From Act V, Scene I of Shakespeare’s Hamlet

HAMLET

To what base uses we may return, Horatio! Why may

not imagination trace the noble dust of Alexander,

till he find it stopping a bung-hole?

HORATIO

'Twere to consider too curiously, to consider so.

HAMLET

No, faith, not a jot; but to follow him thither with

modesty enough, and likelihood to lead it: as

thus: Alexander died, Alexander was buried,

Alexander returneth into dust; the dust is earth; of

earth we make loam; and why of that loam, whereto he

was converted, might they not stop a beer-barrel?

Imperious Caesar, dead and turn'd to clay,

Might stop a hole to keep the wind away:

O, that that earth, which kept the world in awe,

Should patch a wall to expel the winter flaw!

But soft! but soft! aside: here comes the king.

Interlude 6.1: Picture Theory and Projecting

[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).

Interlude 5.1: Schroeder on the Picture Theory of Meaning

Schroeder begins his account of the Picture Theory of Meaning by presenting three puzzles that drove Wittgenstein’s early thought. The first two should feel familiar by this point, and the semantics that he needs to solve those problems stems directly from his logical atomism (although he developed the semantics first and then the ontology that had to go with it). It is the third puzzle that will most interest us, as it is the puzzle that will require the picture theory.

i) Given that language is essentially a matter of signs standing for things (referentialism), how can there be false propositions: i.e., propositions that are meaningful although there is no actual fact represented by them (cf. NB, 30 Sept. 1914)?

[The Puzzle of False Propositions]

ii) How is it possible with a limited number of different signs to describe any of an infinite number of possible states of affairs (cf. NB 98)?

[The Puzzle of Infinite Description]

iii) Words are essentially names, standing for objects (referentialism). A sequence of names (‘Tom Dick Harry’) is not a statement (cf. NB 96, 105). How, then, is it possible for a proposition to be more than just a sequence of names and to make a statement about the world? (Schroeder 52)

[The Puzzle of Propositional Form]

The first puzzle (The Puzzle of False Propositions) stems from the central assumption of referentialism (that language must at some point refer to the world): the puzzle is over how false propositions can make sense to us if they do not point to anything actually in the world. We’ve already seen how Wittgenstein’s logical atomism will help him to address this problem: only names refer to the world (they refer to objects); propositions do not (they picture possible arrangements of objects). Propositions thus do not have meaning, meaning (!) that they do not refer to the actual world as it happens to be right now; instead, propositions pick out a possible fact from all logically possible worlds – and say, as it were, that the fact is true. The proposition pictures a possible fact and so has/makes sense. (And so Wittgenstein says, at TLP 2.221, “What a picture represents is its sense.”) However, one does not need “knowledge of the truth or falsity” of the proposition in order to know its sense. One can know the proposition’s sense – and so understand it – without knowing whether it is true. This fact – that we understand false propositions – is obvious to us, but Wittgenstein is trying to understand this fact philosophically, meaning that he wants to know the ontological, semantic, and logical implications (and underpinnings) of this fact. (He’ll also be interested in the ethical implications of it and the implications it has for our understanding of subjectivity.)

The solution to the first puzzle, then, is that “referentialism must be restricted to [names]” (Schroeder 53), and the idea of sense (Sinn in German) must be introduced. A “fixed one-to-one correlation between language and world” takes place only at the level of names, whereas propositions have a “two-way relationship to [the world]” insofar as they can point toward the world (if true) or away from it (if false – if the world is not in fact as the proposition pictures it but rather the opposite, i.e., when the pictured fact does not obtain) (ibid.; Schroeder spells this out more fully on page 55). One interesting upshot of this solution is that, with respect to language, “what matters is never truth” (to cite Nietzsche from a different context, as Schroeder does at page 54); rather, qua Wittgenstein, what matters is the ability to express truth. Whether something is true is an empirical matter, but that and how we can express potential truths is a philosophical matter.

Puzzle (ii) (The Puzzle of Infinite Description) is, as Schroeder notes, solved using the same conceptual tools (the concepts of object and fact on the side of reality and their linguistic counterparts, names and propositions, which attempt to mirror that reality). I need to understand the reference/meaning of a name in order to understand a name. Wittgenstein assumed that this happened either through direct acquaintance with the object or by having the reference explained to one. However, if every sentence was a sort of “name,” then I’d need to be acquainted with or have explained to me the meaning of every sentence. In other words, someone would have to explain what the sentence is pointing me to (some actual fact) – as if the sentence were not already trying to do that on its own! (And how would you explain the reference of that sentence without explaining the reference of other sentences? An infinite regress looms.) The way around this is to say that only names name objects, and all propositions are built from names. We understand the names and so we can then understand all the different possible arrangements of those names – and this is in fact the case: we understand far more than what we directly experience or have directly explained to us. This is just something that we can do once we grasp a language.

Puzzle (iii) (The Puzzle of Propositional Form) is trickier and it requires that we introduce a new idea (albeit one that we’ve talked about in class): the idea of logical form. The Puzzle is this: Even if I have names for each object, how do I arrange the names in the right way, such that they hang together in the sentence in the same way as the denoted objects are hanging together in the world? The answer, in a simple version, is this: The proposition pictures the fact. Put otherwise: The proposition puts together the names in a way that mirrors the way that the objects are arranged in the fact. A quick insight into what he means is given by the possible arrangement (in Schroeder’s example) of the words ‘Jones,’ ‘Smith,’ and ‘sues.’ Different arrangements yield different senses: “Jones sues Smith” is very different from “Smith sues Jones.” This arrangement is what Wittgenstein calls the “determinate relation” of the parts of a proposition to each other. Of course, this relation is ultimately (insert corny arrhythmic-finger-on-desktop drum roll here) logical!

This then raises the question, What is logical form (as opposed to what we commonly think of when we think of pictorial form), and how does it enable a proposition to picture reality? Of central importance here will be the distinction between a proposition and a propositional sign (which is the sensible manifestation of the proposition) and the idea of thought as projecting the proposition via the propositional sign. These are the central ideas of the 3.1s, which is our primary focus in class tomorrow.

Class 5: Deeper into Logical Atomism; Deeper into Confusion

I don’t have too much to say by way of review of Class 5. Almost everyone seemed a bit befuddled, and I had at least one person confess after class that s/he feels so lost such that s/he might withdraw. That’s more like it! And by that I don’t mean that I want anyone to withdraw, but rather that I need to know where people are at. The student who was (I’m sticking to the past tense here) contemplating withdrawal was clearly grasping what needed to be grasped and is in a safe position as far the ‘Will I be able to write an A paper?’ question, which is always the perennial question (and not one that s/he actually asked, but I always assume that it’s a concern). However, I think that I’ll need to cold call those of you who are quiet so as to draw out your confusions and your thoughts; those who talk up and question or articulate have the grasp they need, but what I say in response to their concerns might not be addressing other pressing concerns that others of you have. Overall, I’m very happy with how you are doing, with emphasis on the adverb.

As for content, I started by going over Schroeder’s quick introduction to symbolic logic (which is also called formal logic). This might have confused you more than helped you. Luckily (?), Section 2.6 is dedicated to the basics of this logic and walks through it more slowly and carefully and – I hope and feel – clearly. But we’ll see. The basic idea that you need to grasp at this point is just that a logical system developed that enabled us to describe ordinary language sentences in logical terms – and in ways that reveal the logical complexity of those grammatically simple statements. Wittgenstein accepted this logico-analytic truth (that apparent grammatical form is different from actual underlying logical form), and it is a primary impetus for the logical atomism that he developed.

We then got further into logical atomism, and most of what we did covered Section 2.5 of Schroeder’s book, which I’ve already presented in Interlude 4.1; thus, that post provides the best review of the content we covered in class. There were fewer questions than usual, but what was said seemed to reflect a continued growing grasp of the material, and there were more attempts to articulate what Wittgenstein is saying (as opposed to asking me questions about what he said); Steven seemed to be very much thinking Wittgenstein’s thoughts near the end of class.

We then got off to a good start with the 3.1s. Steven got us going, and Emerson made a good first foray into restating what Wittgenstein means by “projecting.” He seems to clearly mean “objectifying” (Emerson’s constructive paraphrase) in the sense of making a proposition/thought objectively available to us in a sensible medium (such as visual (writing) or acoustic (speech)). We had just enough time to read the 3.1s and to gather up two strange potential consequences of Wittgenstein picture theory of meaning: it seems that (a) thoughts have a non-worldly form and (b) there is something that thinks/projects these thoughts – a something that is not itself a fact in the world. Cool.

Blog Prompt 2: Trying to Picture Logical Atomism

You are likely in a position similar to where you were when you wrote the first blog: confused and overwhelmed. This is still to be expected, especially insofar as we’ve been working our way through what might be the most difficult part of the TLP: the logical atomism. The idea, however, is that if you grasp the basics of logical atomism, then the rest of the text is more interesting and fruitful. And you most likely grasp these basics already – and that you do so will become evident when we start to apply (so to speak) the logical atomism to thought, subjectivity, logic, and ethics.

The main prompt for your second blog post is quite simple: “Describe the logical atomism as fully and as clearly as you can.” As you do this, you will find yourself perhaps having the thoughts of the TLP – the thoughts without which you cannot understand the text (although one must wonder whether thoughts of logical atomism picture any possible facts – and so whether these thoughts are really thoughts or are instead something else). And what I said in the first blog prompt remains true: “Struggling with these thoughts should lead you to question a lot of what you take for granted – even if you continue to believe what you take for granted.” And what you might take for granted at this point is what simple, everyday words such as ‘object,’ ‘name,’ ‘fact,’ ‘sentence,’ ‘reality,’ and ‘world’ (to mention just a few) really mean. Indeed, with this in mind, another statement that I made in the first blog prompt remains quite true: “Many of these terms are everyday words, but they clearly mean something slightly different here.”

It’s the use of everyday words to denote (if that’s the right word) technical philosophical concepts that makes the initial encounter with the logical atomism of the TLP so frustrating but also so uncanny (with ‘uncanniness’ being the kind of thing that lures one into philosophical reflection). Some of you might have felt that you had a basic grasp of those words and so of logical atomism when I first introduced it in Class 3, but now that we have pushed further into the logical atomism and the reasons for it, you might find yourself doubting what you initially thought. You perhaps had a mere pseudo-grasp of logical atomism, and you’re now on your way to replacing it with an actual grasp of this ontology. This is to be expected – and it is part of why we have pushed further in Classes 4 and 5: we have pushed further not so that you can grasp and understand all the various arguments one might make for logical atomism (although I hope that some of you grasp some or even all of them) or the problems that arise with logical atomism. Rather, asking these questions (What arguments support it? What problems can one find with it (on its own terms)?) help to make clear what the basic parts of this ontology are. And that’s all I want – to make sure that you could spell out, in two or three hundred words or less, what the theory of logical atomism states and maybe also a basic sense of why it states that.

This basic grasp of logical atomism – and it need only be very basic – is necessary to make sense (and have fun with) the rest of the TLP and, beyond that, the Philosophical Investigations. Why you need to know those basics – and why the grasp need only be basic – will become clearer later.

However, the process that we’ve undergone in the past couple of classes is one that will be repeated throughout the course: We’ll introduce ourselves to some philosophical set of concepts or perspective, and it will be introduced using ordinary language, but those ordinary words will be used and joined together in such a way that we question what we think they mean (and how we ourselves see things). Grasping that new meaning will require that we question them thoroughly, and this leads to two things. First, it leads to a better understanding of our ordinary language and our ordinary thinking and how they both work (when they work) and trip us up (when they don’t work so well). It also introduces us – and this is ultimately what is of value – to actual thinking. Wittgenstein wrote in such a way that what he thinks cannot just be handed to you like a piece of information that you memorize or a method that you can then quickly apply for yourself. Rather, you must think the thoughts yourself, and in the process you must work on and refine your own capacities for thinking. It calls for many mental qualities: flexibility; precision; inquisitiveness; endurance; the ability to imagine various reasons for a belief (especially beliefs that are not one’s own); the ability to look at things from many perspectives; and the ability to take a complicated thought and see how all its parts hang together and require each other. The logical atomism of the TLP is indeed faulty; however, it has enormous strength – especially in the context of the text as a whole – as a method for helping you to develop your capacity to think critically and philosophically.

Three last thoughts. First, I’m blogging (here in “The Unsayable Panda”) a review – or in the case of “interlude” posts, a preview – of our classes. I realize that it can be hard to hold onto everything we do in class, and so these posts will help us to keep a record of everything.

Second, in addition to blogging about what logical atomism is and why Wittgenstein believed it was, as an ontology, necessary, you might also begin to closely read and make sense of the 3.1s. They are vexing, but in a very interesting way. If you have a nice clear grasp of logical atomism, you should find that you can both summarize that and then turn to the 3.1s. Of course, you might also wish to present a grasp of logical atomism and then turn to the questions of why one might hold this ontology or how one might defend it or what its main problem is.

Finally, don’t worry about understanding everything. There is a lot in this tiny text, and we just want to grasp the basics, even thought getting that grasp requires that we push beyond the basics. But when it comes time to write about the TLP, you will be able to pick your topic and you will be allowed to write expositions instead of arguments (meaning that you can seek to explain and clarify as opposed to argue for or against). For instance, you might wonder at what the logical atomism is and then, once you grasp it, at how it entails the views on the subject or ethics that Wittgenstein will later introduce. But if you think of each proposition as a battle (a battle to make sense of it), you might then decide not to fight each battle. Instead, fight strategically and aim to win the war (which is the fight to get a basic grasp of the text as a whole).

Interlude 4.1: Schroeder on Logical Atomism

Wittgenstein’s logical atomism stems from his appreciation of the model of analysis developed by the Cambridge philosopher Bertrand Russell. According to Russell, a proposition such as “Scott was the author of Waverly” is actually very complex and can be analyzed into a least three other propositions:

Fact: Scott was the author of Waverly.

Atomic Fact 1: At least one person wrote Waverly.

Atomic Fact 2: At most one person wrote Waverly.

Atomic Fact 3: Whoever wrote Waverly was Scott.

Wittgenstein draws a conclusion from this sort of analysis: “the apparent logical form of a proposition need not be its real one” (TLP 4.0031). (In other words, we confuse ourselves by treating grammar as logic.) A typical proposition of our language is a logically complex one that describes a fact that is itself complex. The proposition can be analyzed (i.e., broken down into) elementary propositions, each of which describes an individual state of affairs (i.e, an atomic fact or Sachverhalt). Taking this to be true, Wittgenstein must then develop an ontology that captures what these individual states of affairs must be like.

Schroeder says that he will look at three propositions (one of which is two combined) in order to develop the logical atomistic ontology associated with the Sachverhalt, although he actually ends up looking at four:

Facts, not things: 1.1 The world is the totality of facts, not of things.

Simple objects: 2.02 + 2.0271 Objects are simple […] unalterable and subsistent.

Determinacy of sense: 3.23 The demand that simple signs be possible is the demand that sense be determinate.

Independent Sachverhalten: 2.061 States of affairs are independent of each other.

I’ll review each in turn.

Facts, not things: A list of all things would not describe the world; we need to know how the things are arranged.

Simple objects: Russell envisaged a complete analysis of any given thought that would trace it back the atoms of language, each bit of which corresponds to some bit of the world with which we are acquainted (mostly just sense-data). Wittgenstein agreed that the aim of analysis is to “uncover the atoms of language”; however, he “did not adopt Russell’s empiricism about those simples” (Schroeder 40). (Whether his simple objects – that that the atoms of language name – must be empirical is unclear; as Schroeder notes, Wittgenstein was undecided on the point, and scholars still debate it.) Wittgenstein postulated the existence of these atoms of reality not on the basis of any empirical evidence (which he did not have) but rather on the basis of what we call a priori reasons: reasons that argue about the nature of something prior to any empirical investigation. Schroeder offers three possible a priori arguments that Wittgenstein might have made or even had in mind.

Analysis must come to an end: Here the idea is that analysis cannot go on forever; we must eventually get to those most basic parts of language that have meaning not on the basis of referring to other bits of language but rather on the basis of referring to bits of the world. Language must, in other words, at some point point to something outside itself. However, while it might seem plausible to claim that analysis of language must in this sense come to an end at some point – we must at some point go outside language to the world that language describes (and makes more fully available to us) – it is not clear why a simple atom of language (a name) must denote a simple atom of reality (an object) and not something complex. Why cannot “tree” be a name that denotes something complex (a tree), even though tree functions as a simple sign in language?

Autonomy of sense: The answer has to do with the ‘fact’ that language can have meaning – i.e., a proposition can have sense – regardless of what happens to be the case. This leads to his second argument for simple objects. This one stems from proposition 2.02, which introduces the claim that objects are simple. The first comment on this (2.021) explains why: these objects make up the substance of the world. The first comment on that (2.0211) explains why: if there was no substance, then the sense of one proposition would depend on the truth of another proposition. The second comment on 2.021 (namely, 2.0212) then further explains that if 2.0211 were so, then we could not make a picture of the world of any kind (true or false). Why is this?

As Schroeder explains, the worry here stems from making the referentialist assumption, namely, that meaning is a matter of the things out in the world to which language ultimately refers. Thus, the “meaning of a name is the object it denotes” (42). (Note that propositions do not have meaning; they have sense.) If the object that a name denotes does not exist, then the name denotes nothing and has no meaning. The propositions in which it occurs will then not have sense, since they contain (perhaps at a deep level available to us only upon a logically possible analysis) a name that points to nothing; this means that some atomic fact that this proposition points to cannot in fact exist and so it cannot in fact be pictured, and the proposition does not picture anything logically possible.

For instance, if we take the statement, “President Washington asked me to call on him,” and we then regard “President Washington” as a name, and we accept that President Washington no longer exists, then the name has no meaning, since there is no object/thing to which it points. Here, the sense of the proposition “President Washington asked me to call on him” (let’s call this proposition p) depends on the truth of the proposition “There exists a man that is President Washington” (let’s call this proposition q). It is possible for p to have sense only if it is possible for the fact it describes to be true; however, q is false, meaning that the fact that it describes could not be true. Thus, p has no sense (it is not bipolar) and in fact is nonsense – it points to no possible fact and is actually not even really a proposition. However, this is clearly not true, and so it must not be the case that the sense of p depends on the truth of q. (Notice also that q is not the name, but rather a proposition about the name “President Washington.” If proper nouns were treated as Tractarian names, then it would be possible for those names to have no meaning, since the referent might not exist; thus, in order to know if we can use a name, we need a proposition – such as “The referent of this name exist” – to be true, but this would be strange, since names are meant to, as it were, speak for themselves as the basic building blocks of language.)

It might seem clear at this point why Wittgenstein thought description would be impossible if the sense of one proposition depended on the truth of another. However, he goes further and offers two more explicit accounts, one which just spells out what I spelled out above with the “President Washington” example. But he (Schroeder) first looks at Max Black’s account (Black was an early and influential Wittgenstein scholar). Black posits (quite plausibly) that this ‘dependency of sense’ (the idea that the sense of one proposition is not autonomous of the truth of other propositions but in fact depends on them) would involve an infinite regress: in analysis, we would have to determine if q is true in order to know if p is true, and q would itself depend on some proposition – say, r – and r would depend on s, and so forth. Schroeder points out that this is flawed as an argument for the problem of the ‘dependency of sense,’ since it is dealing with verification, not sense: yes, we would never be able to verify whether some proposition is true, but we often make claims that make sense to us without our knowing if all the truth-conditions on which those claims rest are themselves true. The issue for Wittgenstein at this point is not whether we could ever actually verify the truth of the proposition; the issue is whether we can know that our proposition does in fact have sense. Is it logically possible for it to pick out a possible state of affairs in the world?

The Status of Proper Names: Wittgenstein’s answer is that if some name within my proposition has no possible referent, then the proposition cannot have sense and cannot possibly (in a logical, not just empirical sense) depict anything. This is the strongest version of the second argument, and Schroeder introduces it on pages 44-45. To develop this explanation and defense of the early Wittgenstein’s views, he turns to the later Wittgenstein’s views of these earlier views. The idea we get from that later account of this earlier view is this: the problem is that we talk about grammatical proper names all the time, and many of those names refer to things that no longer exist (or never existed), and yet the sentences in which those names occur clearly make sense to us. Upon realizing this, the early Wittgenstein had two options: give up referentialism (the idea that names have meaning via denoting existing objects) or redefine what a name is. Wittgenstein (early on) chose the latter option: he claims that what we commonly regard as a proper name is a grammatical concept but not a logical one. Logically speaking, what we call ‘names’ are actually ‘disguised descriptions’ of the world: they are really a set of propositions that describe a possible state of affairs and are not simple atoms of language that pick out simple objects.

This version of the second argument for logical atomism is the strongest of those that depend on the autonomy of sense. And Schroeder rightly notes and emphasizes that this argument in defense of simple objects contains only one dubious premise: the truth of the doctrine of referentialism. Insofar as this second argument stems from the fact that our propositions do in fact have sense even when they depict non-existing facts (which we are erroneously but habitually inclined to call ‘things’) and whether any other proposition is true, we might call this argument for simple objects the ‘Argument from Propositional Sense.’ One might also call it the ‘Argument from the Autonomy of Sense.’

Determinacy of sense: This defense of the existence of simple objects is closely related to Wittgenstein’s assumption that sense be determinate, i.e., that every meaningful proposition of our language have a sense that depicts some possible fact in a determinate way, by which he means that it is possible to then verify that the proposition is true. In 3.23, he refers to this not as an assumption but as a demand: “The demand that simple signs be possible is the demand that sense be determinate.” For some, this points to the central question that motivates the TLP: How is determinate meaning possible, i.e., how is it (logically) possible that our ordinary language works as well as it does?” If we demand that our theory explain the determinacy of sense, then we are, Wittgenstein is claiming, also demanding that there be simple signs (for reasons we have just seen), and this demand for simple signs implies a demand for simple objects, since a simple sign (a name) has no meaning (qua Wittgenstein) if there is no simple object to which it refers.

It might seem clear at this point why determinate sense requires simple things – both simple signs and simple objects – but Schroeder elaborates what we might call the ‘Argument from the Determinacy of Sense’ in case it is not. (Note that we are here dealing not with the simple fact that my propositions have sense – even when they refer to what seem to be non-existent things – or with whether that sense is autonomous but rather with that fact that that sense is also determinate). What Wittgenstein has in mind by ‘determinacy’ is spelled out on pages 46-47 and allows for the fact that I might – at the level of ordinary language – speak in ways that seem general, vague, and imprecise. However, such general statements are made in particular situations that help to give them a particular sense; further, much of that sense might well be ‘in my head,’ so to speak. Thus, when I say, “The book is on the table,” it is possible for you to know exactly what I mean – which book and which table and whether the former is on the latter. The ‘details’ that make the sense of the proposition determinate are, as he put it in his notebooks on 21 June 1915, “added in thought” (47). In other words, an analysis of my ordinary language utterance would reveal that utterance’s sense by analyzing what appear to be general terms into that that connects those terms with simple objects. “The book” is a complex that can be broken down into simple signs that correspond to those and only those objects that are arranged as the particular book that I have in mind. I do not need to actually be consciousness of this exact composition, but it must be there at some level in my thought in order for me to think determinately about this exact book and no other. Thus, the complex “the book” can be analyzed down into more basic parts, each of which has an internal relation to that complex, since it is not logically possible for the complex to obtain if the parts of which it is made do not obtain.

Thus, to say that a sense is determinate is to say that, with any thought that we have (with any proposition that we think or utter or write), it is always logically possible for us to spell out the more basic propositions out of which that complex proposition is built. But doing this is only possible if we get down to lowest level of analysis beyond which we cannot and need not go. This lowest level would be where we have names joined together in atomic (i.e., elementary) propositions that depict objects joined together in atomic facts (i.e., states of affairs).

Schroeder notes that, as with the other arguments for logical atomism, this one also depends on referentialism: in this case, it depends on the corollary that when a name means an object, it means all the essential features of the object even if we are not in (empirical) fact aware of them. “Thus,” Schroeder writes, “the contents of meaning and sense can outstrip what competent speakers know, indeed what they are able to find out” (48). We’ll return to this issue when the later Wittgenstein critiques it, but Schroeder quickly notes that one could have determinacy combined with infinite and endless divisibility if one could assume that that divisions are regular (although this rebuttal seems to me to be rather weak).

Independent Sachverhalten: This idea of the indepenence of the existence of states of affairs follows from the previous one – in particular from the idea that a complex proposition logically entails the simpler propositions out of which it is built. The idea here is that this is the only internal relation one proposition can have to another: a more complex proposition, given its nature as complex, is what it is only through being composed of those simpler propositions. (Wittgenstein will, later in the TLP, say that it is a truth-function of those simpler propositions.) However, those simple propositions contain no such relationship to each other, and so they are logically independent of each other. This must be the case given the nature of the atomic facts that the most simple, elementary propositions depict: whether any objects are arranged in a particular atomic fact is a contingent matter, and so it cannot logically depend on whether other objects are arranged in certain ways. If atomic facts were logically interrelated – such that the existence of one logically entailed the nonexistence of another – then Wittgenstein’s logical atomism falls apart.

Schroeder goes about spelling this out in a slightly different way. He assumes that Tractarian objects are physical (or at least phenomenal in an empirical sense); we need not assume this, but doing so quickly reveals the problem with the idea that atomic facts are independent of each other. The problem, simply put, is this: “There is a speck of blue here.” Assuming that this is an elementary proposition, referring to an atomic fact, then we should not, Wittgenstein claims, be able to infer the existence or non-existence of another atomic fact and so the truth or falsity of another elementary proposition from the truth of “There is a speck of blue here.” However, this is false: If it is true that there is a speck of blue here, then it is false that there is a speck of red (or yellow or green or etc.) here. It was this “color problem” that led Wittgenstein to later – in 1929 – explicitly reject the Tractarian theory.