[Note: What follows has not yet been edited, so there may be typos and/or jumps. But I wanted to get this up for those who read these posts in advance of class. This one is all focused on the Puzzle of Propositional Form and, connected to that, the problematic notion of projecting a proposition. This topic will likely take up most of the hour, such that we’ll only get a short ways into Wittgenstein’s logic, on which I don’t plan to spend too much time anyways.]
Schroeder begins his explanation of the picture theory of meaning by first reminding us of the puzzle that it was intended to solve (the Puzzle of Propositional Form) and then turning to the actual experience that led Wittgenstein to the insight that forms the basis of the theory. The actual experience stems from his having read about a Parisian court case in which a model was used to depict events. It occurred to Wittgenstein that this “model played the role of a proposition” (Schroeder 56). And, if this can happen, then there must be something similar about the function of each – such that a proposition is in fact a kind of model. This is the birth of the picture theory: the proposition is a picture insofar as names stand for objects (as the figures do in the model), and their specific “syntactic arrangements” mirror or ‘model’ (as the spatial placements of the figures do) how those objects are arranged.
It is important, however, to keep in mind that the application of the metaphor of a picture is limited here: Wittgenstein, as is always the case with his use of everyday words, means something very specific by it. What Wittgenstein aims to show with this metaphor are the ‘facts’ that the propositional elements have the possibility of rearrangement and that any actual arrangement of those elements has the ability to mirror an arrangement that one might actually find in the world. (And, since the elements can be rearranged, they can be put together in different ways in order to picture many different possible facts – with each picture being ‘built’ out of the same set of objects.)
Wittgenstein writes that the elements of a picture – what in a proposition are called names – are the “representatives of objects” (TLP 2.131). He then calls the “pictorial relationship” the “correlations” of those elements with objects (although he uses the Tractarian synonym “things”) (TLP 2.1514). This “relationship” is the referential connection between name and object. However, as Schroeder notes, each name is always in two kinds of simultaneous relationship: each refers to an object and each is also connected to the other names in the given proposition. The relationship between the names is the “structure” of the proposition (TLP 2.15). This structure of these names is the (propositional) picture. Note also that a picture is itself a fact (TLP 2.141)! (Recall that we have already mentioned – but not fully discussed – the ‘fact’ that a thought is a fact: “A logical picture of facts is a thought” (TLP 3).
What Schroeder says at this point confuses me: He says that the picture is a fact insofar as it “is the fact that it has a certain structure […]” (57). Further: “This fact (that a model has a certain structure) represents a certain state of affairs” (ibid.).
Pictorial form: This is different from the structure of the proposition. The structure is how the names are actually arranged in the proposition (which may or may not be how the corresponding objects are actually arranged in the world as it now stands). The form, however, is “the potential for all [the model’s] possible structures” (ibid., which refers us to TLP 2.15ff). Thus, the form is all the possible ways in which the elements of the model can be arranged; each structure is one possible arranged. The elements can only be arranged in the way that the corresponding objects can be arranged. This form is what the model and reality have in common: they share “the possible arrangments of their elements: their form” (ibid., which refers us to TLP 2.16-2.171).
There are different ways that a model can mirror reality, and so there are different kinds of pictures: there are colored pictures and spatial pictures and even the kinds of pictures that we get in music, in which a sheet of music and an actual performance of that musical piece can be said to picture the same thing. Thus, pictorial form need not always be spatial or even visual. However, there are also purely verbal pictures. The example that Schroeder gives is the conventions by which a particular moment in a chess game is rendered in language. Such a picture is not really spatial or visual, but the combinatorial possibilities of the elements (representing chess pieces and their locations) are the same as those of the actual pieces on an actual chessboard. These combinatorial possibilities are ultimately logical in nature, and so what makes this picture possible (what makes it possible for a string of letters and numbers to picture the current state of a game of chess) is logic. The possibility of such a picture is important, because in propositions, the pictorial form can obviously not be either spatial or visual. It, too, is logical. And so we have the concept of logical form.
The logical form of a fact or a picture of a fact is just those sets of possible arrangements of the elements involved – and so it also the exclusion of all impossible arrangements. The logical form (the combinatorial possibilities of the objects being pictured) is not, of course, the form of the world but “the form of reality” (TLP 2.18). We are dealing with reality because we are dealing with possibility, not actuality: we are dealing with what makes the picture possible, and so the arrangement must point to a possible arrangement of the actual objects; if the sense of the arrangement in the picture depended on the objects actually being arranged that way, then the proposition would have no sense if they were in fact not arranged that way.
The 2.18s develop the idea of logical form.
Schroeder here develops one of the strange implications of this idea of logical picturing: namely, the seeming empirical impossibility of our ever offering an example of such a picture. This is something we talked about a bit in Class 6. Take, then, the Paris traffic accident model. The model people and cars do not actually have all the combinatorial possibilities of the things that they picture. For instance (to elaborate on Schroeder’s analysis), let’s say that it suddenly became important that Mr. Dupont pulled 500 francs out of his pocket. The model does not allow for this possibility. However, the idea is that our thought of this state of affairs must allow for all the possibilities of what it attempts to picture. This is tied, as Schroeder notes, to the idea of complete analyzability: the thought must be capable of beign analyzed down to the basic elements (names) that stand in a one-to-one correspodance with the objects whose arrangement is being pictured. We also, in Class 6, noted that this ties in with what we discussed earlier with respect to seemingly general statements the meaning of which is entirely clear: often general or even vague statements work well enough (such as, “The book is on the desk”), and while everything in our thought is not apparent on the ‘surface’ of the thought (in the simple sentence we utter), it does not have to be immediately available to us and we do not even have to be conscious of the deeper, underlying complexity. It just needs to be the case that it is logically possible that we use logical analysis to get down to that underlying complexity. As Schroeder puts it here, “And if no such atomic structure meets the eye, it must be assumed that analysis could bring it to light […]” (59; emphasis added).
So, to sum up: a proposition is a picture insofar as (a) each of its elements (names) correspond to the elements (objects) of the possible fact that is being pictured and (b) those names are arranged in a structure that is logically possible for the given set of objects. There need not be a corresponding fact (i.e., the pictured fact need to be true; it need not obtain; things need not stand that way); the only correspodances are among the elements and the combinatorial possibilities (the logical form) of those elements. The logical form is that set of combinatorial possibilities; the structure of the proposition is one such possibility; the proposition is in essence saying that, of all those many combinatorial possibilities, this one (represented by the structure of the proposition) is the case right now.
Schroeder next turns to the idea of bipolarity: any proposition is either true of false (cf. TLP 4.023). How and that this is so should not be clear: if the pictured objects are arranged just as they are in the picture, then the picture (the proposition) is true. Further, we can put the ojbects together in new ways and thus generate new propositions, thereby introducing ourselves and others to new senses – new logically possible ways that the world might be – without our having to be acquainted with or have explained to us this new sense. Indeed, as Wittgenstein says, “A proposition shows its sense” (TLP 4.022); furthermore, “It belongs to the essence of a proposition that it should be able to communicate a new sense to us” (TLP 4.027). The 4.02s discuss this capacity of propositions to show their sense and in doing so to introduce us to new sense, and the 4.03s say a bit more about how they can do this. (One metaphor that he uses is especially suggestive and is one to which we’ll want to return when we got to the ethical implications of the Tractarian view of the world: “In a proposition a situation is, as it were, constructed by way of experiment” (TLP 4.031).)
And now, finally, Schroeder turns to the 3.1s. He does so by turning to the problem of resemblance: In a pictorial model, the elements of the model resemble the elements of the pictured state of affairs, and it is by this means that the elements of the picture and the pictured are related. However, in propositions, we have no resemblance. And Schroeder here asks an excellent question one that we raised in Class 6 but did not get around to answering: “How, then, in the case of verbal representation is the pictorial relationship brought about? How does one manage to make names stand for objects?” (60). Here he quotes 3.1 and 3.2, but it is worth noting a connection with the 4.03s that he overlooks:
4.0311 One name stands for one thing, another for another thing, and they are combined with one another. In this way the whole group--like a tableau vivant--presents a state of affairs.
4.0312 The possibility of propositions is based on the principle that objects have signs as their representatives.
We did not talk explicitly (in Class 6) about these propositions (or the metaphor of the tableau vivant), but we did talk a good deal about what would be involved in “one name stand[ing] for one thing” and thereby tracking it through all its actual positions in reality (meaning those existing structures into which it enters, which set of structures is simpy a subset of all the possible structures into which it can enter; thus, there is an object that could logically have been a part of the complex fact “Alexander the Great” and later a part of the complex fact “this particular bunghole plug”). It seems like an enormous, even empirically impossible task for something like a tiny little atomic name to do, and yet the very “possibility of propositions is based on the principle that objects have signs as their representatives,” i.e., on the possibility of names doing this amazing thing – and doing it in spite of the fact that none of us seem to be consciously aware of us and might never in our life times be able to analyze our way down to even one of these names.
But assuming that such a kind of name exists, how do we ever hook it up to reality? It is here that the ideas of projection and the propositional sign become crucial. These are introduced in 3.11 and 3.12. Schroeder spends the next two pages (60-61) spelling out some of the consequences of these propositions. There are many.
1. The propositional sign is the sensible appearance of a proposition.
2. The proposition “is not an entity distinct from the propositional sign: rather, it is the propositional sign plus something else that makes it meaningful: namely, a mental act of thinking, or meaning.
3. The propositional sign hooks up with reality via its names, which each denote an object in reality.
4. However, there is nothing intrinsic in words (which are just sounds or scribbles) that connects them to objects.
5. Therefore, something must connect them. This something is entailed in projection.
6. As he puts in his notebooks in 1915, a “mental act of meaning something by the world” is what hooks the word up with an object.
7. Schroeder implies that when I “think of the sense of the proposition,” and so putting it into a projective relation with the world, I must also be meaning something by each of the words in the proposition. (Note Schroeder’s amended translation: he has “think out the sense of the proposition” instead of “think of,” suggesting that the thinking of a sense is in fact a matter of thinking or working it out.)
8. Note, however, something that Schroeder doesn’t here spell out: for projection, it is not enough to think of the meaning of each word; I must think of them all in the right structure.
9. When I think of/out the sense of the proposition in a written or spoken sentence, I am projecting that sensible sign onto the world and ‘infusing it’ (Schroeder’s phrase) with sense.
10. At this point, those signs or scribbles become something more than just mere acoustic or visual data; they become an “expressed thought.”
11. “And an expressed thought is a proposition (TLP 4, 3.1)” (60). And remember, a proposition is a propositional sign (something sensible) that is thought/projected. This might seem odd for two reasons:
a. First, it seems to imply that there is an imperceptible version of the proposition; if there weren’t, then why must we specify that we “use the perceptible sign of a proposition”? It suggest that there are other way so to encounter a proposition. So: Does the proposition ‘exist’ withough a perceptible sign? Can I think it without projecting it? Can I think it and so project it in some imperceptible fashion?
b. TLP 4 says, “4 A thought is a proposition with a sense.” Setting aside the suggestion that there is a proposition without sense (there is not – so why say “proposition with a sense” and not just “proposition”?), it would seem that the thought is a proposition, which seems to need a sensible form. But the thought does not need a sensible form, does it?
12. It is thus an act of thinking that “enables those words [the ones written or uttered] to depict the world” (60).
13. Thoughts are intrinsically (i.e., by their very nature) models of reality; linguistic signs are not. Signs thus need something else: they need to be ‘brought to life’ (a phrase used by the later Wittgenstein) by thought; they need to become a vehicle that thought takes up and uses in order to make itself available to others or even in some sense to myself (which is my way of putting it).
14. The fact that thoughts are intrinsically models but not signs explains why the picure theory is first applied to thoughts and only then to language.
15. Thought underlies every possible kind of picture; i.e., all pictures that we encounter in the world are just various means by/mediums in which thoughts can be expressed.
16. The expression enables a thought to become public.
17. Different languages are just different modes or conventions of expression.
All of this leads quite naturally to wonder what a thought is – which is a question to which I pointed up in 11.b. As Schroeder puts it, it is a “mental picture” (61). As Wittgenstein puts it, it is a “logical picture of facts” (TLP 3). Since a thought is a picture, it must have elements. However, Wittgenstein elsewhere insisted that these elements are not words. Schroeder explains why: a word has meaning (is hooked up to reality – to a specific object) only by a mental act of thinking the meaning. If the elements of thought also had to be thought in order to hook up to reality, then there must be some deeper level of thought that thought these meanings, but then … and so on ad inifinitum. Thus, Wittgenstein had to posit that there were mental elements that correspond to the objects of reality, but they did so without some further agency establishing or ensuring the connection; they are intrinsically connected to reality. However, thought is like a language insofar is it must contain atomic elements, each of which corresponds to an object and each of which can be arranged with other elements in those and only those ways that correspond to the combinatorial possibilities of the corresponding object. We might even presume that there is a possible language in which there is a word for every mental element and so a name for every object. But this still leaves us with the vexing issue of how there can be mental elements of this sort (i.e., that are intrinsically related to objects).
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