that there’s nothing more to our thoughts then their being true or false of reality. The world consists of facts; facts are what true statements state; understanding a statement just is understanding how the world would be if it were true.

Perhaps another way to put it is that ‘thought’ and ‘reality’ are interdependent notions in the Tractatus. (One of the last classes I sat in on with Peter Winch was a seminar on Spinoza which touched on this theme; I think also here of Cora Diamond’s portrayal of Berkeley as a certain sort of “realist.”) We have no conception of reality beyond our thoughts of it, beyond the propositions that could be applied to it; that’s the Berkeleyan side. But we likewise have no conception of thought or propositions beyond our ability to apply them to the world; that’s the ‘direct realist’ side, if you like.

So it’s not, it’s never in Wittgenstein, the fact over here and the proposition over there. Rather, the true proposition is the fact; the proposition is the sense is the position in logical space. Reality makes our statements about it true or false, and is thus in a sense ‘independent of our say-so’, but we have no conception of reality other than the one we can state.

The nonsense has gotten pretty heavy now, but I think this is the view. “The proposition determines reality to this extent, that one only needs to say ‘Yes’ or ‘No’ to it to make it agree with reality. Reality therefore must be completely described by the proposition.” (4.023)

“Whether or not ‘Winnie’s on the Tunisian rug’ is true depends on whether or not Winnie’s on the Tunisian rug.” Yes, but only in the sense that whether the light is green depends on whether the light is green.

The question as to how our thoughts and statements can be about reality is on this view simply a bad question. It’s like asking how a mountain can be next to a valley. They’re not the same thing, but they are linked to one another at a fundamental level.

Gorgias’ argument is addressed by the intrinsic bipolarity of thought. To the degree that a proposition like “A man is flying” has a clear sense, we know how to apply it to reality; either it applies or it doesn’t. If it does, the “object of thought” is the “thing with being”; if it doesn’t, there isn’t any “object of thought” either – only a projection which doesn’t meet with success, as it were.

In such a framework the Cartesian problem arguably never even gets off the ground. Likewise, there is no gap between epistemic and metaphysical possibility.

(This is a post that would really benefit from some spirited interrogation and challenge, if any students, friends, or casual passersby want to get into it a bit.)

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5 comments on “The Sense of a Proposition

  1. I’d never thought Tractatus 3.1431 was to be read that way. You may be right of course, but I thought the idea was that representation by objects is a way of making representation by words or in thought more perspicuous.

    I link this remark to the story about how Wittgenstein was struck by reading about the way a car accident had been reconstructed in court by the help of model cars; this supposedly helped inspire his thinking about representation. In this case the representation is literally made up of little “things” organized in spatial space, which means that (some of) the spatial relations between the model cars stand for the same actual spatial relations between the actual cars (“car A hit car B on its left side”, etc). But this of course is still a representation, not the accident itself.
    This connects with the question what Wittgenstein was actually up to in talking about representation the Tractatus. (A daunting question, to be sure.)

    I wonder whether this isn’t a fairly widespread understanding of his thinking: in the modelling of the car accident we can see how we are able to convey an understanding of the actual event: after introducing some “conventions” (the red car is the defendant’s car, the blue car is the claimant’s car, these lines represent the outline of the street, etc), we are ready to go: the directions in the model represent the actual directions in the scene of the accident: thus, by moving the cars around we can simulate and test various scenarios of what actually happened. The model works because some of its elements as it were take care of themselves – can be directly read off. (Something similar happens when we represent a fact in words, only on a more abstract level of projection.)

    But could this really have been his purpose? The account smacks of psychology: people constituted the way we (some of us) are will be able to derive a certain kind of information from this type of exercise. But Wittgenstein explicitly declares he is not interested in psychology. Rather, it appears, he is engaged in a logical inquiry: it would appear he is trying to make clear what it takes for something (a model, a sentence, a picture, a thought) to be a representation of something else (an actual or possible state of affairs) – i.e. to make clear what it takes for the word “representation” correctly to apply to the relation between the something and the other something. “In speaking of X as a representation of Y we are committed to regarding X and Y as made up elements that correspond to one another; the elements of X are supposed to be concatenated in the same way as the corresponding elements of Y are; if they’re not, the representation is false.” This, as he might have put it later, is an account of the grammar of the word “representation”. (From this, then, it would follow that certain things we say aren’t representations – “This is the will of God”, “Suicide is forbidden”, etc – since there is no concatenation of elements.)

    Is this what it’s about?

  2. seancstidd says:

    Hi Lars! It is such a pleasure to see you here. Kira sends her affection as well.

    With the first part of your letter, I think you answered your own question – if that is the standard interpretation of how Wittgenstein took the use of the model cars in the courtroom, I think it is incorrect, in part for the reason you give. The Notebooks passage where he discusses the cars has some of that ‘flash of insight’ feel to me, and I think what was going on there is this – thinking about what happened in the courtroom, the young Wittgenstein had a sense of ‘seeing through’ the models to the car accident itself. Or rather, seeing through if that was how things really were.

    If you see the models as a picture of the facts you see the arrangement of the physical elements of the model as (roughly, although this is always elided in the Tractatus) the arrangement of the the thing modeled. But in seeing them this way (seeing the symbol in the sign) they themselves vanish – or so the Tractarian thought is, I maintain – and their ‘semantic content’ just is the real situation that they model, if the world is the way the model proclaims.

    And then the flash of ‘insight,’ if one wants to call it that, is that all symbols work in essentially this way – the words in sentences are like the cars in the models, so to speak. (cf. the bit about hieroglyphs at 4.016.)

    Let me sketch an argument for why it has to be that way. I mentioned in my “Checking In” post that I think the clearest short way of expressing the difference between the Investigations and the Tractatus is that where in the former we look for ‘use’, ‘forms of life’, ‘things we do with words’ – the way that our terms are woven into our interactions with each other and the world – you are better at Investigations-thinking than I am – in the latter we just look for what I would call descriptive adequacy – a linguistic unit has meaning when it is the sort of thing that the world can make true or false.

    Now if we accept the “you can’t get outside language” principle (perhaps better: “surely, you don’t command a view of language outside of language by talking or writing about it”) then we need to say something very novel and unique about descriptive adequacy. It can’t be that we have the ‘words’ or ‘sentences/propostions’ over here and the ‘things’ and ‘facts’ over there, because that is a relation between objects that is itself expressed in language, and the question just comes up again at this level – “in virtue of what does your picture of the sentences and facts being related in this way correspond to the reality that the sentences and facts are related in this way”?

    But if significant propositions are ones that can be true or false of reality, can be or fail to be descriptively adequate, and all reality does is say “yes” or “no” to them (4.023), then there is no need for any representation of representation, as it were – which is good because we can’t do that anyway. “Representation” is a formal concept which is more or less the same as “symbol” – it is just a fancy way of talking about what propositions, pictures, models, sense-perception, human behavior signaling propositional attitudes, etc. do when they serve as a “logical picture of the facts.”

    Is this helpful? I could say more but I’d rather stop here and check in.

    I don’t think, then, that these are ‘grammatical remarks’ about representation in the sense of the later works, although we might say that the grammar of ‘representation’ in part underlies them. Rather they are one way of working out what a representation (‘distilling the essence of representation’) is in terms of truth-functionality which makes the concept in a sense vanish – there is nothing interesting to be said about representation that you don’t already understand when you hear e.g. “Winnie is on the Tunisian rug.” And this in turn, if correct, would make a lot of discussions of the correspondence theory of truth, realism and idealism, etc. vanish along with it.

    I also think that Wittgenstein absolutely rejects this line of thought in the later work. §94 comes to mind as especially pertinent: “’Remarkable things, propositions!’ Here we have already the sublimation of our whole account of logic. The tendency to assume a pure intermediary between the propositional sign and the facts. Or even to try to purify, to sublimate, the sign itself. – For our forms of expression, which send us in pursuit of chimeras, prevent us in all sorts of ways from seeing that nothing extraordinary is involved.” (My boldface.)

    But more generally, Wittgenstein talks about what we do with our signs and how we relate them to activities and persons and things all the time in the Investigations. The basic setup of the Builders games requires us to think in these terms from the outset, in fact. And when he ‘deconstructs’ the notion of propositionhood starting at §134, he explicitly deals with “this is how things are” in these terms: “It is employed as a propositional schema, but only because it has the construction of an English sentence. But though it is a sentence, still it gets used as a propositional variable. To say that it agrees (or does not agree) with reality would be obvious nonsense, and so it illustrates that one feature of our concept of a proposition is sounding like one.” What sounds like something is the spoken sign.

    I’ll leave it at that for the time being and see what you think. Be well.

  3. Hi, Sean –

    I’m sorry I’m so late in responding, I’ve been quite busy lately for a variety of reasons.

    The issues we are conversing about are not easy.

    You write: “in seeing them this way (seeing the symbol in the sign) they [the model cars] themselves vanish – or so the Tractarian thought is, I maintain – and their ‘semantic content’ just is the real situation that they model, if the world is the way the model proclaims.”

    I do think there’s something right about that, if I catch your drift. There’s no way a model or picture has to be in order for it to be a model or picture of such and such. In most cases we just take in what it depicts, in a sense we are talking “over the head” of the model or picture. And where we don’t see, there may be no remedy: we can’t prove what the picture depicts, though we may nudge someone towards seeing it.

    Sometimes, of course, features of the picture-object may come to matter: “Is that another man standing behind the king, or is it just a discoloration of the paper?” But again there are no rules for settling this.

    I’m here speaking of how things appear to me to be. The feeling I have is that the Tractatus is perhaps compatible with this, just that the range of cases Wittgenstein is thinking about there is so severely limited (matters with truth-value). But I may be wrong.

    Nice to hear from Kira. Say hello to her from me!

  4. seancstidd says:

    As you can see, I am not super-fast about responding all the time either! But thank you for the discussion and the response.

    “The feeling I have is that the Tractatus is perhaps compatible with this, just that the range of cases Wittgenstein is thinking about there is so severely limited (matters with truth-value). But I may be wrong.” I could say this myself! I think some of what I was hashing out here in my posts and in some of the discussions with Philip Cartwright relates to precisely this issue, the sense in which the T is a special case of the I and thus continuous with it, and the sense in which they are completely different pictures. I’m still fairly happy with my ‘early and late’ post on that subject as far as it goes.

    Be well!

  5. seancstidd says:

    In “Remarks on Logical Form,” W says: “I have said elsewhere that a proposition “reaches up to reality,’ and by this I meant that the forms of the entities are contained in the form of the proposition which is about these entities.”

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