Wittgenstein, Ludwig Josef Johann (1889–1951)

4. Negation and tautology

This account does away with the need for a theory of types and Wittgenstein holds that the ideas invoked by Russell to explain the nature of logical truth are similarly unnecessary. His view was that logical truths, such as that all sentences of the form ‘p or not p’ are true, should be explained by pointing to relations holding between some very abstract kind of logical items – negation, disjunction and the like.

Wittgenstein maintains that the negation sign is not a component of a sentence and so does not represent any element of a possible fact (in the quasi-technical sense of ‘component’, ‘element’ and ‘represent’ introduced above). Rather it is the visible mark of an operation one can perform on a meaningful sentence to produce another sentence. The role of the second sentence is to deny that things are as they would need to be to make the first sentence true.

To see the force of this, we must look again at the account of truth given above. What makes a negative sentence true is not the presence of some ‘not-ness’ in a fact but rather the absence of that (the combination of elements) which would have made the unnegated sentence true. This is similarly the case with the other so-called logical constants. Thus ‘or’ does not stand for a possible element in a fact but is a sign by which one can correctly link two sentences if the components of either are so combined as to yield a truth.

Logical tautologies thus do not reveal the nature of special logical objects. Such sentences as ‘It is raining or it is not raining’ do not say anything. But their possibility is a corollary of the existence of a language adequate to say the kind of thing which can be said. So contemplating them can draw our attention to the logical structure of the world (see Logical constants; Logical form; Logical laws).