The Later Wittgenstein’s Critique of His Early View of Facts and Objects
Critique of the View of Facts: The Fallacy of Logical Composition — “Complex–Simple” Cannot Describe Facts
The early Wittgenstein held that facts (in the space of actuality) and states of affairs (in the space of possibility) are ultimately constituted by — that is, composed of — objects. The object was, for the early Wittgenstein, a pure simple posited on logical grounds in the construction of his world-view.
The early Wittgenstein distinguishes two different senses of composition. First, logical composition: for example, objects are composed in some specific way into an atomic fact or atomic state of affairs. Second, spatial composition: for example, smaller constituents are composed, by physical or chemical means, into a compound.
The later Wittgenstein criticizes the misunderstandings to which these two kinds of composition can give rise. Spatial composition has a clear “complex–simple” relation: a compound is composed of simpler things. This “complex–simple” relation is easily — and intuitively — transferred to logical composition; on this assumption, what is logically simplest stands in correspondence with what is spatially simplest, and so the “object” comes to correspond to a spatially simplest thing. The later Wittgenstein criticizes this very point and maintains that expressions like “complex” and “simple” cannot be used to describe facts. That is, Wittgenstein is criticizing logical composition itself.
His mode of critique is “intuitive”: he sets out, from the standpoint of everyday usage, what is “off” about the logical edifice he had built in his earlier work.
Starting from the use of the word “point to,” he clarifies the distinction between things (spatial) and facts (logical). When we “point to” a thing, we really can point at it with the finger. When we “point to” a fact, we are not pointing with the finger, but forming an expression such as: “we point to a fact, namely….” That is to say, facts are always described, never literally “pointed to.”
For this reason, Wittgenstein takes the mechanical association of facts with things to be misleading. He argues that the fact “the bottle is to the right of the cup” cannot be mechanically decomposed into the cup, the bottle, and the left–right relation: the former is on the side of fact — it is the fact itself; the latter is on the side of spatiality — it is the compound.
More forcefully: expressions like “complex” and “simple” cannot describe facts at all. The following example will make the point. Take the compound made of bottle and cup; call it . From the standpoint of spatial composition, “ is on the table” must include the cup, the bottle, and their left–right relation, since “the part of the part is part of the whole.” From the standpoint of logical composition, however, the fact “ is on the table” is not in the least intended to say anything about the cup, the bottle, and their spatial relations.
Thus Wittgenstein has already begun to think about “what language is meant to say.” Because a fact cannot be “pointed to with the finger” but can only be “said,” and what is said as a fact does not exhibit (whether in the fact itself or in the intention of the one saying it) the strict containment relation of the spatial compound — the “part of the part is part of the whole,” that is, the “complex–simple” relation. To state a fact is just to state the fact itself, nothing more.
Critique of the View of Objects: The Fallacy of Pure Simplicity
Wittgenstein’s critique has a second level. Not only is it a fallacy to treat facts as composites of objects, but also the logically posited pure simple object is itself a fallacy with respect to the problems of language. Consider the fact that “the chessboard is composed of squares.” If there are objects that ultimately constitute it, what are they? Are they “the chessboard has square 1,” “the chessboard has square 2,” …, “square 1 of the chessboard is to the left of square 2,” …? Are these the objects? They can be — though by this point the “object” that presupposed pure simplicity has already become meaningless, and Wittgenstein is no longer thinking in such terms — but only relative to “the rules of this chess game.” If the rules were changed so that “a piece must occupy four squares,” then the more appropriate “objects” would be “the chessboard has square-region 1,” …, since saying “the chessboard has square 1” would no longer have any point; no one would speak that way.
From this example, “the chessboard has square-region 1” is complex in context 1 (since it can be further broken down into many facts of the form “the chessboard has square 1”) but simple in context 211 In what follows we again deploy the logic of “simple–complex” upon facts at the level of language, since we are trying to expose, from within early Wittgenstein’s own philosophy, the fallacy of his view of objects. Wittgenstein himself, however, simply abandoned his early philosophy and changed his problematic — he did not first demolish the early philosophy from within and then construct a new one.
Different objects may be complex or simple relative to different facts. With respect to facts, then, simplicity is relative, and so there is no absolutely simple object.
What ultimately constitutes a fact is always relative to a concrete context. The pure simple object is meaningless. We always state facts within concrete contexts; we do not state facts starting from a pure simple object that is universally valid for any context.
From the Logical, Pure Object to the Relative Paradigm in the Language-Game
Having criticized logical composition and the pure simple object, the path of gradually decomposing facts and states of affairs into objects so as to answer “the question of the meaning of language in logical terms” has lost its force. Wittgenstein’s problematic likewise shifts to the question of how everyday language is spoken.
On this question, Wittgenstein indicates that the paradigm is the basis of the “use” of language, and that the selection among uses is to be considered with reference to the rules of a particular language-game.
On the “paradigm.” Consider “one meter.” What is “one meter”? It is because of the existence of “the standard meter” that we know what “one meter” means. The “standard meter” is indifferent as to whether it exists. Its existence provides itself, together with all other usages that take it as a reference — if it did not exist, we should not speak of “meters”; if we speak of “meters,” then the “standard meter” must exist, and vice versa.
On the “language-game.” Consider chess. What is meant by “this is the king”? We are not talking about the chemical elements composing the chess piece called “king,” nor about the basic shapes and colors that make up its appearance. We are talking about the rules of chess and the particularity of “this piece” within this game; we are also speaking of this as a piece in a game, and that a piece such as this can stand and move on the squares of the board. What a concept means in language, and which paradigms are invoked to complete an utterance, are bound up with the language-game we are playing — we are at present saying “this is the king” within the language-game of chess, not within the language-game of a chemistry class.
Hence our invocation of paradigms is relative: paradigms constitute the means or elements of representation within a particular system of representation or language-game; they are not pure objects standing independent of any system of representation or any language-game.