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But nothing could be further from the truth. The fundamental principle underlying Wittgenstein’s argument is that the source of a philosophical problem often lies in a crucial and often elusive difference between the surface grammar of a concept-word and its depth or logical grammar, or in the philosopher’s tendency to treat what are disguised grammatical propositions as if they were empirical propositions. 4 INTRODUCTION Where Russell was certainly right, however, was in thinking that the later Wittgenstein was fundamentally opposed to the scientistic conception of philosophy.

Such restrictions mean that strings such as ‘x nʦx n’ are ill-formed, thereby blocking Russell’s paradox. The ramified theory of types goes further than the simple theory. It does so by describing a hierarchy, not only of objects, but of closed and open sentences (propositions and prepositional functions, respectively) as well. The theory then adds the condition that no proposition or prepositional function may contain quantifiers ranging over propositions or prepositional functions of any order except those lower than itself.

E. e. from the point of view of an interpretation, in which meanings are assigned to the formal symbols of the system). Given a set, S, of wellformed formulas, an interpretation consists of a non-empty set (or domain), together with a function which: 1 2 3 assigns to each individual constant found in members of S an element of the domain; assigns to each n-place predicate found in members of S an n-place relation between members of the domain; assigns to each n-place function-name found in members of S a 22 PHILOSOPHY OF LOGIC 4 function whose arguments are n-tuples of elements of the domain and whose values are also elements of the domain; and assigns to each sentence letter a truth value.

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