This log was inspired by "How to Read Wittgenstein" and "Ludwig Wittgenstein: the duty of genius" by Ray Monk. It is based on reading Tractatus Logico-Philosophicus by Ludwig Wittgenstein translated by D. F. Pears & B. F. McGuinness (Routledge and Kegan Paul:1963)

Monday, March 31, 2008

Only a sentence makes sense; only in the context of a sentence does a name have meaning.

Wittgenstein now explicitly defines the word expression as any part of a sentence that characterizes its sense. (The sentence itself is also an expression.) In terms of making sense, expression is all that sentences can have in common. An expression denotes both a form and a content.

Prerequisite for an expression are the forms of all the sentences in which it can appear. That makes it a common, characteristic attribute of a class of sentences. Thus, an expression will be exemplified by the general form of the sentences that it characterizes. Once in this form, the expression will be constant while all else can vary.

Thus, an expression will be embodied by a variable whose values are all the sentences containing it. (In the limiting case, the variable will have a constant value and the expression will be one sentence.) Wittgenstein calls such a variable a "propositional variable". Because an expression has meaning only in a sentence, all variables can be construed as propositional variables. (Including variable names.)

If we declare a component of a sentence as a variable, the resulting sentence is now variable and constitutes a class of sentences all of which are values of that variable sentence. In general, this class will also depend on what we mean, according to our arbitrary conventions, by components of that sentence. But even if we turn all the signs with arbitrary meanings into variables, such a class will still exist. Only now the class no longer depends on convention, but solely on the nature of the sentence. This nature fulfills the conditions of a logical form - a logical prototype. What values that propositional variable may take must be specified, and that specification is what constitutes the variable.

Specifying the values of a sentential variable is to specify the sentences whose common characteristic the variable is. The specification is a description of these sentences, so it will only deal with symbols, not their meaning. The sole requirement is that the declaration be a mere description of symbols and state nothing about what is signified. How the sentences are described is not essential.

Like Frege and Russell Wittgenstein construes a proposition as a function of the expressions contained in it.

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