Existence predicate

Kant said that existence is not a predicate and Russell agreed, arguing that a sentence such as ‘The king of France exists’, which seems to attribute existence to the king of France, really has a logical form that is not reflected in the surface structure of the sentence at all. While the surface form of the sentence consists of a subject (the noun phrase ‘the king of France’) and a predicate (the verb phrase ‘exists’), the underlying logical form, according to Russell, is the formula given in (1). This formula obviously has no subjectpredicate form and in fact has no single constituent that corresponds to the verb phrase ‘exists’ in the surface sentence. (1) ∃x∀y(Ky ↔ x = y) The importance of Russell’s analysis becomes clear when we consider ‘The king of France does not exist’. If this sentence would attribute non-existence to the king it should entail that there is someone who does not exist, just as ‘Mary doesn’t like bananas’ entails that there is someone who doesn’t like bananas. Thus the idea that all sentences have subject-predicate form has led some philosophers (e.g. Meinong) to the view that there are objects that lack existence. This embarrassing position can be avoided once Russell’s analysis is accepted: if ‘The king of France does not exist’ is formalised as the negation of formula (1), no unwanted consequences follow.
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