Continuing our coverage of the metaphysics of the Tractatus…
(D) Objects are the ultimate constituents of the world. They are non-divisible; they cannot be broken down into anything simpler.
2.02 The object is simple.
2.021 Objects form the substance of the world. Therefore they cannot be compound. (p.119)
[However, recall this claim, already quoted above…]
1.1 The world is the totality of facts, not things. (p.118)
Are 2.021 and 1.1 consistent with each other (i.e., can they both be true)? Perhaps… Here is one interpretation on which they are both true:
· Logical analysis—the sort of analysis that is most relevant to a logician—can proceed only so far: it can break down (non-atomic) facts into atomic facts. But once an atomic fact is reached, logical analysis must cease. It can go no farther. Atomic facts are the smallest constituents of the world that are relevant from the point of view of logic.
· Still, an atomic fact can be analyzed in some sense – not logically analyzed, but we can still understand an atomic fact as consisting of components: objects arranged in a specific way. It cannot be analyzed into further facts (that would be logical analysis)… but it can be understood as consisting of simpler “parts,” none of which is itself a fact.
· The substance of the world consists of objects, which can combine to form atomic facts (which in turn can combine to form non-atomic facts).
· But the world, understood as everything that is the case, consists, in its most basic form, of facts. This is because a fact can be the case, but an object cannot.
· Let “A” be the name of an object; it cannot be the case that A.
· Imagine that a chair is an object in Wittgenstein’s sense—it really isn’t, but just suppose that it is for the sake of the following illustration… It cannot be the case that chair. A chair is too logically simple for it to be the case that chair.
· For it to be the case that ___________, whatever fills in that blank has to have some minimum logical structure or form. And the simplest thing that has any logical structure or form at all is an atomic fact. [For more on this point, see (E), below.]
· So the “smallest” piece of the world with which logic is concerned is not the object but the atomic fact.
(E) An atomic fact (state of affairs) has a logical structure: it is composed of objects in certain relations with one another.
2.0272 The configuration of the objects forms the atomic fact.
2.03 In the atomic fact objects hang one in another, like the links of a chain.
2.031 In the atomic fact the objects are combined in a definite way.
2.032 The way in which objects hang together in the atomic fact is the structure of the atomic fact.
2.033 The form is the possibility of the structure.
2.034 The structure of the fact consists of the structures of the atomic facts. (p.119)
· Imagine the state of affairs consisting of two objects, A and B, being next to each other. Although this state of affairs consists of objects in relation with one another, and thus has a structure, the fact that A is next to B cannot be broken down—the fact is logically simple, basic… “atomic.”
[5.1.3.] The Picture Theory of Meaning.
With the metaphysical background in place, we can now examine the early Wittgenstein’s theory of meaning and of how language can come to be true or false. This theory will amount to a version of the correspondence theory of truth:
the correspondence theory of truth (df.): truth is a relation of correspondence between propositions (or sentences, or beliefs), on one hand, and the world, on the other; for a proposition (etc.) to be true is for it to correspond to the way things are.
As before, the passages in blue are quotations from the Tractatus; the bold claims F through K are my own statements of the central ideas of Wittgenstein’s theory.
(F) “Pictures” or representations (i.e., any of the things that genuinely represent or picture part of the world) are themselves facts.
2.141 A picture is a fact.
(G) It is possible for one fact to picture another if the two facts have the same “form of representation” (“pictorial form”).
2.15 That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another. [Alt. trans.: The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way.]
2.17 What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation. [Alt. trans.: What a picture must have in common with reality, in order to be able to depict it—correctly or incorrectly—in the way it does, is its pictorial form.] (p.120)
The following illustrates how this is supposed to work. Assume that the letters listed below are used as follows:
c = the chair
m = the mug
w = the watch
L = being larger than
T = being on top of
S = being silver
b = the book
d = the desk
Suppose it is a fact that cLb (i.e., suppose that the state of affairs of the chair being larger than the book exists).
In addition to being a fact itself, the fact that cLb is capable of picturing another fact. For example, the fact that cLb is capable of picturing the fact that mTd (the mug on top of the desk).
For the one fact to picture the other, their structure must be the same. A fact of the form wS, for example, cannot picture mTd or cLb — its structure is not the same as the structure of either of those facts.
Now, given that one fact (e.g.,cLb, the fact that the chair is larger than the book) has the same structure as another (e.g., mTd, the fact that the mug is on the desk) and is therefore capable of representing it, how can the first fact come to actually represent the second?
(H) One fact actually pictures another when the objects and relations of the first fact correspond to (i.e., are correlated with) the objects and relations of the second fact.
2.1514 The representing relation consists of the co-ordinations of the elements of the picture and the things. [Alt translation: The pictorial relationship consists of the correlations of the picture’s elements with things.]
2.1515 These co-ordinations are as it were the feelers of its elements with which the picture touches reality. [Alt translation: These correlations are, as it were, the feelers of the picture’s elements, with which the picture touches reality.] (p.120)
For example, suppose that the relation being larger than can correspond to (be the name of) the relation being on top of. The chair can correspond to (be the name of) the mug, and the book can correspond to (be the name of) the desk. In this way, the elements of cLb and mTd come to be correlated with one another, and the first fact becomes an actual picture of the second.
(I) A fact can describe or misdescribe another fact, i.e., it can be true or false.
2.21 The picture agrees with reality or not; it is right or wrong, true or false. [Alt. trans.: A picture agrees with reality or fails to agree; it is correct or incorrect, true or false.] (p.121)
If cLb pictures mTd, then it is possible that that “picture” is true, i.e., if c names m (the chair names the mug), L names T, and b names d.
But that “picture” can also be false, e.g., if c names d, and b represents m, then cLb would state that the desk is on top of the mug. If the mug is actually on the desk rather than vice versa, then what cLb says is false.
So far, we’ve only considered how one fact can picture another fact. But the point of Wittgenstein’s theory is to show us how language can be meaningful. So we still have to see how Wittgenstein answered this question about language: how can a proposition (e.g., “The cat is on the mat”) picture a fact? The answer is:
(J) Propositional signs (i.e., propositions as spoken or written) can picture facts, because propositional signs themselves are facts.
3.14 The propositional sign consists in the fact that its elements, the words, are combined in it in a definite way.
The propositional sign is a fact. …
3.142 Only facts can express a sense, a class of names cannot.
3.143 That the propositional sign is a fact is concealed by the ordinary form of expression, written or printed.
(For in the printed proposition, for example, the sign of a proposition does not appear essentially different from a word. Thus it is possible for Frege to call the proposition a compounded name.)
3.1431 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. (p.121-122)
A propositional sign just is the fact that certain objects are arranged in a certain way. For example, the printed propositional sign “The cat is on the mat” is itself a fact: the fact that “is on” comes after “The cat” and before “the mat.”`
But that example is too quick. 3.143 indicates that Wittgenstein would not accept the foregoing example of “The cat is on the mat” picturing the world as being a specific way because of its words occurring in a specific order. The strong suggestion of 3.143 is that the objects that go together to make up the fact that is a propositional sign are not the written or spoken words…
In fact, Wittgenstein does not take his picture theory of meaning to apply to language in its perceptible aspect…
(We will complete our coverage of the early Wittgenstein’s picture theory of meaning next time.)
Stopping point for Tuesday October 9. No new reading for next time, unless you haven’t yet finished reading ch.10 of your textbook. We will conclude our coverage of that chapter next time. (The reading by A.J. Ayer that was originally scheduled for next time, as well as your third response paper, will now be due one week from today, on Tuesday October 16.)
 For more on the correspondence theory, see “The Correspondence Theory of Truth” in the Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/truth-correspondence/ .
 The alternative translations provided beginning with this passage are from the Pears and McGuiness translation of the Tractatus; the first translation provided, the same as occurs in your textbook, is from the Ogden translation.
This page last updated 10/9/2012.
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