Monday, August 30, 2010

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.

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