Tractatus Logico-Philosophicus - Main Theses - Logical Atomism

Logical Atomism

Although Wittgenstein did not use the term himself, his metaphysical view throughout the Tractatus is commonly referred to as logical atomism. While his logical atomism resembles that of Bertrand Russell, the two views are not strictly the same.

Russell's theory of descriptions is a way of logically analyzing objects in a meaningful way regardless of that object's existence. According to the theory, a statement like "There is a man to my left" is made meaningful by analyzing it into: "There is some x such that x is a man and x is to my left, and for any y, if y is a man and y is to my left, y is identical to x". If the statement is true, x refers to the man to my left.

Whereas Russell believed the names (like x) in his theory should refer to things we can know epistemically, Wittgenstein thought they should refer to the "objects" that make up his metaphysics.

By objects, Wittgenstein did not mean physical objects in the world, but the absolute base of logical analysis, that can be combined but not divided (TLP 2.02–2.0201). According to Wittgenstein's logical-atomistic metaphysical system, objects each have a "nature," which is their capacity to combine with other objects. When combined, objects form "states of affairs." A state of affairs that obtains is a "fact." Facts make up the entirety of the world. Facts are logically independent of one another, as are states of affairs. That is, one state of affair's (or fact's) existence does not allow us to infer whether another state of affairs (or fact) exists or does not exist.

Within states of affairs, objects are in particular relations to one another. This is analogous to the spatial relations between toy cars discussed above. The structure of states of affairs comes from the arrangement of their constituent objects (TLP 2.032), and such arrangement is essential to their intelligibility, just as the toy cars must be arranged in a certain way in order to picture the automobile accident.

A fact might be thought of as the obtaining state of affairs that Madison is in Wisconsin, and a possible (but not obtaining) state of affairs might be Madison's being in Utah. These states of affairs are made up of certain arrangements of objects (TLP 2.023). However, Wittgenstein does not specify what objects are. Madison, Wisconsin, and Utah cannot be atomic objects: they are themselves composed of numerous facts. Instead, Wittgenstein believed objects to be the things in the world that would correlate to the smallest parts of a logically analyzed language, such as names like x. Our language is not sufficiently (i.e., not completely) analyzed for such a correlation, so one cannot say what an object is. We can, however, talk about them as "indestructible" and "common to all possible worlds." Wittgenstein believed that the philosopher's job was to discover the structure of language through analysis.

Anthony Kenny provides a useful analogy for understanding Wittgenstein's logical atomism: a slightly modified game of chess. Just like objects in states of affairs, the chess pieces do not alone constitute the game—their arrangements, together with the pieces (objects) themselves, determine the state of affairs.

Through Kenny's chess analogy, we can see the relationship between Wittgenstein's logical atomism and his picture theory of representation. For the sake of this analogy, the chess pieces are objects, they and their positions constitute states of affairs and therefore facts, and the totality of facts is the entire particular game of chess.

We can communicate such a game of chess in the exact way that Wittgenstein says a proposition represents the world. We might say "WR/KR1" to communicate a white rook's being on the square commonly labeled as king's rook 1. Or, to be more thorough, we might make such a report for every piece's position.

The logical form of our reports must be the same logical form of the chess pieces and their arrangement on the board in order to be meaningful. Our communication about the chess game must have as many possibilities for constituents and their arrangement as the game itself. Kenny points out that such logical form need not strictly resemble the chess game. The logical form can be had by the bouncing of a ball (for example, twenty bounces might communicate a white rook's being on the king's rook 1 square). One can bounce a ball as many times as one wishes, which means the ball's bouncing has "logical multiplicity," and can therefore share the logical form of the game. A motionless ball cannot communicate this same information, as it does not have logical multiplicity.